/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 234 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), 14 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 23.1 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 6 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 540 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 119 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false ---------------------------------------- (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: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false 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: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false 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: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [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: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [0] The TRS has the following type information: cond :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p true :: true:s:0:false:cons_cond:cons_gr:cons_p gr :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p p :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p s :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p 0 :: true:s:0:false:cons_cond:cons_gr:cons_p false :: true:s:0:false:cons_cond:cons_gr:cons_p encArg :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p cons_cond :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p cons_gr :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p cons_p :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p encode_cond :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p encode_true :: true:s:0:false:cons_cond:cons_gr:cons_p encode_gr :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p encode_p :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p encode_s :: true:s:0:false:cons_cond:cons_gr:cons_p -> true:s:0:false:cons_cond:cons_gr:cons_p encode_0 :: true:s:0:false:cons_cond:cons_gr:cons_p encode_false :: true:s:0:false:cons_cond:cons_gr:cons_p Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_true -> null_encode_true [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] cond(v0, v1, v2) -> null_cond [0] gr(v0, v1) -> null_gr [0] p(v0) -> null_p [0] And the following fresh constants: null_encArg, null_encode_cond, null_encode_true, null_encode_gr, null_encode_p, null_encode_s, null_encode_0, null_encode_false, null_cond, null_gr, null_p ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [0] encArg(v0) -> null_encArg [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_true -> null_encode_true [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] cond(v0, v1, v2) -> null_cond [0] gr(v0, v1) -> null_gr [0] p(v0) -> null_p [0] The TRS has the following type information: cond :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p true :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p gr :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p p :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p s :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p 0 :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p false :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encArg :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p cons_cond :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p cons_gr :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p cons_p :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_cond :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_true :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_gr :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_p :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_s :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p -> true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_0 :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p encode_false :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encArg :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_cond :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_true :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_gr :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_p :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_s :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_0 :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_encode_false :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_cond :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_gr :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p null_p :: true:s:0:false:cons_cond:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_gr:null_encode_p:null_encode_s:null_encode_0:null_encode_false:null_cond:null_gr:null_p Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: true => 2 0 => 0 false => 1 null_encArg => 0 null_encode_cond => 0 null_encode_true => 0 null_encode_gr => 0 null_encode_p => 0 null_encode_s => 0 null_encode_0 => 0 null_encode_false => 0 null_cond => 0 null_gr => 0 null_p => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond(z, z', z'') -{ 1 }-> cond(gr(x, y), p(x), 1 + y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond(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_cond(z, z', z'') -{ 0 }-> cond(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_cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0 gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x p(z) -{ 1 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V2),0,[cond(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[gr(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[p(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun1(Out)],[]). eq(start(V1, V, V2),0,[fun2(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun3(V1, Out)],[V1 >= 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(Out)],[]). eq(cond(V1, V, V2, Out),1,[gr(V4, V3, Ret0),p(V4, Ret1),cond(Ret0, Ret1, 1 + V3, Ret)],[Out = Ret,V1 = 2,V = V4,V2 = V3,V4 >= 0,V3 >= 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V = V5,V5 >= 0,V1 = 0]). eq(gr(V1, V, Out),1,[],[Out = 2,V6 >= 0,V1 = 1 + V6,V = 0]). eq(gr(V1, V, Out),1,[gr(V7, V8, Ret2)],[Out = Ret2,V = 1 + V8,V7 >= 0,V8 >= 0,V1 = 1 + V7]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V9,V9 >= 0,V1 = 1 + V9]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V10, Ret11)],[Out = 1 + Ret11,V1 = 1 + V10,V10 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V12, Ret01),encArg(V13, Ret12),encArg(V11, Ret21),cond(Ret01, Ret12, Ret21, Ret3)],[Out = Ret3,V12 >= 0,V1 = 1 + V11 + V12 + V13,V11 >= 0,V13 >= 0]). eq(encArg(V1, Out),0,[encArg(V14, Ret02),encArg(V15, Ret13),gr(Ret02, Ret13, Ret4)],[Out = Ret4,V14 >= 0,V1 = 1 + V14 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret03),p(Ret03, Ret5)],[Out = Ret5,V1 = 1 + V16,V16 >= 0]). eq(fun(V1, V, V2, Out),0,[encArg(V19, Ret04),encArg(V17, Ret14),encArg(V18, Ret22),cond(Ret04, Ret14, Ret22, Ret6)],[Out = Ret6,V19 >= 0,V18 >= 0,V17 >= 0,V1 = V19,V = V17,V2 = V18]). eq(fun1(Out),0,[],[Out = 2]). eq(fun2(V1, V, Out),0,[encArg(V21, Ret05),encArg(V20, Ret15),gr(Ret05, Ret15, Ret7)],[Out = Ret7,V21 >= 0,V20 >= 0,V1 = V21,V = V20]). eq(fun3(V1, Out),0,[encArg(V22, Ret06),p(Ret06, Ret8)],[Out = Ret8,V22 >= 0,V1 = V22]). eq(fun4(V1, Out),0,[encArg(V23, Ret16)],[Out = 1 + Ret16,V23 >= 0,V1 = V23]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V24 >= 0,V1 = V24]). eq(fun(V1, V, V2, Out),0,[],[Out = 0,V26 >= 0,V2 = V27,V25 >= 0,V1 = V26,V = V25,V27 >= 0]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, V, Out),0,[],[Out = 0,V29 >= 0,V28 >= 0,V1 = V29,V = V28]). eq(fun3(V1, Out),0,[],[Out = 0,V30 >= 0,V1 = V30]). eq(fun4(V1, Out),0,[],[Out = 0,V31 >= 0,V1 = V31]). eq(fun6(Out),0,[],[Out = 0]). eq(cond(V1, V, V2, Out),0,[],[Out = 0,V32 >= 0,V2 = V33,V34 >= 0,V1 = V32,V = V34,V33 >= 0]). eq(gr(V1, V, Out),0,[],[Out = 0,V35 >= 0,V36 >= 0,V1 = V35,V = V36]). eq(p(V1, Out),0,[],[Out = 0,V37 >= 0,V1 = V37]). input_output_vars(cond(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(gr(V1,V,Out),[V1,V],[Out]). input_output_vars(p(V1,Out),[V1],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V1,V,Out),[V1,V],[Out]). input_output_vars(fun3(V1,Out),[V1],[Out]). input_output_vars(fun4(V1,Out),[V1],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(Out),[],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [gr/3] 1. non_recursive : [p/2] 2. recursive : [cond/4] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun/4] 5. non_recursive : [fun1/1] 6. non_recursive : [fun2/3] 7. non_recursive : [fun3/2] 8. non_recursive : [fun4/2] 9. non_recursive : [fun5/1] 10. non_recursive : [fun6/1] 11. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into gr/3 1. SCC is partially evaluated into p/2 2. SCC is partially evaluated into cond/4 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun/4 5. SCC is partially evaluated into fun1/1 6. SCC is partially evaluated into fun2/3 7. SCC is partially evaluated into fun3/2 8. SCC is partially evaluated into fun4/2 9. SCC is completely evaluated into other SCCs 10. SCC is partially evaluated into fun6/1 11. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations gr/3 * CE 17 is refined into CE [40] * CE 15 is refined into CE [41] * CE 14 is refined into CE [42] * CE 16 is refined into CE [43] ### Cost equations --> "Loop" of gr/3 * CEs [43] --> Loop 24 * CEs [40] --> Loop 25 * CEs [41] --> Loop 26 * CEs [42] --> Loop 27 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [24]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [24]: - RF of loop [24:1]: V V1 ### Specialization of cost equations p/2 * CE 19 is refined into CE [44] * CE 18 is refined into CE [45] * CE 20 is refined into CE [46] ### Cost equations --> "Loop" of p/2 * CEs [44] --> Loop 28 * CEs [45,46] --> Loop 29 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations cond/4 * CE 13 is refined into CE [47] * CE 12 is refined into CE [48,49,50,51,52,53,54,55,56] ### Cost equations --> "Loop" of cond/4 * CEs [56] --> Loop 30 * CEs [55] --> Loop 31 * CEs [54] --> Loop 32 * CEs [53] --> Loop 33 * CEs [52] --> Loop 34 * CEs [51] --> Loop 35 * CEs [50] --> Loop 36 * CEs [49] --> Loop 37 * CEs [48] --> Loop 38 * CEs [47] --> Loop 39 ### Ranking functions of CR cond(V1,V,V2,Out) * RF of phase [30]: [V-1,V/2-V2/2] #### Partial ranking functions of CR cond(V1,V,V2,Out) * Partial RF of phase [30]: - RF of loop [30:1]: V-1 V/2-V2/2 ### Specialization of cost equations encArg/2 * CE 23 is refined into CE [57] * CE 21 is refined into CE [58] * CE 24 is refined into CE [59] * CE 22 is refined into CE [60] * CE 27 is refined into CE [61,62] * CE 26 is refined into CE [63,64,65,66,67] * CE 25 is refined into CE [68,69,70] ### Cost equations --> "Loop" of encArg/2 * CEs [68,69,70] --> Loop 40 * CEs [67] --> Loop 41 * CEs [64] --> Loop 42 * CEs [66] --> Loop 43 * CEs [63] --> Loop 44 * CEs [65] --> Loop 45 * CEs [60] --> Loop 46 * CEs [62] --> Loop 47 * CEs [61] --> Loop 48 * CEs [57] --> Loop 49 * CEs [58] --> Loop 50 * CEs [59] --> Loop 51 ### Ranking functions of CR encArg(V1,Out) * RF of phase [40,41,42,43,44,45,46,47,48]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [40,41,42,43,44,45,46,47,48]: - RF of loop [40:1,40:2,40:3,41:1,41:2,42:1,42:2,43:1,43:2,44:1,44:2,45:1,45:2,46:1,47:1,48:1]: V1 ### Specialization of cost equations fun/4 * CE 28 is refined into CE [71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113] * CE 29 is refined into CE [114] ### Cost equations --> "Loop" of fun/4 * CEs [78,79,80,81,82,83,84,108,109,110] --> Loop 52 * CEs [74,86,91,103,106,112] --> Loop 53 * CEs [71,72,73,75,76,77,85,87,88,89,90,92,93,94,95,96,97,98,99,100,101,102,104,105,107,111,113,114] --> Loop 54 ### 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 30 is refined into CE [115] * CE 31 is refined into CE [116] ### Cost equations --> "Loop" of fun1/1 * CEs [115] --> Loop 55 * CEs [116] --> Loop 56 ### Ranking functions of CR fun1(Out) #### Partial ranking functions of CR fun1(Out) ### Specialization of cost equations fun2/3 * CE 32 is refined into CE [117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142] * CE 33 is refined into CE [143] ### Cost equations --> "Loop" of fun2/3 * CEs [125] --> Loop 57 * CEs [122,124,139] --> Loop 58 * CEs [123,140] --> Loop 59 * CEs [118,121,127,129,132,135] --> Loop 60 * CEs [117,120,126,131,134,137,141] --> Loop 61 * CEs [119,128,130,133,136,138,142,143] --> Loop 62 ### Ranking functions of CR fun2(V1,V,Out) #### Partial ranking functions of CR fun2(V1,V,Out) ### Specialization of cost equations fun3/2 * CE 34 is refined into CE [144,145,146,147,148] * CE 35 is refined into CE [149] ### Cost equations --> "Loop" of fun3/2 * CEs [145,147] --> Loop 63 * CEs [144,146,148,149] --> Loop 64 ### Ranking functions of CR fun3(V1,Out) #### Partial ranking functions of CR fun3(V1,Out) ### Specialization of cost equations fun4/2 * CE 36 is refined into CE [150,151,152] * CE 37 is refined into CE [153] ### Cost equations --> "Loop" of fun4/2 * CEs [152] --> Loop 65 * CEs [153] --> Loop 66 * CEs [150,151] --> Loop 67 ### Ranking functions of CR fun4(V1,Out) #### Partial ranking functions of CR fun4(V1,Out) ### Specialization of cost equations fun6/1 * CE 38 is refined into CE [154] * CE 39 is refined into CE [155] ### Cost equations --> "Loop" of fun6/1 * CEs [154] --> Loop 68 * CEs [155] --> Loop 69 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [156,157,158] * CE 2 is refined into CE [159,160,161,162,163] * CE 3 is refined into CE [164,165] * CE 4 is refined into CE [166,167,168] * CE 5 is refined into CE [169,170] * CE 6 is refined into CE [171,172] * CE 7 is refined into CE [173,174,175] * CE 8 is refined into CE [176,177] * CE 9 is refined into CE [178,179,180] * CE 10 is refined into CE [181] * CE 11 is refined into CE [182,183] ### Cost equations --> "Loop" of start/3 * CEs [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] --> Loop 70 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of gr(V1,V,Out): * Chain [[24],27]: 1*it(24)+1 Such that:it(24) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[24],26]: 1*it(24)+1 Such that:it(24) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[24],25]: 1*it(24)+0 Such that:it(24) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [27]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [26]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [25]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of p(V1,Out): * Chain [29]: 1 with precondition: [Out=0,V1>=0] * Chain [28]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of cond(V1,V,V2,Out): * Chain [[30],39]: 3*it(30)+1*s(4)+0 Such that:it(30) =< V/2-V2/2 aux(1) =< V/2+V2/2+1/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[30],35,39]: 3*it(30)+1*s(4)+1*s(5)+2 Such that:it(30) =< V/2-V2/2 aux(1) =< V/2+V2/2+1/2 s(5) =< V/2+V2/2+3/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[30],34,39]: 3*it(30)+1*s(4)+1*s(6)+2 Such that:it(30) =< V/2-V2/2 aux(1) =< V/2+V2/2+1/2 s(6) =< V/2+V2/2+3/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[30],33,39]: 3*it(30)+1*s(4)+1*s(7)+3 Such that:it(30) =< V/2-V2/2 s(7) =< V/2+V2/2 aux(1) =< V/2+V2/2+1/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[30],32,39]: 3*it(30)+1*s(4)+1*s(8)+3 Such that:it(30) =< V/2-V2/2 s(8) =< V/2+V2/2 aux(1) =< V/2+V2/2+1/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[30],31,39]: 3*it(30)+1*s(4)+1*s(9)+3 Such that:it(30) =< V/2-V2/2 aux(2) =< V/2+V2/2+1/2 s(9) =< aux(2) s(4) =< it(30)*aux(2) with precondition: [V1=2,Out=0,V2>=1,V>=V2+3] * Chain [[30],31,38,39]: 3*it(30)+1*s(4)+1*s(9)+6 Such that:it(30) =< V/2-V2/2 aux(3) =< V/2+V2/2+1/2 s(9) =< aux(3) s(4) =< it(30)*aux(3) with precondition: [V1=2,Out=0,V2>=1,V>=V2+3] * Chain [[30],31,35,39]: 3*it(30)+1*s(4)+1*s(5)+1*s(9)+5 Such that:it(30) =< V/2-V2/2 s(5) =< V/2+V2/2+3/2 aux(4) =< V/2+V2/2+1/2 s(9) =< aux(4) s(4) =< it(30)*aux(4) with precondition: [V1=2,Out=0,V2>=1,V>=V2+3] * Chain [39]: 0 with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [38,39]: 3 with precondition: [V1=2,V=0,Out=0,V2>=0] * Chain [37,39]: 3 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [37,38,39]: 6 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [37,35,39]: 1*s(5)+5 Such that:s(5) =< 2 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [36,[30],39]: 3*it(30)+1*s(4)+3 Such that:it(30) =< V/2 aux(1) =< V/2+1/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,[30],35,39]: 3*it(30)+1*s(4)+1*s(5)+5 Such that:it(30) =< V/2 aux(1) =< V/2+1/2 s(5) =< V/2+3/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,[30],34,39]: 3*it(30)+1*s(4)+1*s(6)+5 Such that:it(30) =< V/2 aux(1) =< V/2+1/2 s(6) =< V/2+3/2 s(4) =< it(30)*aux(1) with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,[30],33,39]: 4*it(30)+1*s(4)+6 Such that:aux(1) =< V/2+1/2 aux(5) =< V/2 it(30) =< aux(5) s(4) =< it(30)*aux(1) with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,[30],32,39]: 4*it(30)+1*s(4)+6 Such that:aux(1) =< V/2+1/2 aux(6) =< V/2 it(30) =< aux(6) s(4) =< it(30)*aux(1) with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,[30],31,39]: 3*it(30)+1*s(4)+1*s(9)+6 Such that:it(30) =< V/2 aux(2) =< V/2+1/2 s(9) =< aux(2) s(4) =< it(30)*aux(2) with precondition: [V1=2,V2=0,Out=0,V>=5] * Chain [36,[30],31,38,39]: 3*it(30)+1*s(4)+1*s(9)+9 Such that:it(30) =< V/2 aux(3) =< V/2+1/2 s(9) =< aux(3) s(4) =< it(30)*aux(3) with precondition: [V1=2,V2=0,Out=0,V>=5] * Chain [36,[30],31,35,39]: 3*it(30)+1*s(4)+1*s(5)+1*s(9)+8 Such that:it(30) =< V/2 aux(4) =< V/2+1/2 s(5) =< V/2+3/2 s(9) =< aux(4) s(4) =< it(30)*aux(4) with precondition: [V1=2,V2=0,Out=0,V>=5] * Chain [36,39]: 3 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [36,38,39]: 6 with precondition: [V1=2,V=1,V2=0,Out=0] * Chain [36,35,39]: 1*s(5)+5 Such that:s(5) =< 2 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [36,34,39]: 1*s(6)+5 Such that:s(6) =< 2 with precondition: [V1=2,V2=0,Out=0,V>=2] * Chain [36,33,39]: 1*s(7)+6 Such that:s(7) =< 1 with precondition: [V1=2,V=2,V2=0,Out=0] * Chain [36,32,39]: 1*s(8)+6 Such that:s(8) =< 1 with precondition: [V1=2,V=2,V2=0,Out=0] * Chain [36,31,39]: 1*s(9)+6 Such that:s(9) =< 2 with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,31,38,39]: 1*s(9)+9 Such that:s(9) =< 2 with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [36,31,35,39]: 1*s(5)+1*s(9)+8 Such that:s(9) =< 2 s(5) =< 3 with precondition: [V1=2,V2=0,Out=0,V>=3] * Chain [35,39]: 1*s(5)+2 Such that:s(5) =< V2+1 with precondition: [V1=2,Out=0,V>=0,V2>=0] * Chain [34,39]: 1*s(6)+2 Such that:s(6) =< V2+1 with precondition: [V1=2,Out=0,V>=1,V2>=0] * Chain [33,39]: 1*s(7)+3 Such that:s(7) =< V with precondition: [V1=2,Out=0,V>=1,V2>=V] * Chain [32,39]: 1*s(8)+3 Such that:s(8) =< V with precondition: [V1=2,Out=0,V>=1,V2>=V] * Chain [31,39]: 1*s(9)+3 Such that:s(9) =< V2+1 with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [31,38,39]: 1*s(9)+6 Such that:s(9) =< V2+1 with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [31,35,39]: 1*s(5)+1*s(9)+5 Such that:s(9) =< V2+1 s(5) =< V2+2 with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] #### Cost of chains of encArg(V1,Out): * Chain [51]: 0 with precondition: [V1=1,Out=1] * Chain [50]: 0 with precondition: [V1=2,Out=2] * Chain [49]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([40,41,42,43,44,45,46,47,48],[[51],[50],[49]])]: 11*it(40)+1*it(41)+1*it(42)+1*it(43)+1*it(44)+1*s(143)+2*s(144)+50*s(145)+2*s(146)+6*s(147)+5*s(148)+6*s(149)+8*s(150)+1*s(151)+6*s(152)+8*s(155)+1*s(165)+1*s(166)+1*s(167)+0 Such that:it([51]) =< 2/3*V1+1/3 aux(36) =< V1 aux(37) =< 2*V1+1 aux(38) =< V1/2 aux(39) =< 2/3*V1 aux(40) =< 2/5*V1 it(40) =< aux(36) it(41) =< aux(36) it(42) =< aux(36) it(43) =< aux(36) it(44) =< aux(36) it(45) =< aux(36) it([51]) =< aux(36) it([49]) =< aux(37) it([51]) =< aux(37) it(43) =< aux(38) it(42) =< aux(39) it(43) =< aux(39) it(41) =< aux(40) aux(21) =< aux(38)*2-1 aux(34) =< aux(38)*2-2 aux(31) =< aux(38)*2-3 aux(29) =< aux(38)*2+1 aux(28) =< aux(38)*2 aux(24) =< aux(38)+1 aux(23) =< aux(38) aux(25) =< aux(38)-1/2 it(43) =< it([49])*(1/2)+aux(38) it(44) =< it([49])*(1/2)+aux(38) it(45) =< it([49])*(1/2)+aux(38) it(42) =< it([49])*(1/3)+aux(39) it(43) =< it([49])*(1/3)+aux(39) it(44) =< it([49])*(1/3)+aux(39) it(45) =< it([49])*(1/3)+aux(39) it(41) =< it([49])*(3/5)+it([51])*(1/5)+aux(40) it(42) =< it([49])*(3/5)+it([51])*(1/5)+aux(40) it(43) =< it([49])*(3/5)+it([51])*(1/5)+aux(40) it(44) =< it([49])*(3/5)+it([51])*(1/5)+aux(40) it(45) =< it([49])*(3/5)+it([51])*(1/5)+aux(40) s(151) =< aux(36)*3 s(164) =< aux(36)*2 s(167) =< it(45)*aux(21) s(166) =< it(43)*aux(34) s(165) =< it(41)*aux(31) s(143) =< it(40)*aux(29) s(157) =< it(40)*aux(28) s(158) =< it(40)*aux(24) s(156) =< it(40)*aux(23) s(159) =< it(40)*aux(25) aux(22) =< it(40)*aux(21) s(163) =< aux(22)*(1/2) s(152) =< s(164) s(145) =< s(163) s(147) =< s(158) s(149) =< s(156) s(155) =< s(145)*aux(38) s(144) =< aux(22) s(146) =< s(159) s(148) =< s(157) s(150) =< s(145)*aux(23) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,V2,Out): * Chain [54]: 88*s(216)+8*s(217)+8*s(218)+8*s(219)+8*s(220)+8*s(230)+8*s(232)+8*s(233)+8*s(234)+8*s(235)+48*s(242)+400*s(243)+48*s(244)+48*s(245)+64*s(246)+16*s(247)+16*s(248)+40*s(249)+64*s(250)+166*s(257)+14*s(258)+14*s(259)+14*s(260)+14*s(261)+14*s(271)+14*s(273)+14*s(274)+14*s(275)+14*s(276)+84*s(283)+700*s(284)+84*s(285)+84*s(286)+112*s(287)+28*s(288)+28*s(289)+70*s(290)+112*s(291)+143*s(298)+13*s(299)+13*s(300)+13*s(301)+13*s(302)+13*s(312)+13*s(314)+13*s(315)+13*s(316)+13*s(317)+78*s(324)+650*s(325)+78*s(326)+78*s(327)+104*s(328)+26*s(329)+26*s(330)+65*s(331)+104*s(332)+7*s(333)+254*s(341)+6*s(342)+9*s(343)+35*s(344)+9*s(345)+24*s(346)+11*s(470)+51*s(475)+21*s(477)+21*s(478)+56*s(479)+137*s(696)+6*s(964)+12*s(965)+9*s(967)+18*s(1020)+9*s(1022)+2*s(1491)+3*s(1492)+8*s(1495)+12*s(1544)+24*s(1546)+1*s(1588)+3*s(1598)+9 Such that:s(1588) =< 4 s(1593) =< 7/2 s(1485) =< V2/2+1 s(1487) =< V2/2+5/2 aux(69) =< 1 aux(70) =< 2 aux(71) =< 3 aux(72) =< 1/2 aux(73) =< 3/2 aux(74) =< 5/2 aux(75) =< V1 aux(76) =< 2*V1+1 aux(77) =< V1/2 aux(78) =< 2/3*V1 aux(79) =< 2/3*V1+1/3 aux(80) =< 2/5*V1 aux(81) =< V aux(82) =< 2*V+1 aux(83) =< V/2 aux(84) =< V/2+1/2 aux(85) =< V/2+3/2 aux(86) =< V/2+V2/2 aux(87) =< V/2+V2/2+1/2 aux(88) =< V/2+V2/2+3/2 aux(89) =< 2/3*V aux(90) =< 2/3*V+1/3 aux(91) =< 2/5*V aux(92) =< V2 aux(93) =< V2+1 aux(94) =< V2+2 aux(95) =< 2*V2+1 aux(96) =< V2/2 aux(97) =< V2/2+1/2 aux(98) =< V2/2+3/2 aux(99) =< 2/3*V2 aux(100) =< 2/3*V2+1/3 aux(101) =< 2/5*V2 s(475) =< aux(70) s(470) =< aux(71) s(214) =< aux(79) s(255) =< aux(90) s(333) =< aux(94) s(296) =< aux(100) s(257) =< aux(81) s(341) =< aux(83) s(477) =< aux(85) s(696) =< aux(69) s(478) =< aux(84) s(479) =< s(341)*aux(84) s(258) =< aux(81) s(259) =< aux(81) s(260) =< aux(81) s(261) =< aux(81) s(262) =< aux(81) s(255) =< aux(81) s(255) =< aux(82) s(260) =< aux(83) s(259) =< aux(89) s(260) =< aux(89) s(258) =< aux(91) s(263) =< aux(83)*2-1 s(264) =< aux(83)*2-2 s(265) =< aux(83)*2-3 s(266) =< aux(83)*2+1 s(267) =< aux(83)*2 s(268) =< aux(83)+1 s(269) =< aux(83) s(270) =< aux(83)-1/2 s(260) =< aux(82)*(1/2)+aux(83) s(261) =< aux(82)*(1/2)+aux(83) s(262) =< aux(82)*(1/2)+aux(83) s(259) =< aux(82)*(1/3)+aux(89) s(260) =< aux(82)*(1/3)+aux(89) s(261) =< aux(82)*(1/3)+aux(89) s(262) =< aux(82)*(1/3)+aux(89) s(258) =< aux(82)*(3/5)+s(255)*(1/5)+aux(91) s(259) =< aux(82)*(3/5)+s(255)*(1/5)+aux(91) s(260) =< aux(82)*(3/5)+s(255)*(1/5)+aux(91) s(261) =< aux(82)*(3/5)+s(255)*(1/5)+aux(91) s(262) =< aux(82)*(3/5)+s(255)*(1/5)+aux(91) s(271) =< aux(81)*3 s(272) =< aux(81)*2 s(273) =< s(262)*s(263) s(274) =< s(260)*s(264) s(275) =< s(258)*s(265) s(276) =< s(257)*s(266) s(277) =< s(257)*s(267) s(278) =< s(257)*s(268) s(279) =< s(257)*s(269) s(280) =< s(257)*s(270) s(281) =< s(257)*s(263) s(282) =< s(281)*(1/2) s(283) =< s(272) s(284) =< s(282) s(285) =< s(278) s(286) =< s(279) s(287) =< s(284)*aux(83) s(288) =< s(281) s(289) =< s(280) s(290) =< s(277) s(291) =< s(284)*s(269) s(216) =< aux(75) s(217) =< aux(75) s(218) =< aux(75) s(219) =< aux(75) s(220) =< aux(75) s(221) =< aux(75) s(214) =< aux(75) s(214) =< aux(76) s(219) =< aux(77) s(218) =< aux(78) s(219) =< aux(78) s(217) =< aux(80) s(222) =< aux(77)*2-1 s(223) =< aux(77)*2-2 s(224) =< aux(77)*2-3 s(225) =< aux(77)*2+1 s(226) =< aux(77)*2 s(227) =< aux(77)+1 s(228) =< aux(77) s(229) =< aux(77)-1/2 s(219) =< aux(76)*(1/2)+aux(77) s(220) =< aux(76)*(1/2)+aux(77) s(221) =< aux(76)*(1/2)+aux(77) s(218) =< aux(76)*(1/3)+aux(78) s(219) =< aux(76)*(1/3)+aux(78) s(220) =< aux(76)*(1/3)+aux(78) s(221) =< aux(76)*(1/3)+aux(78) s(217) =< aux(76)*(3/5)+s(214)*(1/5)+aux(80) s(218) =< aux(76)*(3/5)+s(214)*(1/5)+aux(80) s(219) =< aux(76)*(3/5)+s(214)*(1/5)+aux(80) s(220) =< aux(76)*(3/5)+s(214)*(1/5)+aux(80) s(221) =< aux(76)*(3/5)+s(214)*(1/5)+aux(80) s(230) =< aux(75)*3 s(231) =< aux(75)*2 s(232) =< s(221)*s(222) s(233) =< s(219)*s(223) s(234) =< s(217)*s(224) s(235) =< s(216)*s(225) s(236) =< s(216)*s(226) s(237) =< s(216)*s(227) s(238) =< s(216)*s(228) s(239) =< s(216)*s(229) s(240) =< s(216)*s(222) s(241) =< s(240)*(1/2) s(242) =< s(231) s(243) =< s(241) s(244) =< s(237) s(245) =< s(238) s(246) =< s(243)*aux(77) s(247) =< s(240) s(248) =< s(239) s(249) =< s(236) s(250) =< s(243)*s(228) s(1020) =< aux(73) s(1022) =< aux(72) s(1491) =< s(1485) s(1492) =< s(1487) s(344) =< aux(93) s(965) =< aux(98) s(1495) =< s(696)*aux(98) s(298) =< aux(92) s(299) =< aux(92) s(300) =< aux(92) s(301) =< aux(92) s(302) =< aux(92) s(303) =< aux(92) s(296) =< aux(92) s(296) =< aux(95) s(301) =< aux(96) s(300) =< aux(99) s(301) =< aux(99) s(299) =< aux(101) s(304) =< aux(96)*2-1 s(305) =< aux(96)*2-2 s(306) =< aux(96)*2-3 s(307) =< aux(96)*2+1 s(308) =< aux(96)*2 s(309) =< aux(96)+1 s(310) =< aux(96) s(311) =< aux(96)-1/2 s(301) =< aux(95)*(1/2)+aux(96) s(302) =< aux(95)*(1/2)+aux(96) s(303) =< aux(95)*(1/2)+aux(96) s(300) =< aux(95)*(1/3)+aux(99) s(301) =< aux(95)*(1/3)+aux(99) s(302) =< aux(95)*(1/3)+aux(99) s(303) =< aux(95)*(1/3)+aux(99) s(299) =< aux(95)*(3/5)+s(296)*(1/5)+aux(101) s(300) =< aux(95)*(3/5)+s(296)*(1/5)+aux(101) s(301) =< aux(95)*(3/5)+s(296)*(1/5)+aux(101) s(302) =< aux(95)*(3/5)+s(296)*(1/5)+aux(101) s(303) =< aux(95)*(3/5)+s(296)*(1/5)+aux(101) s(312) =< aux(92)*3 s(313) =< aux(92)*2 s(314) =< s(303)*s(304) s(315) =< s(301)*s(305) s(316) =< s(299)*s(306) s(317) =< s(298)*s(307) s(318) =< s(298)*s(308) s(319) =< s(298)*s(309) s(320) =< s(298)*s(310) s(321) =< s(298)*s(311) s(322) =< s(298)*s(304) s(323) =< s(322)*(1/2) s(324) =< s(313) s(325) =< s(323) s(326) =< s(319) s(327) =< s(320) s(328) =< s(325)*aux(96) s(329) =< s(322) s(330) =< s(321) s(331) =< s(318) s(332) =< s(325)*s(310) s(1544) =< aux(74) s(1546) =< s(696)*aux(73) s(1598) =< s(1593) s(342) =< aux(86) s(343) =< aux(88) s(345) =< aux(87) s(346) =< s(341)*aux(87) s(964) =< aux(96) s(967) =< aux(97) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [53]: 22*s(1921)+2*s(1922)+2*s(1923)+2*s(1924)+2*s(1925)+2*s(1935)+2*s(1937)+2*s(1938)+2*s(1939)+2*s(1940)+12*s(1947)+100*s(1948)+12*s(1949)+12*s(1950)+16*s(1951)+4*s(1952)+4*s(1953)+10*s(1954)+16*s(1955)+39*s(1962)+3*s(1963)+3*s(1964)+3*s(1965)+3*s(1966)+3*s(1976)+3*s(1978)+3*s(1979)+3*s(1980)+3*s(1981)+18*s(1988)+150*s(1989)+18*s(1990)+18*s(1991)+24*s(1992)+6*s(1993)+6*s(1994)+15*s(1995)+24*s(1996)+6*s(1997)+72*s(2005)+6*s(2006)+9*s(2007)+30*s(2008)+9*s(2009)+24*s(2010)+6*s(2061)+9*s(2062)+9*s(2064)+6 Such that:aux(111) =< 1 aux(112) =< 3 aux(113) =< 4 aux(114) =< 3/2 aux(115) =< 5/2 aux(116) =< V1 aux(117) =< 2*V1+1 aux(118) =< V1/2 aux(119) =< 2/3*V1 aux(120) =< 2/3*V1+1/3 aux(121) =< 2/5*V1 aux(122) =< V aux(123) =< 2*V+1 aux(124) =< V/2 aux(125) =< V/2+1 aux(126) =< V/2+3/2 aux(127) =< V/2+5/2 aux(128) =< 2/3*V aux(129) =< 2/3*V+1/3 aux(130) =< 2/5*V s(1997) =< aux(113) s(1919) =< aux(120) s(1960) =< aux(129) s(2061) =< aux(111) s(2062) =< aux(115) s(2008) =< aux(112) s(2064) =< aux(114) s(1921) =< aux(116) s(1922) =< aux(116) s(1923) =< aux(116) s(1924) =< aux(116) s(1925) =< aux(116) s(1926) =< aux(116) s(1919) =< aux(116) s(1919) =< aux(117) s(1924) =< aux(118) s(1923) =< aux(119) s(1924) =< aux(119) s(1922) =< aux(121) s(1927) =< aux(118)*2-1 s(1928) =< aux(118)*2-2 s(1929) =< aux(118)*2-3 s(1930) =< aux(118)*2+1 s(1931) =< aux(118)*2 s(1932) =< aux(118)+1 s(1933) =< aux(118) s(1934) =< aux(118)-1/2 s(1924) =< aux(117)*(1/2)+aux(118) s(1925) =< aux(117)*(1/2)+aux(118) s(1926) =< aux(117)*(1/2)+aux(118) s(1923) =< aux(117)*(1/3)+aux(119) s(1924) =< aux(117)*(1/3)+aux(119) s(1925) =< aux(117)*(1/3)+aux(119) s(1926) =< aux(117)*(1/3)+aux(119) s(1922) =< aux(117)*(3/5)+s(1919)*(1/5)+aux(121) s(1923) =< aux(117)*(3/5)+s(1919)*(1/5)+aux(121) s(1924) =< aux(117)*(3/5)+s(1919)*(1/5)+aux(121) s(1925) =< aux(117)*(3/5)+s(1919)*(1/5)+aux(121) s(1926) =< aux(117)*(3/5)+s(1919)*(1/5)+aux(121) s(1935) =< aux(116)*3 s(1936) =< aux(116)*2 s(1937) =< s(1926)*s(1927) s(1938) =< s(1924)*s(1928) s(1939) =< s(1922)*s(1929) s(1940) =< s(1921)*s(1930) s(1941) =< s(1921)*s(1931) s(1942) =< s(1921)*s(1932) s(1943) =< s(1921)*s(1933) s(1944) =< s(1921)*s(1934) s(1945) =< s(1921)*s(1927) s(1946) =< s(1945)*(1/2) s(1947) =< s(1936) s(1948) =< s(1946) s(1949) =< s(1942) s(1950) =< s(1943) s(1951) =< s(1948)*aux(118) s(1952) =< s(1945) s(1953) =< s(1944) s(1954) =< s(1941) s(1955) =< s(1948)*s(1933) s(1962) =< aux(122) s(2005) =< aux(124) s(2006) =< aux(125) s(2007) =< aux(127) s(2009) =< aux(126) s(2010) =< s(2005)*aux(126) s(1963) =< aux(122) s(1964) =< aux(122) s(1965) =< aux(122) s(1966) =< aux(122) s(1967) =< aux(122) s(1960) =< aux(122) s(1960) =< aux(123) s(1965) =< aux(124) s(1964) =< aux(128) s(1965) =< aux(128) s(1963) =< aux(130) s(1968) =< aux(124)*2-1 s(1969) =< aux(124)*2-2 s(1970) =< aux(124)*2-3 s(1971) =< aux(124)*2+1 s(1972) =< aux(124)*2 s(1973) =< aux(124)+1 s(1974) =< aux(124) s(1975) =< aux(124)-1/2 s(1965) =< aux(123)*(1/2)+aux(124) s(1966) =< aux(123)*(1/2)+aux(124) s(1967) =< aux(123)*(1/2)+aux(124) s(1964) =< aux(123)*(1/3)+aux(128) s(1965) =< aux(123)*(1/3)+aux(128) s(1966) =< aux(123)*(1/3)+aux(128) s(1967) =< aux(123)*(1/3)+aux(128) s(1963) =< aux(123)*(3/5)+s(1960)*(1/5)+aux(130) s(1964) =< aux(123)*(3/5)+s(1960)*(1/5)+aux(130) s(1965) =< aux(123)*(3/5)+s(1960)*(1/5)+aux(130) s(1966) =< aux(123)*(3/5)+s(1960)*(1/5)+aux(130) s(1967) =< aux(123)*(3/5)+s(1960)*(1/5)+aux(130) s(1976) =< aux(122)*3 s(1977) =< aux(122)*2 s(1978) =< s(1967)*s(1968) s(1979) =< s(1965)*s(1969) s(1980) =< s(1963)*s(1970) s(1981) =< s(1962)*s(1971) s(1982) =< s(1962)*s(1972) s(1983) =< s(1962)*s(1973) s(1984) =< s(1962)*s(1974) s(1985) =< s(1962)*s(1975) s(1986) =< s(1962)*s(1968) s(1987) =< s(1986)*(1/2) s(1988) =< s(1977) s(1989) =< s(1987) s(1990) =< s(1983) s(1991) =< s(1984) s(1992) =< s(1989)*aux(124) s(1993) =< s(1986) s(1994) =< s(1985) s(1995) =< s(1982) s(1996) =< s(1989)*s(1974) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [52]: 77*s(2210)+7*s(2211)+7*s(2212)+7*s(2213)+7*s(2214)+7*s(2224)+7*s(2226)+7*s(2227)+7*s(2228)+7*s(2229)+42*s(2236)+350*s(2237)+42*s(2238)+42*s(2239)+56*s(2240)+14*s(2241)+14*s(2242)+35*s(2243)+56*s(2244)+44*s(2251)+4*s(2252)+4*s(2253)+4*s(2254)+4*s(2255)+4*s(2265)+4*s(2267)+4*s(2268)+4*s(2269)+4*s(2270)+24*s(2277)+200*s(2278)+24*s(2279)+24*s(2280)+32*s(2281)+8*s(2282)+8*s(2283)+20*s(2284)+32*s(2285)+2*s(2286)+30*s(2293)+162*s(2294)+4*s(2295)+6*s(2296)+10*s(2297)+6*s(2298)+16*s(2299)+12*s(2382)+18*s(2389)+12*s(2390)+32*s(2391)+2*s(2515)+6*s(2525)+9 Such that:aux(137) =< 1 aux(138) =< 2 aux(139) =< 3 aux(140) =< 4 aux(141) =< 3/2 aux(142) =< 5/2 aux(143) =< 7/2 aux(144) =< V1 aux(145) =< 2*V1+1 aux(146) =< V1/2 aux(147) =< 2/3*V1 aux(148) =< 2/3*V1+1/3 aux(149) =< 2/5*V1 aux(150) =< V2 aux(151) =< V2+1 aux(152) =< V2+2 aux(153) =< 2*V2+1 aux(154) =< V2/2 aux(155) =< V2/2+1 aux(156) =< V2/2+3/2 aux(157) =< V2/2+5/2 aux(158) =< 2/3*V2 aux(159) =< 2/3*V2+1/3 aux(160) =< 2/5*V2 s(2382) =< aux(139) s(2515) =< aux(140) s(2208) =< aux(148) s(2286) =< aux(152) s(2249) =< aux(159) s(2293) =< aux(138) s(2294) =< aux(137) s(2295) =< aux(155) s(2296) =< aux(157) s(2297) =< aux(151) s(2298) =< aux(156) s(2299) =< s(2294)*aux(156) s(2251) =< aux(150) s(2252) =< aux(150) s(2253) =< aux(150) s(2254) =< aux(150) s(2255) =< aux(150) s(2256) =< aux(150) s(2249) =< aux(150) s(2249) =< aux(153) s(2254) =< aux(154) s(2253) =< aux(158) s(2254) =< aux(158) s(2252) =< aux(160) s(2257) =< aux(154)*2-1 s(2258) =< aux(154)*2-2 s(2259) =< aux(154)*2-3 s(2260) =< aux(154)*2+1 s(2261) =< aux(154)*2 s(2262) =< aux(154)+1 s(2263) =< aux(154) s(2264) =< aux(154)-1/2 s(2254) =< aux(153)*(1/2)+aux(154) s(2255) =< aux(153)*(1/2)+aux(154) s(2256) =< aux(153)*(1/2)+aux(154) s(2253) =< aux(153)*(1/3)+aux(158) s(2254) =< aux(153)*(1/3)+aux(158) s(2255) =< aux(153)*(1/3)+aux(158) s(2256) =< aux(153)*(1/3)+aux(158) s(2252) =< aux(153)*(3/5)+s(2249)*(1/5)+aux(160) s(2253) =< aux(153)*(3/5)+s(2249)*(1/5)+aux(160) s(2254) =< aux(153)*(3/5)+s(2249)*(1/5)+aux(160) s(2255) =< aux(153)*(3/5)+s(2249)*(1/5)+aux(160) s(2256) =< aux(153)*(3/5)+s(2249)*(1/5)+aux(160) s(2265) =< aux(150)*3 s(2266) =< aux(150)*2 s(2267) =< s(2256)*s(2257) s(2268) =< s(2254)*s(2258) s(2269) =< s(2252)*s(2259) s(2270) =< s(2251)*s(2260) s(2271) =< s(2251)*s(2261) s(2272) =< s(2251)*s(2262) s(2273) =< s(2251)*s(2263) s(2274) =< s(2251)*s(2264) s(2275) =< s(2251)*s(2257) s(2276) =< s(2275)*(1/2) s(2277) =< s(2266) s(2278) =< s(2276) s(2279) =< s(2272) s(2280) =< s(2273) s(2281) =< s(2278)*aux(154) s(2282) =< s(2275) s(2283) =< s(2274) s(2284) =< s(2271) s(2285) =< s(2278)*s(2263) s(2210) =< aux(144) s(2211) =< aux(144) s(2212) =< aux(144) s(2213) =< aux(144) s(2214) =< aux(144) s(2215) =< aux(144) s(2208) =< aux(144) s(2208) =< aux(145) s(2213) =< aux(146) s(2212) =< aux(147) s(2213) =< aux(147) s(2211) =< aux(149) s(2216) =< aux(146)*2-1 s(2217) =< aux(146)*2-2 s(2218) =< aux(146)*2-3 s(2219) =< aux(146)*2+1 s(2220) =< aux(146)*2 s(2221) =< aux(146)+1 s(2222) =< aux(146) s(2223) =< aux(146)-1/2 s(2213) =< aux(145)*(1/2)+aux(146) s(2214) =< aux(145)*(1/2)+aux(146) s(2215) =< aux(145)*(1/2)+aux(146) s(2212) =< aux(145)*(1/3)+aux(147) s(2213) =< aux(145)*(1/3)+aux(147) s(2214) =< aux(145)*(1/3)+aux(147) s(2215) =< aux(145)*(1/3)+aux(147) s(2211) =< aux(145)*(3/5)+s(2208)*(1/5)+aux(149) s(2212) =< aux(145)*(3/5)+s(2208)*(1/5)+aux(149) s(2213) =< aux(145)*(3/5)+s(2208)*(1/5)+aux(149) s(2214) =< aux(145)*(3/5)+s(2208)*(1/5)+aux(149) s(2215) =< aux(145)*(3/5)+s(2208)*(1/5)+aux(149) s(2224) =< aux(144)*3 s(2225) =< aux(144)*2 s(2226) =< s(2215)*s(2216) s(2227) =< s(2213)*s(2217) s(2228) =< s(2211)*s(2218) s(2229) =< s(2210)*s(2219) s(2230) =< s(2210)*s(2220) s(2231) =< s(2210)*s(2221) s(2232) =< s(2210)*s(2222) s(2233) =< s(2210)*s(2223) s(2234) =< s(2210)*s(2216) s(2235) =< s(2234)*(1/2) s(2236) =< s(2225) s(2237) =< s(2235) s(2238) =< s(2231) s(2239) =< s(2232) s(2240) =< s(2237)*aux(146) s(2241) =< s(2234) s(2242) =< s(2233) s(2243) =< s(2230) s(2244) =< s(2237)*s(2222) s(2389) =< aux(142) s(2390) =< aux(141) s(2391) =< s(2294)*aux(141) s(2525) =< aux(143) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun1(Out): * Chain [56]: 0 with precondition: [Out=0] * Chain [55]: 0 with precondition: [Out=2] #### Cost of chains of fun2(V1,V,Out): * Chain [62]: 22*s(3044)+2*s(3045)+2*s(3046)+2*s(3047)+2*s(3048)+2*s(3058)+2*s(3060)+2*s(3061)+2*s(3062)+2*s(3063)+12*s(3070)+100*s(3071)+12*s(3072)+12*s(3073)+16*s(3074)+4*s(3075)+4*s(3076)+10*s(3077)+16*s(3078)+36*s(3085)+3*s(3086)+3*s(3087)+3*s(3088)+3*s(3089)+3*s(3099)+3*s(3101)+3*s(3102)+3*s(3103)+3*s(3104)+18*s(3111)+150*s(3112)+18*s(3113)+18*s(3114)+24*s(3115)+6*s(3116)+6*s(3117)+15*s(3118)+24*s(3119)+1*s(3205)+0 Such that:s(3205) =< 2 aux(188) =< V1 aux(189) =< 2*V1+1 aux(190) =< V1/2 aux(191) =< 2/3*V1 aux(192) =< 2/3*V1+1/3 aux(193) =< 2/5*V1 aux(194) =< V aux(195) =< 2*V+1 aux(196) =< V/2 aux(197) =< 2/3*V aux(198) =< 2/3*V+1/3 aux(199) =< 2/5*V s(3042) =< aux(192) s(3083) =< aux(198) s(3085) =< aux(194) s(3086) =< aux(194) s(3087) =< aux(194) s(3088) =< aux(194) s(3089) =< aux(194) s(3090) =< aux(194) s(3083) =< aux(194) s(3083) =< aux(195) s(3088) =< aux(196) s(3087) =< aux(197) s(3088) =< aux(197) s(3086) =< aux(199) s(3091) =< aux(196)*2-1 s(3092) =< aux(196)*2-2 s(3093) =< aux(196)*2-3 s(3094) =< aux(196)*2+1 s(3095) =< aux(196)*2 s(3096) =< aux(196)+1 s(3097) =< aux(196) s(3098) =< aux(196)-1/2 s(3088) =< aux(195)*(1/2)+aux(196) s(3089) =< aux(195)*(1/2)+aux(196) s(3090) =< aux(195)*(1/2)+aux(196) s(3087) =< aux(195)*(1/3)+aux(197) s(3088) =< aux(195)*(1/3)+aux(197) s(3089) =< aux(195)*(1/3)+aux(197) s(3090) =< aux(195)*(1/3)+aux(197) s(3086) =< aux(195)*(3/5)+s(3083)*(1/5)+aux(199) s(3087) =< aux(195)*(3/5)+s(3083)*(1/5)+aux(199) s(3088) =< aux(195)*(3/5)+s(3083)*(1/5)+aux(199) s(3089) =< aux(195)*(3/5)+s(3083)*(1/5)+aux(199) s(3090) =< aux(195)*(3/5)+s(3083)*(1/5)+aux(199) s(3099) =< aux(194)*3 s(3100) =< aux(194)*2 s(3101) =< s(3090)*s(3091) s(3102) =< s(3088)*s(3092) s(3103) =< s(3086)*s(3093) s(3104) =< s(3085)*s(3094) s(3105) =< s(3085)*s(3095) s(3106) =< s(3085)*s(3096) s(3107) =< s(3085)*s(3097) s(3108) =< s(3085)*s(3098) s(3109) =< s(3085)*s(3091) s(3110) =< s(3109)*(1/2) s(3111) =< s(3100) s(3112) =< s(3110) s(3113) =< s(3106) s(3114) =< s(3107) s(3115) =< s(3112)*aux(196) s(3116) =< s(3109) s(3117) =< s(3108) s(3118) =< s(3105) s(3119) =< s(3112)*s(3097) s(3044) =< aux(188) s(3045) =< aux(188) s(3046) =< aux(188) s(3047) =< aux(188) s(3048) =< aux(188) s(3049) =< aux(188) s(3042) =< aux(188) s(3042) =< aux(189) s(3047) =< aux(190) s(3046) =< aux(191) s(3047) =< aux(191) s(3045) =< aux(193) s(3050) =< aux(190)*2-1 s(3051) =< aux(190)*2-2 s(3052) =< aux(190)*2-3 s(3053) =< aux(190)*2+1 s(3054) =< aux(190)*2 s(3055) =< aux(190)+1 s(3056) =< aux(190) s(3057) =< aux(190)-1/2 s(3047) =< aux(189)*(1/2)+aux(190) s(3048) =< aux(189)*(1/2)+aux(190) s(3049) =< aux(189)*(1/2)+aux(190) s(3046) =< aux(189)*(1/3)+aux(191) s(3047) =< aux(189)*(1/3)+aux(191) s(3048) =< aux(189)*(1/3)+aux(191) s(3049) =< aux(189)*(1/3)+aux(191) s(3045) =< aux(189)*(3/5)+s(3042)*(1/5)+aux(193) s(3046) =< aux(189)*(3/5)+s(3042)*(1/5)+aux(193) s(3047) =< aux(189)*(3/5)+s(3042)*(1/5)+aux(193) s(3048) =< aux(189)*(3/5)+s(3042)*(1/5)+aux(193) s(3049) =< aux(189)*(3/5)+s(3042)*(1/5)+aux(193) s(3058) =< aux(188)*3 s(3059) =< aux(188)*2 s(3060) =< s(3049)*s(3050) s(3061) =< s(3047)*s(3051) s(3062) =< s(3045)*s(3052) s(3063) =< s(3044)*s(3053) s(3064) =< s(3044)*s(3054) s(3065) =< s(3044)*s(3055) s(3066) =< s(3044)*s(3056) s(3067) =< s(3044)*s(3057) s(3068) =< s(3044)*s(3050) s(3069) =< s(3068)*(1/2) s(3070) =< s(3059) s(3071) =< s(3069) s(3072) =< s(3065) s(3073) =< s(3066) s(3074) =< s(3071)*aux(190) s(3075) =< s(3068) s(3076) =< s(3067) s(3077) =< s(3064) s(3078) =< s(3071)*s(3056) with precondition: [Out=0,V1>=0,V>=0] * Chain [61]: 33*s(3256)+3*s(3257)+3*s(3258)+3*s(3259)+3*s(3260)+3*s(3270)+3*s(3272)+3*s(3273)+3*s(3274)+3*s(3275)+18*s(3282)+150*s(3283)+18*s(3284)+18*s(3285)+24*s(3286)+6*s(3287)+6*s(3288)+15*s(3289)+24*s(3290)+45*s(3297)+4*s(3298)+4*s(3299)+4*s(3300)+4*s(3301)+4*s(3311)+4*s(3313)+4*s(3314)+4*s(3315)+4*s(3316)+24*s(3323)+200*s(3324)+24*s(3325)+24*s(3326)+32*s(3327)+8*s(3328)+8*s(3329)+20*s(3330)+32*s(3331)+2*s(3497)+1 Such that:aux(201) =< 2 aux(202) =< V1 aux(203) =< 2*V1+1 aux(204) =< V1/2 aux(205) =< 2/3*V1 aux(206) =< 2/3*V1+1/3 aux(207) =< 2/5*V1 aux(208) =< V aux(209) =< 2*V+1 aux(210) =< V/2 aux(211) =< 2/3*V aux(212) =< 2/3*V+1/3 aux(213) =< 2/5*V s(3497) =< aux(201) s(3254) =< aux(206) s(3295) =< aux(212) s(3297) =< aux(208) s(3298) =< aux(208) s(3299) =< aux(208) s(3300) =< aux(208) s(3301) =< aux(208) s(3302) =< aux(208) s(3295) =< aux(208) s(3295) =< aux(209) s(3300) =< aux(210) s(3299) =< aux(211) s(3300) =< aux(211) s(3298) =< aux(213) s(3303) =< aux(210)*2-1 s(3304) =< aux(210)*2-2 s(3305) =< aux(210)*2-3 s(3306) =< aux(210)*2+1 s(3307) =< aux(210)*2 s(3308) =< aux(210)+1 s(3309) =< aux(210) s(3310) =< aux(210)-1/2 s(3300) =< aux(209)*(1/2)+aux(210) s(3301) =< aux(209)*(1/2)+aux(210) s(3302) =< aux(209)*(1/2)+aux(210) s(3299) =< aux(209)*(1/3)+aux(211) s(3300) =< aux(209)*(1/3)+aux(211) s(3301) =< aux(209)*(1/3)+aux(211) s(3302) =< aux(209)*(1/3)+aux(211) s(3298) =< aux(209)*(3/5)+s(3295)*(1/5)+aux(213) s(3299) =< aux(209)*(3/5)+s(3295)*(1/5)+aux(213) s(3300) =< aux(209)*(3/5)+s(3295)*(1/5)+aux(213) s(3301) =< aux(209)*(3/5)+s(3295)*(1/5)+aux(213) s(3302) =< aux(209)*(3/5)+s(3295)*(1/5)+aux(213) s(3311) =< aux(208)*3 s(3312) =< aux(208)*2 s(3313) =< s(3302)*s(3303) s(3314) =< s(3300)*s(3304) s(3315) =< s(3298)*s(3305) s(3316) =< s(3297)*s(3306) s(3317) =< s(3297)*s(3307) s(3318) =< s(3297)*s(3308) s(3319) =< s(3297)*s(3309) s(3320) =< s(3297)*s(3310) s(3321) =< s(3297)*s(3303) s(3322) =< s(3321)*(1/2) s(3323) =< s(3312) s(3324) =< s(3322) s(3325) =< s(3318) s(3326) =< s(3319) s(3327) =< s(3324)*aux(210) s(3328) =< s(3321) s(3329) =< s(3320) s(3330) =< s(3317) s(3331) =< s(3324)*s(3309) s(3256) =< aux(202) s(3257) =< aux(202) s(3258) =< aux(202) s(3259) =< aux(202) s(3260) =< aux(202) s(3261) =< aux(202) s(3254) =< aux(202) s(3254) =< aux(203) s(3259) =< aux(204) s(3258) =< aux(205) s(3259) =< aux(205) s(3257) =< aux(207) s(3262) =< aux(204)*2-1 s(3263) =< aux(204)*2-2 s(3264) =< aux(204)*2-3 s(3265) =< aux(204)*2+1 s(3266) =< aux(204)*2 s(3267) =< aux(204)+1 s(3268) =< aux(204) s(3269) =< aux(204)-1/2 s(3259) =< aux(203)*(1/2)+aux(204) s(3260) =< aux(203)*(1/2)+aux(204) s(3261) =< aux(203)*(1/2)+aux(204) s(3258) =< aux(203)*(1/3)+aux(205) s(3259) =< aux(203)*(1/3)+aux(205) s(3260) =< aux(203)*(1/3)+aux(205) s(3261) =< aux(203)*(1/3)+aux(205) s(3257) =< aux(203)*(3/5)+s(3254)*(1/5)+aux(207) s(3258) =< aux(203)*(3/5)+s(3254)*(1/5)+aux(207) s(3259) =< aux(203)*(3/5)+s(3254)*(1/5)+aux(207) s(3260) =< aux(203)*(3/5)+s(3254)*(1/5)+aux(207) s(3261) =< aux(203)*(3/5)+s(3254)*(1/5)+aux(207) s(3270) =< aux(202)*3 s(3271) =< aux(202)*2 s(3272) =< s(3261)*s(3262) s(3273) =< s(3259)*s(3263) s(3274) =< s(3257)*s(3264) s(3275) =< s(3256)*s(3265) s(3276) =< s(3256)*s(3266) s(3277) =< s(3256)*s(3267) s(3278) =< s(3256)*s(3268) s(3279) =< s(3256)*s(3269) s(3280) =< s(3256)*s(3262) s(3281) =< s(3280)*(1/2) s(3282) =< s(3271) s(3283) =< s(3281) s(3284) =< s(3277) s(3285) =< s(3278) s(3286) =< s(3283)*aux(204) s(3287) =< s(3280) s(3288) =< s(3279) s(3289) =< s(3276) s(3290) =< s(3283)*s(3268) with precondition: [Out=1,V1>=0,V>=0] * Chain [60]: 33*s(3546)+3*s(3547)+3*s(3548)+3*s(3549)+3*s(3550)+3*s(3560)+3*s(3562)+3*s(3563)+3*s(3564)+3*s(3565)+18*s(3572)+150*s(3573)+18*s(3574)+18*s(3575)+24*s(3576)+6*s(3577)+6*s(3578)+15*s(3579)+24*s(3580)+45*s(3587)+4*s(3588)+4*s(3589)+4*s(3590)+4*s(3591)+4*s(3601)+4*s(3603)+4*s(3604)+4*s(3605)+4*s(3606)+24*s(3613)+200*s(3614)+24*s(3615)+24*s(3616)+32*s(3617)+8*s(3618)+8*s(3619)+20*s(3620)+32*s(3621)+1*s(3828)+1 Such that:s(3828) =< 1 aux(215) =< V1 aux(216) =< 2*V1+1 aux(217) =< V1/2 aux(218) =< 2/3*V1 aux(219) =< 2/3*V1+1/3 aux(220) =< 2/5*V1 aux(221) =< V aux(222) =< 2*V+1 aux(223) =< V/2 aux(224) =< 2/3*V aux(225) =< 2/3*V+1/3 aux(226) =< 2/5*V s(3544) =< aux(219) s(3585) =< aux(225) s(3587) =< aux(221) s(3588) =< aux(221) s(3589) =< aux(221) s(3590) =< aux(221) s(3591) =< aux(221) s(3592) =< aux(221) s(3585) =< aux(221) s(3585) =< aux(222) s(3590) =< aux(223) s(3589) =< aux(224) s(3590) =< aux(224) s(3588) =< aux(226) s(3593) =< aux(223)*2-1 s(3594) =< aux(223)*2-2 s(3595) =< aux(223)*2-3 s(3596) =< aux(223)*2+1 s(3597) =< aux(223)*2 s(3598) =< aux(223)+1 s(3599) =< aux(223) s(3600) =< aux(223)-1/2 s(3590) =< aux(222)*(1/2)+aux(223) s(3591) =< aux(222)*(1/2)+aux(223) s(3592) =< aux(222)*(1/2)+aux(223) s(3589) =< aux(222)*(1/3)+aux(224) s(3590) =< aux(222)*(1/3)+aux(224) s(3591) =< aux(222)*(1/3)+aux(224) s(3592) =< aux(222)*(1/3)+aux(224) s(3588) =< aux(222)*(3/5)+s(3585)*(1/5)+aux(226) s(3589) =< aux(222)*(3/5)+s(3585)*(1/5)+aux(226) s(3590) =< aux(222)*(3/5)+s(3585)*(1/5)+aux(226) s(3591) =< aux(222)*(3/5)+s(3585)*(1/5)+aux(226) s(3592) =< aux(222)*(3/5)+s(3585)*(1/5)+aux(226) s(3601) =< aux(221)*3 s(3602) =< aux(221)*2 s(3603) =< s(3592)*s(3593) s(3604) =< s(3590)*s(3594) s(3605) =< s(3588)*s(3595) s(3606) =< s(3587)*s(3596) s(3607) =< s(3587)*s(3597) s(3608) =< s(3587)*s(3598) s(3609) =< s(3587)*s(3599) s(3610) =< s(3587)*s(3600) s(3611) =< s(3587)*s(3593) s(3612) =< s(3611)*(1/2) s(3613) =< s(3602) s(3614) =< s(3612) s(3615) =< s(3608) s(3616) =< s(3609) s(3617) =< s(3614)*aux(223) s(3618) =< s(3611) s(3619) =< s(3610) s(3620) =< s(3607) s(3621) =< s(3614)*s(3599) s(3546) =< aux(215) s(3547) =< aux(215) s(3548) =< aux(215) s(3549) =< aux(215) s(3550) =< aux(215) s(3551) =< aux(215) s(3544) =< aux(215) s(3544) =< aux(216) s(3549) =< aux(217) s(3548) =< aux(218) s(3549) =< aux(218) s(3547) =< aux(220) s(3552) =< aux(217)*2-1 s(3553) =< aux(217)*2-2 s(3554) =< aux(217)*2-3 s(3555) =< aux(217)*2+1 s(3556) =< aux(217)*2 s(3557) =< aux(217)+1 s(3558) =< aux(217) s(3559) =< aux(217)-1/2 s(3549) =< aux(216)*(1/2)+aux(217) s(3550) =< aux(216)*(1/2)+aux(217) s(3551) =< aux(216)*(1/2)+aux(217) s(3548) =< aux(216)*(1/3)+aux(218) s(3549) =< aux(216)*(1/3)+aux(218) s(3550) =< aux(216)*(1/3)+aux(218) s(3551) =< aux(216)*(1/3)+aux(218) s(3547) =< aux(216)*(3/5)+s(3544)*(1/5)+aux(220) s(3548) =< aux(216)*(3/5)+s(3544)*(1/5)+aux(220) s(3549) =< aux(216)*(3/5)+s(3544)*(1/5)+aux(220) s(3550) =< aux(216)*(3/5)+s(3544)*(1/5)+aux(220) s(3551) =< aux(216)*(3/5)+s(3544)*(1/5)+aux(220) s(3560) =< aux(215)*3 s(3561) =< aux(215)*2 s(3562) =< s(3551)*s(3552) s(3563) =< s(3549)*s(3553) s(3564) =< s(3547)*s(3554) s(3565) =< s(3546)*s(3555) s(3566) =< s(3546)*s(3556) s(3567) =< s(3546)*s(3557) s(3568) =< s(3546)*s(3558) s(3569) =< s(3546)*s(3559) s(3570) =< s(3546)*s(3552) s(3571) =< s(3570)*(1/2) s(3572) =< s(3561) s(3573) =< s(3571) s(3574) =< s(3567) s(3575) =< s(3568) s(3576) =< s(3573)*aux(217) s(3577) =< s(3570) s(3578) =< s(3569) s(3579) =< s(3566) s(3580) =< s(3573)*s(3558) with precondition: [Out=2,V1>=1,V>=0] * Chain [59]: 11*s(3835)+1*s(3836)+1*s(3837)+1*s(3838)+1*s(3839)+1*s(3849)+1*s(3851)+1*s(3852)+1*s(3853)+1*s(3854)+6*s(3861)+50*s(3862)+6*s(3863)+6*s(3864)+8*s(3865)+2*s(3866)+2*s(3867)+5*s(3868)+8*s(3869)+2*s(3870)+0 Such that:s(3829) =< V1 s(3830) =< 2*V1+1 s(3831) =< V1/2 s(3832) =< 2/3*V1 s(3833) =< 2/3*V1+1/3 s(3834) =< 2/5*V1 aux(227) =< 2 s(3870) =< aux(227) s(3835) =< s(3829) s(3836) =< s(3829) s(3837) =< s(3829) s(3838) =< s(3829) s(3839) =< s(3829) s(3840) =< s(3829) s(3833) =< s(3829) s(3833) =< s(3830) s(3838) =< s(3831) s(3837) =< s(3832) s(3838) =< s(3832) s(3836) =< s(3834) s(3841) =< s(3831)*2-1 s(3842) =< s(3831)*2-2 s(3843) =< s(3831)*2-3 s(3844) =< s(3831)*2+1 s(3845) =< s(3831)*2 s(3846) =< s(3831)+1 s(3847) =< s(3831) s(3848) =< s(3831)-1/2 s(3838) =< s(3830)*(1/2)+s(3831) s(3839) =< s(3830)*(1/2)+s(3831) s(3840) =< s(3830)*(1/2)+s(3831) s(3837) =< s(3830)*(1/3)+s(3832) s(3838) =< s(3830)*(1/3)+s(3832) s(3839) =< s(3830)*(1/3)+s(3832) s(3840) =< s(3830)*(1/3)+s(3832) s(3836) =< s(3830)*(3/5)+s(3833)*(1/5)+s(3834) s(3837) =< s(3830)*(3/5)+s(3833)*(1/5)+s(3834) s(3838) =< s(3830)*(3/5)+s(3833)*(1/5)+s(3834) s(3839) =< s(3830)*(3/5)+s(3833)*(1/5)+s(3834) s(3840) =< s(3830)*(3/5)+s(3833)*(1/5)+s(3834) s(3849) =< s(3829)*3 s(3850) =< s(3829)*2 s(3851) =< s(3840)*s(3841) s(3852) =< s(3838)*s(3842) s(3853) =< s(3836)*s(3843) s(3854) =< s(3835)*s(3844) s(3855) =< s(3835)*s(3845) s(3856) =< s(3835)*s(3846) s(3857) =< s(3835)*s(3847) s(3858) =< s(3835)*s(3848) s(3859) =< s(3835)*s(3841) s(3860) =< s(3859)*(1/2) s(3861) =< s(3850) s(3862) =< s(3860) s(3863) =< s(3856) s(3864) =< s(3857) s(3865) =< s(3862)*s(3831) s(3866) =< s(3859) s(3867) =< s(3858) s(3868) =< s(3855) s(3869) =< s(3862)*s(3847) with precondition: [V=2,Out=0,V1>=0] * Chain [58]: 23*s(3878)+2*s(3879)+2*s(3880)+2*s(3881)+2*s(3882)+2*s(3892)+2*s(3894)+2*s(3895)+2*s(3896)+2*s(3897)+12*s(3904)+100*s(3905)+12*s(3906)+12*s(3907)+16*s(3908)+4*s(3909)+4*s(3910)+10*s(3911)+16*s(3912)+1 Such that:aux(229) =< V1 aux(230) =< 2*V1+1 aux(231) =< V1/2 aux(232) =< 2/3*V1 aux(233) =< 2/3*V1+1/3 aux(234) =< 2/5*V1 s(3876) =< aux(233) s(3878) =< aux(229) s(3879) =< aux(229) s(3880) =< aux(229) s(3881) =< aux(229) s(3882) =< aux(229) s(3883) =< aux(229) s(3876) =< aux(229) s(3876) =< aux(230) s(3881) =< aux(231) s(3880) =< aux(232) s(3881) =< aux(232) s(3879) =< aux(234) s(3884) =< aux(231)*2-1 s(3885) =< aux(231)*2-2 s(3886) =< aux(231)*2-3 s(3887) =< aux(231)*2+1 s(3888) =< aux(231)*2 s(3889) =< aux(231)+1 s(3890) =< aux(231) s(3891) =< aux(231)-1/2 s(3881) =< aux(230)*(1/2)+aux(231) s(3882) =< aux(230)*(1/2)+aux(231) s(3883) =< aux(230)*(1/2)+aux(231) s(3880) =< aux(230)*(1/3)+aux(232) s(3881) =< aux(230)*(1/3)+aux(232) s(3882) =< aux(230)*(1/3)+aux(232) s(3883) =< aux(230)*(1/3)+aux(232) s(3879) =< aux(230)*(3/5)+s(3876)*(1/5)+aux(234) s(3880) =< aux(230)*(3/5)+s(3876)*(1/5)+aux(234) s(3881) =< aux(230)*(3/5)+s(3876)*(1/5)+aux(234) s(3882) =< aux(230)*(3/5)+s(3876)*(1/5)+aux(234) s(3883) =< aux(230)*(3/5)+s(3876)*(1/5)+aux(234) s(3892) =< aux(229)*3 s(3893) =< aux(229)*2 s(3894) =< s(3883)*s(3884) s(3895) =< s(3881)*s(3885) s(3896) =< s(3879)*s(3886) s(3897) =< s(3878)*s(3887) s(3898) =< s(3878)*s(3888) s(3899) =< s(3878)*s(3889) s(3900) =< s(3878)*s(3890) s(3901) =< s(3878)*s(3891) s(3902) =< s(3878)*s(3884) s(3903) =< s(3902)*(1/2) s(3904) =< s(3893) s(3905) =< s(3903) s(3906) =< s(3899) s(3907) =< s(3900) s(3908) =< s(3905)*aux(231) s(3909) =< s(3902) s(3910) =< s(3901) s(3911) =< s(3898) s(3912) =< s(3905)*s(3890) with precondition: [V=2,Out=1,V1>=0] * Chain [57]: 11*s(3961)+1*s(3962)+1*s(3963)+1*s(3964)+1*s(3965)+1*s(3975)+1*s(3977)+1*s(3978)+1*s(3979)+1*s(3980)+6*s(3987)+50*s(3988)+6*s(3989)+6*s(3990)+8*s(3991)+2*s(3992)+2*s(3993)+5*s(3994)+8*s(3995)+1*s(3996)+1 Such that:s(3996) =< 2 s(3955) =< V1 s(3956) =< 2*V1+1 s(3957) =< V1/2 s(3958) =< 2/3*V1 s(3959) =< 2/3*V1+1/3 s(3960) =< 2/5*V1 s(3961) =< s(3955) s(3962) =< s(3955) s(3963) =< s(3955) s(3964) =< s(3955) s(3965) =< s(3955) s(3966) =< s(3955) s(3959) =< s(3955) s(3959) =< s(3956) s(3964) =< s(3957) s(3963) =< s(3958) s(3964) =< s(3958) s(3962) =< s(3960) s(3967) =< s(3957)*2-1 s(3968) =< s(3957)*2-2 s(3969) =< s(3957)*2-3 s(3970) =< s(3957)*2+1 s(3971) =< s(3957)*2 s(3972) =< s(3957)+1 s(3973) =< s(3957) s(3974) =< s(3957)-1/2 s(3964) =< s(3956)*(1/2)+s(3957) s(3965) =< s(3956)*(1/2)+s(3957) s(3966) =< s(3956)*(1/2)+s(3957) s(3963) =< s(3956)*(1/3)+s(3958) s(3964) =< s(3956)*(1/3)+s(3958) s(3965) =< s(3956)*(1/3)+s(3958) s(3966) =< s(3956)*(1/3)+s(3958) s(3962) =< s(3956)*(3/5)+s(3959)*(1/5)+s(3960) s(3963) =< s(3956)*(3/5)+s(3959)*(1/5)+s(3960) s(3964) =< s(3956)*(3/5)+s(3959)*(1/5)+s(3960) s(3965) =< s(3956)*(3/5)+s(3959)*(1/5)+s(3960) s(3966) =< s(3956)*(3/5)+s(3959)*(1/5)+s(3960) s(3975) =< s(3955)*3 s(3976) =< s(3955)*2 s(3977) =< s(3966)*s(3967) s(3978) =< s(3964)*s(3968) s(3979) =< s(3962)*s(3969) s(3980) =< s(3961)*s(3970) s(3981) =< s(3961)*s(3971) s(3982) =< s(3961)*s(3972) s(3983) =< s(3961)*s(3973) s(3984) =< s(3961)*s(3974) s(3985) =< s(3961)*s(3967) s(3986) =< s(3985)*(1/2) s(3987) =< s(3976) s(3988) =< s(3986) s(3989) =< s(3982) s(3990) =< s(3983) s(3991) =< s(3988)*s(3957) s(3992) =< s(3985) s(3993) =< s(3984) s(3994) =< s(3981) s(3995) =< s(3988)*s(3973) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun3(V1,Out): * Chain [64]: 11*s(4386)+1*s(4387)+1*s(4388)+1*s(4389)+1*s(4390)+1*s(4400)+1*s(4402)+1*s(4403)+1*s(4404)+1*s(4405)+6*s(4412)+50*s(4413)+6*s(4414)+6*s(4415)+8*s(4416)+2*s(4417)+2*s(4418)+5*s(4419)+8*s(4420)+1 Such that:s(4380) =< V1 s(4381) =< 2*V1+1 s(4382) =< V1/2 s(4383) =< 2/3*V1 s(4384) =< 2/3*V1+1/3 s(4385) =< 2/5*V1 s(4386) =< s(4380) s(4387) =< s(4380) s(4388) =< s(4380) s(4389) =< s(4380) s(4390) =< s(4380) s(4391) =< s(4380) s(4384) =< s(4380) s(4384) =< s(4381) s(4389) =< s(4382) s(4388) =< s(4383) s(4389) =< s(4383) s(4387) =< s(4385) s(4392) =< s(4382)*2-1 s(4393) =< s(4382)*2-2 s(4394) =< s(4382)*2-3 s(4395) =< s(4382)*2+1 s(4396) =< s(4382)*2 s(4397) =< s(4382)+1 s(4398) =< s(4382) s(4399) =< s(4382)-1/2 s(4389) =< s(4381)*(1/2)+s(4382) s(4390) =< s(4381)*(1/2)+s(4382) s(4391) =< s(4381)*(1/2)+s(4382) s(4388) =< s(4381)*(1/3)+s(4383) s(4389) =< s(4381)*(1/3)+s(4383) s(4390) =< s(4381)*(1/3)+s(4383) s(4391) =< s(4381)*(1/3)+s(4383) s(4387) =< s(4381)*(3/5)+s(4384)*(1/5)+s(4385) s(4388) =< s(4381)*(3/5)+s(4384)*(1/5)+s(4385) s(4389) =< s(4381)*(3/5)+s(4384)*(1/5)+s(4385) s(4390) =< s(4381)*(3/5)+s(4384)*(1/5)+s(4385) s(4391) =< s(4381)*(3/5)+s(4384)*(1/5)+s(4385) s(4400) =< s(4380)*3 s(4401) =< s(4380)*2 s(4402) =< s(4391)*s(4392) s(4403) =< s(4389)*s(4393) s(4404) =< s(4387)*s(4394) s(4405) =< s(4386)*s(4395) s(4406) =< s(4386)*s(4396) s(4407) =< s(4386)*s(4397) s(4408) =< s(4386)*s(4398) s(4409) =< s(4386)*s(4399) s(4410) =< s(4386)*s(4392) s(4411) =< s(4410)*(1/2) s(4412) =< s(4401) s(4413) =< s(4411) s(4414) =< s(4407) s(4415) =< s(4408) s(4416) =< s(4413)*s(4382) s(4417) =< s(4410) s(4418) =< s(4409) s(4419) =< s(4406) s(4420) =< s(4413)*s(4398) with precondition: [Out=0,V1>=0] * Chain [63]: 11*s(4427)+1*s(4428)+1*s(4429)+1*s(4430)+1*s(4431)+1*s(4441)+1*s(4443)+1*s(4444)+1*s(4445)+1*s(4446)+6*s(4453)+50*s(4454)+6*s(4455)+6*s(4456)+8*s(4457)+2*s(4458)+2*s(4459)+5*s(4460)+8*s(4461)+1 Such that:s(4421) =< V1 s(4422) =< 2*V1+1 s(4423) =< V1/2 s(4424) =< 2/3*V1 s(4425) =< 2/3*V1+1/3 s(4426) =< 2/5*V1 s(4427) =< s(4421) s(4428) =< s(4421) s(4429) =< s(4421) s(4430) =< s(4421) s(4431) =< s(4421) s(4432) =< s(4421) s(4425) =< s(4421) s(4425) =< s(4422) s(4430) =< s(4423) s(4429) =< s(4424) s(4430) =< s(4424) s(4428) =< s(4426) s(4433) =< s(4423)*2-1 s(4434) =< s(4423)*2-2 s(4435) =< s(4423)*2-3 s(4436) =< s(4423)*2+1 s(4437) =< s(4423)*2 s(4438) =< s(4423)+1 s(4439) =< s(4423) s(4440) =< s(4423)-1/2 s(4430) =< s(4422)*(1/2)+s(4423) s(4431) =< s(4422)*(1/2)+s(4423) s(4432) =< s(4422)*(1/2)+s(4423) s(4429) =< s(4422)*(1/3)+s(4424) s(4430) =< s(4422)*(1/3)+s(4424) s(4431) =< s(4422)*(1/3)+s(4424) s(4432) =< s(4422)*(1/3)+s(4424) s(4428) =< s(4422)*(3/5)+s(4425)*(1/5)+s(4426) s(4429) =< s(4422)*(3/5)+s(4425)*(1/5)+s(4426) s(4430) =< s(4422)*(3/5)+s(4425)*(1/5)+s(4426) s(4431) =< s(4422)*(3/5)+s(4425)*(1/5)+s(4426) s(4432) =< s(4422)*(3/5)+s(4425)*(1/5)+s(4426) s(4441) =< s(4421)*3 s(4442) =< s(4421)*2 s(4443) =< s(4432)*s(4433) s(4444) =< s(4430)*s(4434) s(4445) =< s(4428)*s(4435) s(4446) =< s(4427)*s(4436) s(4447) =< s(4427)*s(4437) s(4448) =< s(4427)*s(4438) s(4449) =< s(4427)*s(4439) s(4450) =< s(4427)*s(4440) s(4451) =< s(4427)*s(4433) s(4452) =< s(4451)*(1/2) s(4453) =< s(4442) s(4454) =< s(4452) s(4455) =< s(4448) s(4456) =< s(4449) s(4457) =< s(4454)*s(4423) s(4458) =< s(4451) s(4459) =< s(4450) s(4460) =< s(4447) s(4461) =< s(4454)*s(4439) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun4(V1,Out): * Chain [67]: 11*s(4468)+1*s(4469)+1*s(4470)+1*s(4471)+1*s(4472)+1*s(4482)+1*s(4484)+1*s(4485)+1*s(4486)+1*s(4487)+6*s(4494)+50*s(4495)+6*s(4496)+6*s(4497)+8*s(4498)+2*s(4499)+2*s(4500)+5*s(4501)+8*s(4502)+0 Such that:s(4462) =< V1 s(4463) =< 2*V1+1 s(4464) =< V1/2 s(4465) =< 2/3*V1 s(4466) =< 2/3*V1+1/3 s(4467) =< 2/5*V1 s(4468) =< s(4462) s(4469) =< s(4462) s(4470) =< s(4462) s(4471) =< s(4462) s(4472) =< s(4462) s(4473) =< s(4462) s(4466) =< s(4462) s(4466) =< s(4463) s(4471) =< s(4464) s(4470) =< s(4465) s(4471) =< s(4465) s(4469) =< s(4467) s(4474) =< s(4464)*2-1 s(4475) =< s(4464)*2-2 s(4476) =< s(4464)*2-3 s(4477) =< s(4464)*2+1 s(4478) =< s(4464)*2 s(4479) =< s(4464)+1 s(4480) =< s(4464) s(4481) =< s(4464)-1/2 s(4471) =< s(4463)*(1/2)+s(4464) s(4472) =< s(4463)*(1/2)+s(4464) s(4473) =< s(4463)*(1/2)+s(4464) s(4470) =< s(4463)*(1/3)+s(4465) s(4471) =< s(4463)*(1/3)+s(4465) s(4472) =< s(4463)*(1/3)+s(4465) s(4473) =< s(4463)*(1/3)+s(4465) s(4469) =< s(4463)*(3/5)+s(4466)*(1/5)+s(4467) s(4470) =< s(4463)*(3/5)+s(4466)*(1/5)+s(4467) s(4471) =< s(4463)*(3/5)+s(4466)*(1/5)+s(4467) s(4472) =< s(4463)*(3/5)+s(4466)*(1/5)+s(4467) s(4473) =< s(4463)*(3/5)+s(4466)*(1/5)+s(4467) s(4482) =< s(4462)*3 s(4483) =< s(4462)*2 s(4484) =< s(4473)*s(4474) s(4485) =< s(4471)*s(4475) s(4486) =< s(4469)*s(4476) s(4487) =< s(4468)*s(4477) s(4488) =< s(4468)*s(4478) s(4489) =< s(4468)*s(4479) s(4490) =< s(4468)*s(4480) s(4491) =< s(4468)*s(4481) s(4492) =< s(4468)*s(4474) s(4493) =< s(4492)*(1/2) s(4494) =< s(4483) s(4495) =< s(4493) s(4496) =< s(4489) s(4497) =< s(4490) s(4498) =< s(4495)*s(4464) s(4499) =< s(4492) s(4500) =< s(4491) s(4501) =< s(4488) s(4502) =< s(4495)*s(4480) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [66]: 0 with precondition: [Out=0,V1>=0] * Chain [65]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun6(Out): * Chain [69]: 0 with precondition: [Out=0] * Chain [68]: 0 with precondition: [Out=1] #### Cost of chains of start(V1,V,V2): * Chain [70]: 10*s(4503)+335*s(4510)+24*s(4511)+8*s(4512)+12*s(4513)+50*s(4514)+12*s(4515)+8*s(4516)+54*s(4517)+93*s(4522)+352*s(4523)+33*s(4524)+24*s(4525)+64*s(4526)+365*s(4528)+33*s(4537)+33*s(4538)+33*s(4539)+33*s(4540)+33*s(4550)+33*s(4552)+33*s(4553)+33*s(4554)+33*s(4555)+198*s(4562)+1650*s(4563)+198*s(4564)+198*s(4565)+264*s(4566)+66*s(4567)+66*s(4568)+165*s(4569)+264*s(4570)+9*s(4608)+306*s(4614)+6*s(4615)+9*s(4616)+18*s(4618)+24*s(4619)+187*s(4620)+17*s(4621)+17*s(4622)+17*s(4623)+17*s(4624)+17*s(4634)+17*s(4636)+17*s(4637)+17*s(4638)+17*s(4639)+102*s(4646)+850*s(4647)+102*s(4648)+102*s(4649)+136*s(4650)+34*s(4651)+34*s(4652)+85*s(4653)+136*s(4654)+39*s(4690)+39*s(4691)+56*s(4692)+9*s(4693)+28*s(4700)+28*s(4701)+28*s(4702)+28*s(4703)+28*s(4713)+28*s(4715)+28*s(4716)+28*s(4717)+28*s(4718)+168*s(4725)+1400*s(4726)+168*s(4727)+168*s(4728)+224*s(4729)+56*s(4730)+56*s(4731)+140*s(4732)+224*s(4733)+9*s(4734)+24*s(4738)+6*s(4739)+9*s(4740)+6*s(4805)+9*s(4806)+24*s(4808)+9 Such that:s(4571) =< 1/2 s(4590) =< 7/2 s(4755) =< V/2+1 s(4757) =< V/2+5/2 s(4505) =< V/2-V2/2 s(4597) =< V2 s(4600) =< 2*V2+1 s(4601) =< V2/2 s(4602) =< V2/2+1 s(4583) =< V2/2+1/2 s(4603) =< V2/2+3/2 s(4604) =< V2/2+5/2 s(4605) =< 2/3*V2 s(4606) =< 2/3*V2+1/3 s(4607) =< 2/5*V2 aux(254) =< 1 aux(255) =< 2 aux(256) =< 3 aux(257) =< 4 aux(258) =< 3/2 aux(259) =< 5/2 aux(260) =< V1 aux(261) =< 2*V1+1 aux(262) =< V1/2 aux(263) =< 2/3*V1 aux(264) =< 2/3*V1+1/3 aux(265) =< 2/5*V1 aux(266) =< V aux(267) =< 2*V+1 aux(268) =< V/2 aux(269) =< V/2+1/2 aux(270) =< V/2+3/2 aux(271) =< V/2+V2/2 aux(272) =< V/2+V2/2+1/2 aux(273) =< V/2+V2/2+3/2 aux(274) =< 2/3*V aux(275) =< 2/3*V+1/3 aux(276) =< 2/5*V aux(277) =< V2+1 aux(278) =< V2+2 s(4614) =< aux(254) s(4522) =< aux(255) s(4517) =< aux(256) s(4528) =< aux(260) s(4534) =< aux(264) s(4510) =< aux(266) s(4503) =< aux(278) s(4608) =< aux(257) s(4612) =< s(4606) s(4615) =< s(4602) s(4616) =< s(4604) s(4514) =< aux(277) s(4618) =< s(4603) s(4619) =< s(4614)*s(4603) s(4620) =< s(4597) s(4621) =< s(4597) s(4622) =< s(4597) s(4623) =< s(4597) s(4624) =< s(4597) s(4625) =< s(4597) s(4612) =< s(4597) s(4612) =< s(4600) s(4623) =< s(4601) s(4622) =< s(4605) s(4623) =< s(4605) s(4621) =< s(4607) s(4626) =< s(4601)*2-1 s(4627) =< s(4601)*2-2 s(4628) =< s(4601)*2-3 s(4629) =< s(4601)*2+1 s(4630) =< s(4601)*2 s(4631) =< s(4601)+1 s(4632) =< s(4601) s(4633) =< s(4601)-1/2 s(4623) =< s(4600)*(1/2)+s(4601) s(4624) =< s(4600)*(1/2)+s(4601) s(4625) =< s(4600)*(1/2)+s(4601) s(4622) =< s(4600)*(1/3)+s(4605) s(4623) =< s(4600)*(1/3)+s(4605) s(4624) =< s(4600)*(1/3)+s(4605) s(4625) =< s(4600)*(1/3)+s(4605) s(4621) =< s(4600)*(3/5)+s(4612)*(1/5)+s(4607) s(4622) =< s(4600)*(3/5)+s(4612)*(1/5)+s(4607) s(4623) =< s(4600)*(3/5)+s(4612)*(1/5)+s(4607) s(4624) =< s(4600)*(3/5)+s(4612)*(1/5)+s(4607) s(4625) =< s(4600)*(3/5)+s(4612)*(1/5)+s(4607) s(4634) =< s(4597)*3 s(4635) =< s(4597)*2 s(4636) =< s(4625)*s(4626) s(4637) =< s(4623)*s(4627) s(4638) =< s(4621)*s(4628) s(4639) =< s(4620)*s(4629) s(4640) =< s(4620)*s(4630) s(4641) =< s(4620)*s(4631) s(4642) =< s(4620)*s(4632) s(4643) =< s(4620)*s(4633) s(4644) =< s(4620)*s(4626) s(4645) =< s(4644)*(1/2) s(4646) =< s(4635) s(4647) =< s(4645) s(4648) =< s(4641) s(4649) =< s(4642) s(4650) =< s(4647)*s(4601) s(4651) =< s(4644) s(4652) =< s(4643) s(4653) =< s(4640) s(4654) =< s(4647)*s(4632) s(4537) =< aux(260) s(4538) =< aux(260) s(4539) =< aux(260) s(4540) =< aux(260) s(4541) =< aux(260) s(4534) =< aux(260) s(4534) =< aux(261) s(4539) =< aux(262) s(4538) =< aux(263) s(4539) =< aux(263) s(4537) =< aux(265) s(4542) =< aux(262)*2-1 s(4543) =< aux(262)*2-2 s(4544) =< aux(262)*2-3 s(4545) =< aux(262)*2+1 s(4546) =< aux(262)*2 s(4547) =< aux(262)+1 s(4548) =< aux(262) s(4549) =< aux(262)-1/2 s(4539) =< aux(261)*(1/2)+aux(262) s(4540) =< aux(261)*(1/2)+aux(262) s(4541) =< aux(261)*(1/2)+aux(262) s(4538) =< aux(261)*(1/3)+aux(263) s(4539) =< aux(261)*(1/3)+aux(263) s(4540) =< aux(261)*(1/3)+aux(263) s(4541) =< aux(261)*(1/3)+aux(263) s(4537) =< aux(261)*(3/5)+s(4534)*(1/5)+aux(265) s(4538) =< aux(261)*(3/5)+s(4534)*(1/5)+aux(265) s(4539) =< aux(261)*(3/5)+s(4534)*(1/5)+aux(265) s(4540) =< aux(261)*(3/5)+s(4534)*(1/5)+aux(265) s(4541) =< aux(261)*(3/5)+s(4534)*(1/5)+aux(265) s(4550) =< aux(260)*3 s(4551) =< aux(260)*2 s(4552) =< s(4541)*s(4542) s(4553) =< s(4539)*s(4543) s(4554) =< s(4537)*s(4544) s(4555) =< s(4528)*s(4545) s(4556) =< s(4528)*s(4546) s(4557) =< s(4528)*s(4547) s(4558) =< s(4528)*s(4548) s(4559) =< s(4528)*s(4549) s(4560) =< s(4528)*s(4542) s(4561) =< s(4560)*(1/2) s(4562) =< s(4551) s(4563) =< s(4561) s(4564) =< s(4557) s(4565) =< s(4558) s(4566) =< s(4563)*aux(262) s(4567) =< s(4560) s(4568) =< s(4559) s(4569) =< s(4556) s(4570) =< s(4563)*s(4548) s(4690) =< aux(259) s(4691) =< aux(258) s(4692) =< s(4614)*aux(258) s(4693) =< s(4590) s(4694) =< aux(275) s(4523) =< aux(268) s(4524) =< aux(270) s(4525) =< aux(269) s(4526) =< s(4523)*aux(269) s(4700) =< aux(266) s(4701) =< aux(266) s(4702) =< aux(266) s(4703) =< aux(266) s(4704) =< aux(266) s(4694) =< aux(266) s(4694) =< aux(267) s(4702) =< aux(268) s(4701) =< aux(274) s(4702) =< aux(274) s(4700) =< aux(276) s(4705) =< aux(268)*2-1 s(4706) =< aux(268)*2-2 s(4707) =< aux(268)*2-3 s(4708) =< aux(268)*2+1 s(4709) =< aux(268)*2 s(4710) =< aux(268)+1 s(4711) =< aux(268) s(4712) =< aux(268)-1/2 s(4702) =< aux(267)*(1/2)+aux(268) s(4703) =< aux(267)*(1/2)+aux(268) s(4704) =< aux(267)*(1/2)+aux(268) s(4701) =< aux(267)*(1/3)+aux(274) s(4702) =< aux(267)*(1/3)+aux(274) s(4703) =< aux(267)*(1/3)+aux(274) s(4704) =< aux(267)*(1/3)+aux(274) s(4700) =< aux(267)*(3/5)+s(4694)*(1/5)+aux(276) s(4701) =< aux(267)*(3/5)+s(4694)*(1/5)+aux(276) s(4702) =< aux(267)*(3/5)+s(4694)*(1/5)+aux(276) s(4703) =< aux(267)*(3/5)+s(4694)*(1/5)+aux(276) s(4704) =< aux(267)*(3/5)+s(4694)*(1/5)+aux(276) s(4713) =< aux(266)*3 s(4714) =< aux(266)*2 s(4715) =< s(4704)*s(4705) s(4716) =< s(4702)*s(4706) s(4717) =< s(4700)*s(4707) s(4718) =< s(4510)*s(4708) s(4719) =< s(4510)*s(4709) s(4720) =< s(4510)*s(4710) s(4721) =< s(4510)*s(4711) s(4722) =< s(4510)*s(4712) s(4723) =< s(4510)*s(4705) s(4724) =< s(4723)*(1/2) s(4725) =< s(4714) s(4726) =< s(4724) s(4727) =< s(4720) s(4728) =< s(4721) s(4729) =< s(4726)*aux(268) s(4730) =< s(4723) s(4731) =< s(4722) s(4732) =< s(4719) s(4733) =< s(4726)*s(4711) s(4734) =< s(4571) s(4512) =< aux(271) s(4513) =< aux(273) s(4515) =< aux(272) s(4738) =< s(4523)*aux(272) s(4739) =< s(4601) s(4740) =< s(4583) s(4805) =< s(4755) s(4806) =< s(4757) s(4808) =< s(4523)*aux(270) s(4511) =< s(4505) s(4516) =< s(4511)*aux(272) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [70] with precondition: [] - Upper bound: nat(V1)*1223+975+nat(V1)*33*nat(nat(V1/2)*2+ -3)+nat(V1)*33*nat(nat(V1/2)*2+ -2)+nat(V1)*924*nat(nat(V1/2)*2+ -1)+nat(V1)*264*nat(nat(V1/2)*2+ -1)*nat(V1/2)+nat(V1)*66*nat(-1/2+nat(V1/2))+nat(V1)*792*nat(V1/2)+nat(V)*1063+nat(V)*28*nat(nat(V/2)*2+ -3)+nat(V)*28*nat(nat(V/2)*2+ -2)+nat(V)*784*nat(nat(V/2)*2+ -1)+nat(V)*224*nat(nat(V/2)*2+ -1)*nat(V/2)+nat(V)*56*nat(-1/2+nat(V/2))+nat(V)*672*nat(V/2)+nat(V2)*629+nat(V2)*17*nat(nat(V2/2)*2+ -3)+nat(V2)*17*nat(nat(V2/2)*2+ -2)+nat(V2)*476*nat(nat(V2/2)*2+ -1)+nat(V2)*136*nat(nat(V2/2)*2+ -1)*nat(V2/2)+nat(V2)*34*nat(-1/2+nat(V2/2))+nat(V2)*408*nat(V2/2)+nat(V2+1)*50+nat(V2+2)*10+nat(V/2+V2/2+1/2)*12+nat(V/2+V2/2+1/2)*8*nat(V/2-V2/2)+nat(V/2+V2/2+1/2)*24*nat(V/2)+nat(V/2+V2/2+3/2)*12+nat(V/2+1)*6+nat(V/2+V2/2)*8+nat(V/2+1/2)*24+nat(V/2+1/2)*64*nat(V/2)+nat(V/2+3/2)*33+nat(V/2+3/2)*24*nat(V/2)+nat(V/2+5/2)*9+nat(V2/2+1)*6+nat(V2/2+1/2)*9+nat(V2/2+3/2)*42+nat(V2/2+5/2)*9+nat(V/2-V2/2)*24+nat(V/2)*352+nat(V2/2)*6 - Complexity: n^3 ### Maximum cost of start(V1,V,V2): nat(V1)*1223+975+nat(V1)*33*nat(nat(V1/2)*2+ -3)+nat(V1)*33*nat(nat(V1/2)*2+ -2)+nat(V1)*924*nat(nat(V1/2)*2+ -1)+nat(V1)*264*nat(nat(V1/2)*2+ -1)*nat(V1/2)+nat(V1)*66*nat(-1/2+nat(V1/2))+nat(V1)*792*nat(V1/2)+nat(V)*1063+nat(V)*28*nat(nat(V/2)*2+ -3)+nat(V)*28*nat(nat(V/2)*2+ -2)+nat(V)*784*nat(nat(V/2)*2+ -1)+nat(V)*224*nat(nat(V/2)*2+ -1)*nat(V/2)+nat(V)*56*nat(-1/2+nat(V/2))+nat(V)*672*nat(V/2)+nat(V2)*629+nat(V2)*17*nat(nat(V2/2)*2+ -3)+nat(V2)*17*nat(nat(V2/2)*2+ -2)+nat(V2)*476*nat(nat(V2/2)*2+ -1)+nat(V2)*136*nat(nat(V2/2)*2+ -1)*nat(V2/2)+nat(V2)*34*nat(-1/2+nat(V2/2))+nat(V2)*408*nat(V2/2)+nat(V2+1)*50+nat(V2+2)*10+nat(V/2+V2/2+1/2)*12+nat(V/2+V2/2+1/2)*8*nat(V/2-V2/2)+nat(V/2+V2/2+1/2)*24*nat(V/2)+nat(V/2+V2/2+3/2)*12+nat(V/2+1)*6+nat(V/2+V2/2)*8+nat(V/2+1/2)*24+nat(V/2+1/2)*64*nat(V/2)+nat(V/2+3/2)*33+nat(V/2+3/2)*24*nat(V/2)+nat(V/2+5/2)*9+nat(V2/2+1)*6+nat(V2/2+1/2)*9+nat(V2/2+3/2)*42+nat(V2/2+5/2)*9+nat(V/2-V2/2)*24+nat(V/2)*352+nat(V2/2)*6 Asymptotic class: n^3 * Total analysis performed in 20443 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p true :: true:s:0':false:cons_cond:cons_gr:cons_p gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p 0' :: true:s:0':false:cons_cond:cons_gr:cons_p false :: true:s:0':false:cons_cond:cons_gr:cons_p encArg :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_true :: true:s:0':false:cons_cond:cons_gr:cons_p encode_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_0 :: true:s:0':false:cons_cond:cons_gr:cons_p encode_false :: true:s:0':false:cons_cond:cons_gr:cons_p hole_true:s:0':false:cons_cond:cons_gr:cons_p1_4 :: true:s:0':false:cons_cond:cons_gr:cons_p gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:s:0':false:cons_cond:cons_gr:cons_p ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: cond, gr, encArg They will be analysed ascendingly in the following order: gr < cond cond < encArg gr < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p true :: true:s:0':false:cons_cond:cons_gr:cons_p gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p 0' :: true:s:0':false:cons_cond:cons_gr:cons_p false :: true:s:0':false:cons_cond:cons_gr:cons_p encArg :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_true :: true:s:0':false:cons_cond:cons_gr:cons_p encode_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_0 :: true:s:0':false:cons_cond:cons_gr:cons_p encode_false :: true:s:0':false:cons_cond:cons_gr:cons_p hole_true:s:0':false:cons_cond:cons_gr:cons_p1_4 :: true:s:0':false:cons_cond:cons_gr:cons_p gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:s:0':false:cons_cond:cons_gr:cons_p Generator Equations: gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(0) <=> true gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond, encArg They will be analysed ascendingly in the following order: gr < cond cond < encArg gr < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: gr(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: gr(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, 0)), gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, 0))) Induction Step: gr(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, +(n4_4, 1))), gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) gr(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4))) ->_IH *3_4 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p true :: true:s:0':false:cons_cond:cons_gr:cons_p gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p 0' :: true:s:0':false:cons_cond:cons_gr:cons_p false :: true:s:0':false:cons_cond:cons_gr:cons_p encArg :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_true :: true:s:0':false:cons_cond:cons_gr:cons_p encode_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_0 :: true:s:0':false:cons_cond:cons_gr:cons_p encode_false :: true:s:0':false:cons_cond:cons_gr:cons_p hole_true:s:0':false:cons_cond:cons_gr:cons_p1_4 :: true:s:0':false:cons_cond:cons_gr:cons_p gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:s:0':false:cons_cond:cons_gr:cons_p Generator Equations: gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(0) <=> true gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond, encArg They will be analysed ascendingly in the following order: gr < cond cond < encArg gr < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p true :: true:s:0':false:cons_cond:cons_gr:cons_p gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p 0' :: true:s:0':false:cons_cond:cons_gr:cons_p false :: true:s:0':false:cons_cond:cons_gr:cons_p encArg :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p cons_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_cond :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_true :: true:s:0':false:cons_cond:cons_gr:cons_p encode_gr :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_p :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_s :: true:s:0':false:cons_cond:cons_gr:cons_p -> true:s:0':false:cons_cond:cons_gr:cons_p encode_0 :: true:s:0':false:cons_cond:cons_gr:cons_p encode_false :: true:s:0':false:cons_cond:cons_gr:cons_p hole_true:s:0':false:cons_cond:cons_gr:cons_p1_4 :: true:s:0':false:cons_cond:cons_gr:cons_p gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4 :: Nat -> true:s:0':false:cons_cond:cons_gr:cons_p Lemmas: gr(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(0) <=> true gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: cond, encArg They will be analysed ascendingly in the following order: cond < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(n2279_4)) -> gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(n2279_4), rt in Omega(0) Induction Base: encArg(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(0)) ->_R^Omega(0) true Induction Step: encArg(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(+(n2279_4, 1))) ->_R^Omega(0) s(encArg(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(n2279_4))) ->_IH s(gen_true:s:0':false:cons_cond:cons_gr:cons_p2_4(c2280_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)