/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 151 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 22.0 s] (14) BOUNDS(1, n^2) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 560 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), 73 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 87 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0, 0) -> false gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0, 0) -> false gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0, 0) -> false gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) [1] and(true, true) -> true [1] and(x, false) -> false [1] and(false, x) -> false [1] gr(0, 0) -> false [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_false -> false [0] encode_s(x_1) -> s(encArg(x_1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond(true, x, y) -> cond(and(gr(x, 0), gr(y, 0)), p(x), p(y)) [1] and(true, true) -> true [1] and(x, false) -> false [1] and(false, x) -> false [1] gr(0, 0) -> false [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_false -> false [0] encode_s(x_1) -> s(encArg(x_1)) [0] The TRS has the following type information: cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p 0 :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0:false:s:cons_cond:cons_and: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_and(v0, v1) -> null_encode_and [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_0 -> null_encode_0 [0] encode_p(v0) -> null_encode_p [0] encode_false -> null_encode_false [0] encode_s(v0) -> null_encode_s [0] cond(v0, v1, v2) -> null_cond [0] and(v0, v1) -> null_and [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_and, null_encode_gr, null_encode_0, null_encode_p, null_encode_false, null_encode_s, null_cond, null_and, 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(and(gr(x, 0), gr(y, 0)), p(x), p(y)) [1] and(true, true) -> true [1] and(x, false) -> false [1] and(false, x) -> false [1] gr(0, 0) -> false [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_false -> false [0] encode_s(x_1) -> s(encArg(x_1)) [0] encArg(v0) -> null_encArg [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_true -> null_encode_true [0] encode_and(v0, v1) -> null_encode_and [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_0 -> null_encode_0 [0] encode_p(v0) -> null_encode_p [0] encode_false -> null_encode_false [0] encode_s(v0) -> null_encode_s [0] cond(v0, v1, v2) -> null_cond [0] and(v0, v1) -> null_and [0] gr(v0, v1) -> null_gr [0] p(v0) -> null_p [0] The TRS has the following type information: cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p true :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p 0 :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p false :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p s :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encArg :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p cons_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p cons_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p cons_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p cons_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_true :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_0 :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_false :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p encode_s :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p -> true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encArg :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_true :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_0 :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_false :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_encode_s :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_cond :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_and :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_gr :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and:null_gr:null_p null_p :: true:0:false:s:cons_cond:cons_and:cons_gr:cons_p:null_encArg:null_encode_cond:null_encode_true:null_encode_and:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_s:null_cond:null_and: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_and => 0 null_encode_gr => 0 null_encode_0 => 0 null_encode_p => 0 null_encode_false => 0 null_encode_s => 0 null_cond => 0 null_and => 0 null_gr => 0 null_p => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x and(z, z') -{ 1 }-> 1 :|: z' = x, z = 1, x >= 0 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond(z, z', z'') -{ 1 }-> cond(and(gr(x, 0), gr(y, 0)), p(x), p(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 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, 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_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 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 = 0, 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,[and(V1, V, Out)],[V1 >= 0,V >= 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, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun4(Out)],[]). eq(start(V1, V, V2),0,[fun5(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun6(Out)],[]). eq(start(V1, V, V2),0,[fun7(V1, Out)],[V1 >= 0]). eq(cond(V1, V, V2, Out),1,[gr(V4, 0, Ret00),gr(V3, 0, Ret01),and(Ret00, Ret01, Ret0),p(V4, Ret1),p(V3, Ret2),cond(Ret0, Ret1, Ret2, Ret)],[Out = Ret,V1 = 2,V = V4,V2 = V3,V4 >= 0,V3 >= 0]). eq(and(V1, V, Out),1,[],[Out = 2,V1 = 2,V = 2]). eq(and(V1, V, Out),1,[],[Out = 1,V5 >= 0,V = 1,V1 = V5]). eq(and(V1, V, Out),1,[],[Out = 1,V = V6,V1 = 1,V6 >= 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V1 = 0,V = 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V = V7,V7 >= 0,V1 = 0]). eq(gr(V1, V, Out),1,[],[Out = 2,V8 >= 0,V1 = 1 + V8,V = 0]). eq(gr(V1, V, Out),1,[gr(V9, V10, Ret3)],[Out = Ret3,V = 1 + V10,V9 >= 0,V10 >= 0,V1 = 1 + V9]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V11,V11 >= 0,V1 = 1 + V11]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V12, Ret11)],[Out = 1 + Ret11,V1 = 1 + V12,V12 >= 0]). eq(encArg(V1, Out),0,[encArg(V14, Ret02),encArg(V15, Ret12),encArg(V13, Ret21),cond(Ret02, Ret12, Ret21, Ret4)],[Out = Ret4,V14 >= 0,V1 = 1 + V13 + V14 + V15,V13 >= 0,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret03),encArg(V17, Ret13),and(Ret03, Ret13, Ret5)],[Out = Ret5,V16 >= 0,V1 = 1 + V16 + V17,V17 >= 0]). eq(encArg(V1, Out),0,[encArg(V19, Ret04),encArg(V18, Ret14),gr(Ret04, Ret14, Ret6)],[Out = Ret6,V19 >= 0,V1 = 1 + V18 + V19,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V20, Ret05),p(Ret05, Ret7)],[Out = Ret7,V1 = 1 + V20,V20 >= 0]). eq(fun(V1, V, V2, Out),0,[encArg(V23, Ret06),encArg(V21, Ret15),encArg(V22, Ret22),cond(Ret06, Ret15, Ret22, Ret8)],[Out = Ret8,V23 >= 0,V22 >= 0,V21 >= 0,V1 = V23,V = V21,V2 = V22]). eq(fun1(Out),0,[],[Out = 2]). eq(fun2(V1, V, Out),0,[encArg(V24, Ret07),encArg(V25, Ret16),and(Ret07, Ret16, Ret9)],[Out = Ret9,V24 >= 0,V25 >= 0,V1 = V24,V = V25]). eq(fun3(V1, V, Out),0,[encArg(V27, Ret08),encArg(V26, Ret17),gr(Ret08, Ret17, Ret10)],[Out = Ret10,V27 >= 0,V26 >= 0,V1 = V27,V = V26]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(V1, Out),0,[encArg(V28, Ret09),p(Ret09, Ret18)],[Out = Ret18,V28 >= 0,V1 = V28]). eq(fun6(Out),0,[],[Out = 1]). eq(fun7(V1, Out),0,[encArg(V29, Ret19)],[Out = 1 + Ret19,V29 >= 0,V1 = V29]). eq(encArg(V1, Out),0,[],[Out = 0,V30 >= 0,V1 = V30]). eq(fun(V1, V, V2, Out),0,[],[Out = 0,V32 >= 0,V2 = V33,V31 >= 0,V1 = V32,V = V31,V33 >= 0]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, V, Out),0,[],[Out = 0,V35 >= 0,V34 >= 0,V1 = V35,V = V34]). eq(fun3(V1, V, Out),0,[],[Out = 0,V36 >= 0,V37 >= 0,V1 = V36,V = V37]). eq(fun5(V1, Out),0,[],[Out = 0,V38 >= 0,V1 = V38]). eq(fun6(Out),0,[],[Out = 0]). eq(fun7(V1, Out),0,[],[Out = 0,V39 >= 0,V1 = V39]). eq(cond(V1, V, V2, Out),0,[],[Out = 0,V40 >= 0,V2 = V41,V42 >= 0,V1 = V40,V = V42,V41 >= 0]). eq(and(V1, V, Out),0,[],[Out = 0,V43 >= 0,V44 >= 0,V1 = V43,V = V44]). eq(gr(V1, V, Out),0,[],[Out = 0,V45 >= 0,V46 >= 0,V1 = V45,V = V46]). eq(p(V1, Out),0,[],[Out = 0,V47 >= 0,V1 = V47]). input_output_vars(cond(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(and(V1,V,Out),[V1,V],[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,V,Out),[V1,V],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(V1,Out),[V1],[Out]). input_output_vars(fun6(Out),[],[Out]). input_output_vars(fun7(V1,Out),[V1],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [and/3] 1. recursive : [gr/3] 2. non_recursive : [p/2] 3. recursive : [cond/4] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/4] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/3] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/1] 10. non_recursive : [fun5/2] 11. non_recursive : [fun6/1] 12. non_recursive : [fun7/2] 13. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into and/3 1. SCC is partially evaluated into gr/3 2. SCC is partially evaluated into p/2 3. SCC is partially evaluated into cond/4 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/4 6. SCC is partially evaluated into fun1/1 7. SCC is partially evaluated into fun2/3 8. SCC is partially evaluated into fun3/3 9. SCC is completely evaluated into other SCCs 10. SCC is partially evaluated into fun5/2 11. SCC is partially evaluated into fun6/1 12. SCC is partially evaluated into fun7/2 13. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations and/3 * CE 19 is refined into CE [49] * CE 17 is refined into CE [50] * CE 16 is refined into CE [51] * CE 18 is refined into CE [52] ### Cost equations --> "Loop" of and/3 * CEs [49] --> Loop 29 * CEs [50] --> Loop 30 * CEs [51] --> Loop 31 * CEs [52] --> Loop 32 ### Ranking functions of CR and(V1,V,Out) #### Partial ranking functions of CR and(V1,V,Out) ### Specialization of cost equations gr/3 * CE 23 is refined into CE [53] * CE 21 is refined into CE [54] * CE 20 is refined into CE [55] * CE 22 is refined into CE [56] ### Cost equations --> "Loop" of gr/3 * CEs [56] --> Loop 33 * CEs [53] --> Loop 34 * CEs [54] --> Loop 35 * CEs [55] --> Loop 36 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [33]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [33]: - RF of loop [33:1]: V V1 ### Specialization of cost equations p/2 * CE 25 is refined into CE [57] * CE 24 is refined into CE [58] * CE 26 is refined into CE [59] ### Cost equations --> "Loop" of p/2 * CEs [57] --> Loop 37 * CEs [58,59] --> Loop 38 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations cond/4 * CE 15 is refined into CE [60] * CE 14 is refined into CE [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99] ### Cost equations --> "Loop" of cond/4 * CEs [79] --> Loop 39 * CEs [78] --> Loop 40 * CEs [77] --> Loop 41 * CEs [76] --> Loop 42 * CEs [83,87,95,99] --> Loop 43 * CEs [73,89] --> Loop 44 * CEs [72,88] --> Loop 45 * CEs [75,82,86,91,94,98] --> Loop 46 * CEs [74,90] --> Loop 47 * CEs [65,69] --> Loop 48 * CEs [67,71,81,85,93,97] --> Loop 49 * CEs [61,62,64,68] --> Loop 50 * CEs [63,66,70,80,84,92,96] --> Loop 51 * CEs [60] --> Loop 52 ### Ranking functions of CR cond(V1,V,V2,Out) * RF of phase [39]: [V,V2] #### Partial ranking functions of CR cond(V1,V,V2,Out) * Partial RF of phase [39]: - RF of loop [39:1]: V V2 ### Specialization of cost equations encArg/2 * CE 28 is refined into CE [100] * CE 27 is refined into CE [101] * CE 29 is refined into CE [102] * CE 30 is refined into CE [103] * CE 34 is refined into CE [104,105] * CE 32 is refined into CE [106,107,108,109] * CE 33 is refined into CE [110,111,112,113,114] * CE 31 is refined into CE [115,116,117,118] ### Cost equations --> "Loop" of encArg/2 * CEs [118] --> Loop 53 * CEs [117] --> Loop 54 * CEs [115,116] --> Loop 55 * CEs [114] --> Loop 56 * CEs [111] --> Loop 57 * CEs [107] --> Loop 58 * CEs [113] --> Loop 59 * CEs [108] --> Loop 60 * CEs [106] --> Loop 61 * CEs [110] --> Loop 62 * CEs [109,112] --> Loop 63 * CEs [103] --> Loop 64 * CEs [105] --> Loop 65 * CEs [104] --> Loop 66 * CEs [100] --> Loop 67 * CEs [101] --> Loop 68 * CEs [102] --> Loop 69 ### Ranking functions of CR encArg(V1,Out) * RF of phase [53,54,55,56,57,58,59,60,61,62,63,64,65,66]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [53,54,55,56,57,58,59,60,61,62,63,64,65,66]: - RF of loop [53:1,53:2,53:3,54:1,54:2,54:3,55:1,55:2,55:3,56:1,56:2,57:1,57:2,58:1,58:2,59:1,59:2,60:1,60:2,61:1,61:2,62:1,62:2,63:1,63:2,64:1,65:1,66:1]: V1 ### Specialization of cost equations fun/4 * CE 35 is refined into CE [119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165] * CE 36 is refined into CE [166] ### Cost equations --> "Loop" of fun/4 * CEs [127,128,129,130,131,132,160,161,162] --> Loop 70 * CEs [123,124,135,142,143,154,158,164] --> Loop 71 * CEs [119,120,121,122,125,126,133,134,136,137,138,139,140,141,144,145,146,147,148,149,150,151,152,153,155,156,157,159,163,165,166] --> Loop 72 ### 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 37 is refined into CE [167] * CE 38 is refined into CE [168] ### Cost equations --> "Loop" of fun1/1 * CEs [167] --> Loop 73 * CEs [168] --> Loop 74 ### Ranking functions of CR fun1(Out) #### Partial ranking functions of CR fun1(Out) ### Specialization of cost equations fun2/3 * CE 39 is refined into CE [169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187] * CE 40 is refined into CE [188] ### Cost equations --> "Loop" of fun2/3 * CEs [174] --> Loop 75 * CEs [173,176] --> Loop 76 * CEs [175,186] --> Loop 77 * CEs [169,171,179,184] --> Loop 78 * CEs [170,178,181] --> Loop 79 * CEs [172,177,180,182,183,185,187,188] --> Loop 80 ### Ranking functions of CR fun2(V1,V,Out) #### Partial ranking functions of CR fun2(V1,V,Out) ### Specialization of cost equations fun3/3 * CE 41 is refined into CE [189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214] * CE 42 is refined into CE [215] ### Cost equations --> "Loop" of fun3/3 * CEs [197] --> Loop 81 * CEs [194,196,211] --> Loop 82 * CEs [195,212] --> Loop 83 * CEs [190,193,199,201,204,207] --> Loop 84 * CEs [189,192,198,203,206,209,213] --> Loop 85 * CEs [191,200,202,205,208,210,214,215] --> Loop 86 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun5/2 * CE 43 is refined into CE [216,217,218,219,220] * CE 44 is refined into CE [221] ### Cost equations --> "Loop" of fun5/2 * CEs [217,219] --> Loop 87 * CEs [216,218,220,221] --> Loop 88 ### Ranking functions of CR fun5(V1,Out) #### Partial ranking functions of CR fun5(V1,Out) ### Specialization of cost equations fun6/1 * CE 45 is refined into CE [222] * CE 46 is refined into CE [223] ### Cost equations --> "Loop" of fun6/1 * CEs [222] --> Loop 89 * CEs [223] --> Loop 90 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations fun7/2 * CE 47 is refined into CE [224,225,226] * CE 48 is refined into CE [227] ### Cost equations --> "Loop" of fun7/2 * CEs [226] --> Loop 91 * CEs [227] --> Loop 92 * CEs [224,225] --> Loop 93 ### Ranking functions of CR fun7(V1,Out) #### Partial ranking functions of CR fun7(V1,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [228,229,230,231] * CE 2 is refined into CE [232,233,234,235] * CE 3 is refined into CE [236,237,238,239,240] * CE 4 is refined into CE [241,242] * CE 5 is refined into CE [243,244,245] * CE 6 is refined into CE [246,247] * CE 7 is refined into CE [248,249] * CE 8 is refined into CE [250,251,252,253] * CE 9 is refined into CE [254,255,256] * CE 10 is refined into CE [257] * CE 11 is refined into CE [258,259] * CE 12 is refined into CE [260,261] * CE 13 is refined into CE [262,263,264] ### Cost equations --> "Loop" of start/3 * CEs [228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264] --> Loop 94 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of and(V1,V,Out): * Chain [32]: 1 with precondition: [V1=1,Out=1,V>=0] * Chain [31]: 1 with precondition: [V1=2,V=2,Out=2] * Chain [30]: 1 with precondition: [V=1,Out=1,V1>=0] * Chain [29]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of gr(V1,V,Out): * Chain [[33],36]: 1*it(33)+1 Such that:it(33) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[33],35]: 1*it(33)+1 Such that:it(33) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[33],34]: 1*it(33)+0 Such that:it(33) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [36]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [35]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [34]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of p(V1,Out): * Chain [38]: 1 with precondition: [Out=0,V1>=0] * Chain [37]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of cond(V1,V,V2,Out): * Chain [[39],52]: 6*it(39)+0 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [[39],51,52]: 6*it(39)+5 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [[39],50,52]: 6*it(39)+6 Such that:it(39) =< V with precondition: [V1=2,Out=0,V>=1,V2>=V] * Chain [[39],49,52]: 6*it(39)+5 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [[39],48,52]: 6*it(39)+6 Such that:it(39) =< V with precondition: [V1=2,Out=0,V>=1,V2>=V+1] * Chain [[39],47,52]: 6*it(39)+5 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V2>=1,V>=V2] * Chain [[39],46,52]: 6*it(39)+5 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=1] * Chain [[39],45,52]: 6*it(39)+6 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V2>=1,V>=V2] * Chain [[39],44,52]: 6*it(39)+6 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] * Chain [[39],43,52]: 6*it(39)+5 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],42,52]: 6*it(39)+6 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],42,51,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],42,50,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],42,47,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],42,45,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],41,52]: 6*it(39)+6 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],41,51,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],41,50,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],41,49,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=3] * Chain [[39],41,48,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=3] * Chain [[39],41,47,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V2>=2,V>=V2] * Chain [[39],41,45,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V2>=2,V>=V2] * Chain [[39],40,52]: 6*it(39)+6 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],40,51,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],40,50,52]: 6*it(39)+12 Such that:it(39) =< V with precondition: [V1=2,Out=0,V>=2,V2>=V] * Chain [[39],40,47,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],40,46,52]: 6*it(39)+11 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=3,V2>=2] * Chain [[39],40,45,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=2,V2>=2] * Chain [[39],40,44,52]: 6*it(39)+12 Such that:it(39) =< V2 with precondition: [V1=2,Out=0,V>=3,V2>=2] * Chain [52]: 0 with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [51,52]: 5 with precondition: [V1=2,Out=0,V>=0,V2>=0] * Chain [50,52]: 6 with precondition: [V1=2,V=0,Out=0,V2>=0] * Chain [49,52]: 5 with precondition: [V1=2,Out=0,V>=0,V2>=1] * Chain [48,52]: 6 with precondition: [V1=2,V=0,Out=0,V2>=1] * Chain [47,52]: 5 with precondition: [V1=2,V2=0,Out=0,V>=0] * Chain [46,52]: 5 with precondition: [V1=2,Out=0,V>=1,V2>=0] * Chain [45,52]: 6 with precondition: [V1=2,V2=0,Out=0,V>=0] * Chain [44,52]: 6 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [43,52]: 5 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [42,52]: 6 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [42,51,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [42,50,52]: 12 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [42,47,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [42,45,52]: 12 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,52]: 6 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,51,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,50,52]: 12 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,49,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,48,52]: 12 with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,47,52]: 11 with precondition: [V1=2,V2=1,Out=0,V>=1] * Chain [41,45,52]: 12 with precondition: [V1=2,V2=1,Out=0,V>=1] * Chain [40,52]: 6 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [40,51,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [40,50,52]: 12 with precondition: [V1=2,V=1,Out=0,V2>=1] * Chain [40,47,52]: 11 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [40,46,52]: 11 with precondition: [V1=2,Out=0,V>=2,V2>=1] * Chain [40,45,52]: 12 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [40,44,52]: 12 with precondition: [V1=2,Out=0,V>=2,V2>=1] #### Cost of chains of encArg(V1,Out): * Chain [69]: 0 with precondition: [V1=1,Out=1] * Chain [68]: 0 with precondition: [V1=2,Out=2] * Chain [67]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([53,54,55,56,57,58,59,60,61,62,63,64,65,66],[[69],[68],[67]])]: 12*it(53)+6*it(54)+12*it(55)+1*it(56)+1*it(57)+1*it(58)+1*it(59)+2*it(60)+1*it(62)+2*it(65)+18*s(69)+156*s(70)+1*s(73)+1*s(74)+1*s(75)+0 Such that:it([69]) =< 2/3*V1+1/3 aux(20) =< V1 aux(21) =< 2*V1+1 aux(22) =< V1/2 aux(23) =< V1/3 aux(24) =< 2/3*V1 aux(25) =< 2/5*V1 aux(26) =< 3/7*V1 aux(27) =< 3/11*V1 it(55) =< aux(20) it(56) =< aux(20) it(57) =< aux(20) it(58) =< aux(20) it(59) =< aux(20) it(60) =< aux(20) it(62) =< aux(20) it(63) =< aux(20) it(65) =< aux(20) it([69]) =< aux(20) it([67]) =< aux(21) it([69]) =< aux(21) it(59) =< aux(22) it(58) =< aux(23) it(57) =< aux(24) it(58) =< aux(24) it(59) =< aux(24) it(60) =< aux(24) it(56) =< aux(25) it(58) =< aux(25) it(54) =< aux(26) it(53) =< aux(27) aux(10) =< aux(20)-1 aux(16) =< aux(20)-2 aux(12) =< aux(20)-3 it(57) =< it([67])*(1/3)+aux(24) it(58) =< it([67])*(1/3)+aux(24) it(59) =< it([67])*(1/3)+aux(24) it(60) =< it([67])*(1/3)+aux(24) it(62) =< it([67])*(1/3)+aux(24) it(63) =< it([67])*(1/3)+aux(24) it(59) =< it([67])*(1/2)+aux(22) it(60) =< it([67])*(1/2)+aux(22) it(62) =< it([67])*(1/2)+aux(22) it(63) =< it([67])*(1/2)+aux(22) it(58) =< it([67])*(2/3)+it([69])*(1/3)+aux(23) it(59) =< it([67])*(2/3)+it([69])*(1/3)+aux(23) it(60) =< it([67])*(2/3)+it([69])*(1/3)+aux(23) it(62) =< it([67])*(2/3)+it([69])*(1/3)+aux(23) it(63) =< it([67])*(2/3)+it([69])*(1/3)+aux(23) it(56) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(57) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(58) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(59) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(60) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(62) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(63) =< it([67])*(3/5)+it([69])*(1/5)+aux(25) it(54) =< it([67])*(2/7)+aux(26) it(55) =< it([67])*(2/7)+aux(26) it(53) =< it([67])*(4/11)+it([69])*(1/11)+aux(27) it(54) =< it([67])*(4/11)+it([69])*(1/11)+aux(27) it(55) =< it([67])*(4/11)+it([69])*(1/11)+aux(27) s(75) =< it(63)*aux(10) s(74) =< it(59)*aux(16) s(73) =< it(56)*aux(12) s(71) =< it(55)*aux(10) s(72) =< it(55)*aux(20) s(69) =< s(72) s(70) =< s(71) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,V2,Out): * Chain [72]: 120*s(116)+10*s(117)+10*s(118)+10*s(119)+10*s(120)+20*s(121)+10*s(122)+20*s(124)+60*s(125)+120*s(126)+10*s(130)+10*s(131)+10*s(132)+180*s(135)+1560*s(136)+168*s(146)+14*s(147)+14*s(148)+14*s(149)+14*s(150)+28*s(151)+14*s(152)+136*s(154)+84*s(155)+168*s(156)+14*s(160)+14*s(161)+14*s(162)+252*s(165)+2184*s(166)+204*s(176)+17*s(177)+17*s(178)+17*s(179)+17*s(180)+34*s(181)+17*s(182)+1126*s(184)+102*s(185)+204*s(186)+17*s(190)+17*s(191)+17*s(192)+306*s(195)+2652*s(196)+210*s(1123)+12 Such that:aux(45) =< 2 aux(46) =< V1 aux(47) =< 2*V1+1 aux(48) =< V1/2 aux(49) =< V1/3 aux(50) =< 2/3*V1 aux(51) =< 2/3*V1+1/3 aux(52) =< 2/5*V1 aux(53) =< 3/7*V1 aux(54) =< 3/11*V1 aux(55) =< V aux(56) =< 2*V+1 aux(57) =< V/2 aux(58) =< V/3 aux(59) =< 2/3*V aux(60) =< 2/3*V+1/3 aux(61) =< 2/5*V aux(62) =< 3/7*V aux(63) =< 3/11*V aux(64) =< V2 aux(65) =< 2*V2+1 aux(66) =< V2/2 aux(67) =< V2/3 aux(68) =< 2/3*V2 aux(69) =< 2/3*V2+1/3 aux(70) =< 2/5*V2 aux(71) =< 3/7*V2 aux(72) =< 3/11*V2 s(112) =< aux(51) s(142) =< aux(60) s(172) =< aux(69) s(1123) =< aux(45) s(184) =< aux(64) s(176) =< aux(64) s(177) =< aux(64) s(178) =< aux(64) s(179) =< aux(64) s(180) =< aux(64) s(181) =< aux(64) s(182) =< aux(64) s(183) =< aux(64) s(172) =< aux(64) s(172) =< aux(65) s(180) =< aux(66) s(179) =< aux(67) s(178) =< aux(68) s(179) =< aux(68) s(180) =< aux(68) s(181) =< aux(68) s(177) =< aux(70) s(179) =< aux(70) s(185) =< aux(71) s(186) =< aux(72) s(187) =< aux(64)-1 s(188) =< aux(64)-2 s(189) =< aux(64)-3 s(178) =< aux(65)*(1/3)+aux(68) s(179) =< aux(65)*(1/3)+aux(68) s(180) =< aux(65)*(1/3)+aux(68) s(181) =< aux(65)*(1/3)+aux(68) s(182) =< aux(65)*(1/3)+aux(68) s(183) =< aux(65)*(1/3)+aux(68) s(180) =< aux(65)*(1/2)+aux(66) s(181) =< aux(65)*(1/2)+aux(66) s(182) =< aux(65)*(1/2)+aux(66) s(183) =< aux(65)*(1/2)+aux(66) s(179) =< aux(65)*(2/3)+s(172)*(1/3)+aux(67) s(180) =< aux(65)*(2/3)+s(172)*(1/3)+aux(67) s(181) =< aux(65)*(2/3)+s(172)*(1/3)+aux(67) s(182) =< aux(65)*(2/3)+s(172)*(1/3)+aux(67) s(183) =< aux(65)*(2/3)+s(172)*(1/3)+aux(67) s(177) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(178) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(179) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(180) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(181) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(182) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(183) =< aux(65)*(3/5)+s(172)*(1/5)+aux(70) s(185) =< aux(65)*(2/7)+aux(71) s(176) =< aux(65)*(2/7)+aux(71) s(186) =< aux(65)*(4/11)+s(172)*(1/11)+aux(72) s(185) =< aux(65)*(4/11)+s(172)*(1/11)+aux(72) s(176) =< aux(65)*(4/11)+s(172)*(1/11)+aux(72) s(190) =< s(183)*s(187) s(191) =< s(180)*s(188) s(192) =< s(177)*s(189) s(193) =< s(176)*s(187) s(194) =< s(176)*aux(64) s(195) =< s(194) s(196) =< s(193) s(154) =< aux(55) s(146) =< aux(55) s(147) =< aux(55) s(148) =< aux(55) s(149) =< aux(55) s(150) =< aux(55) s(151) =< aux(55) s(152) =< aux(55) s(153) =< aux(55) s(142) =< aux(55) s(142) =< aux(56) s(150) =< aux(57) s(149) =< aux(58) s(148) =< aux(59) s(149) =< aux(59) s(150) =< aux(59) s(151) =< aux(59) s(147) =< aux(61) s(149) =< aux(61) s(155) =< aux(62) s(156) =< aux(63) s(157) =< aux(55)-1 s(158) =< aux(55)-2 s(159) =< aux(55)-3 s(148) =< aux(56)*(1/3)+aux(59) s(149) =< aux(56)*(1/3)+aux(59) s(150) =< aux(56)*(1/3)+aux(59) s(151) =< aux(56)*(1/3)+aux(59) s(152) =< aux(56)*(1/3)+aux(59) s(153) =< aux(56)*(1/3)+aux(59) s(150) =< aux(56)*(1/2)+aux(57) s(151) =< aux(56)*(1/2)+aux(57) s(152) =< aux(56)*(1/2)+aux(57) s(153) =< aux(56)*(1/2)+aux(57) s(149) =< aux(56)*(2/3)+s(142)*(1/3)+aux(58) s(150) =< aux(56)*(2/3)+s(142)*(1/3)+aux(58) s(151) =< aux(56)*(2/3)+s(142)*(1/3)+aux(58) s(152) =< aux(56)*(2/3)+s(142)*(1/3)+aux(58) s(153) =< aux(56)*(2/3)+s(142)*(1/3)+aux(58) s(147) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(148) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(149) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(150) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(151) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(152) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(153) =< aux(56)*(3/5)+s(142)*(1/5)+aux(61) s(155) =< aux(56)*(2/7)+aux(62) s(146) =< aux(56)*(2/7)+aux(62) s(156) =< aux(56)*(4/11)+s(142)*(1/11)+aux(63) s(155) =< aux(56)*(4/11)+s(142)*(1/11)+aux(63) s(146) =< aux(56)*(4/11)+s(142)*(1/11)+aux(63) s(160) =< s(153)*s(157) s(161) =< s(150)*s(158) s(162) =< s(147)*s(159) s(163) =< s(146)*s(157) s(164) =< s(146)*aux(55) s(165) =< s(164) s(166) =< s(163) s(116) =< aux(46) s(117) =< aux(46) s(118) =< aux(46) s(119) =< aux(46) s(120) =< aux(46) s(121) =< aux(46) s(122) =< aux(46) s(123) =< aux(46) s(124) =< aux(46) s(112) =< aux(46) s(112) =< aux(47) s(120) =< aux(48) s(119) =< aux(49) s(118) =< aux(50) s(119) =< aux(50) s(120) =< aux(50) s(121) =< aux(50) s(117) =< aux(52) s(119) =< aux(52) s(125) =< aux(53) s(126) =< aux(54) s(127) =< aux(46)-1 s(128) =< aux(46)-2 s(129) =< aux(46)-3 s(118) =< aux(47)*(1/3)+aux(50) s(119) =< aux(47)*(1/3)+aux(50) s(120) =< aux(47)*(1/3)+aux(50) s(121) =< aux(47)*(1/3)+aux(50) s(122) =< aux(47)*(1/3)+aux(50) s(123) =< aux(47)*(1/3)+aux(50) s(120) =< aux(47)*(1/2)+aux(48) s(121) =< aux(47)*(1/2)+aux(48) s(122) =< aux(47)*(1/2)+aux(48) s(123) =< aux(47)*(1/2)+aux(48) s(119) =< aux(47)*(2/3)+s(112)*(1/3)+aux(49) s(120) =< aux(47)*(2/3)+s(112)*(1/3)+aux(49) s(121) =< aux(47)*(2/3)+s(112)*(1/3)+aux(49) s(122) =< aux(47)*(2/3)+s(112)*(1/3)+aux(49) s(123) =< aux(47)*(2/3)+s(112)*(1/3)+aux(49) s(117) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(118) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(119) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(120) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(121) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(122) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(123) =< aux(47)*(3/5)+s(112)*(1/5)+aux(52) s(125) =< aux(47)*(2/7)+aux(53) s(116) =< aux(47)*(2/7)+aux(53) s(126) =< aux(47)*(4/11)+s(112)*(1/11)+aux(54) s(125) =< aux(47)*(4/11)+s(112)*(1/11)+aux(54) s(116) =< aux(47)*(4/11)+s(112)*(1/11)+aux(54) s(130) =< s(123)*s(127) s(131) =< s(120)*s(128) s(132) =< s(117)*s(129) s(133) =< s(116)*s(127) s(134) =< s(116)*aux(46) s(135) =< s(134) s(136) =< s(133) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [71]: 36*s(1406)+3*s(1407)+3*s(1408)+3*s(1409)+3*s(1410)+6*s(1411)+3*s(1412)+6*s(1414)+18*s(1415)+36*s(1416)+3*s(1420)+3*s(1421)+3*s(1422)+54*s(1425)+468*s(1426)+60*s(1436)+5*s(1437)+5*s(1438)+5*s(1439)+5*s(1440)+10*s(1441)+5*s(1442)+64*s(1444)+30*s(1445)+60*s(1446)+5*s(1450)+5*s(1451)+5*s(1452)+90*s(1455)+780*s(1456)+936*s(1460)+12 Such that:aux(76) =< 2 aux(77) =< V1 aux(78) =< 2*V1+1 aux(79) =< V1/2 aux(80) =< V1/3 aux(81) =< 2/3*V1 aux(82) =< 2/3*V1+1/3 aux(83) =< 2/5*V1 aux(84) =< 3/7*V1 aux(85) =< 3/11*V1 aux(86) =< V aux(87) =< 2*V+1 aux(88) =< V/2 aux(89) =< V/3 aux(90) =< 2/3*V aux(91) =< 2/3*V+1/3 aux(92) =< 2/5*V aux(93) =< 3/7*V aux(94) =< 3/11*V s(1402) =< aux(82) s(1432) =< aux(91) s(1444) =< aux(86) s(1460) =< aux(76) s(1436) =< aux(86) s(1437) =< aux(86) s(1438) =< aux(86) s(1439) =< aux(86) s(1440) =< aux(86) s(1441) =< aux(86) s(1442) =< aux(86) s(1443) =< aux(86) s(1432) =< aux(86) s(1432) =< aux(87) s(1440) =< aux(88) s(1439) =< aux(89) s(1438) =< aux(90) s(1439) =< aux(90) s(1440) =< aux(90) s(1441) =< aux(90) s(1437) =< aux(92) s(1439) =< aux(92) s(1445) =< aux(93) s(1446) =< aux(94) s(1447) =< aux(86)-1 s(1448) =< aux(86)-2 s(1449) =< aux(86)-3 s(1438) =< aux(87)*(1/3)+aux(90) s(1439) =< aux(87)*(1/3)+aux(90) s(1440) =< aux(87)*(1/3)+aux(90) s(1441) =< aux(87)*(1/3)+aux(90) s(1442) =< aux(87)*(1/3)+aux(90) s(1443) =< aux(87)*(1/3)+aux(90) s(1440) =< aux(87)*(1/2)+aux(88) s(1441) =< aux(87)*(1/2)+aux(88) s(1442) =< aux(87)*(1/2)+aux(88) s(1443) =< aux(87)*(1/2)+aux(88) s(1439) =< aux(87)*(2/3)+s(1432)*(1/3)+aux(89) s(1440) =< aux(87)*(2/3)+s(1432)*(1/3)+aux(89) s(1441) =< aux(87)*(2/3)+s(1432)*(1/3)+aux(89) s(1442) =< aux(87)*(2/3)+s(1432)*(1/3)+aux(89) s(1443) =< aux(87)*(2/3)+s(1432)*(1/3)+aux(89) s(1437) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1438) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1439) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1440) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1441) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1442) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1443) =< aux(87)*(3/5)+s(1432)*(1/5)+aux(92) s(1445) =< aux(87)*(2/7)+aux(93) s(1436) =< aux(87)*(2/7)+aux(93) s(1446) =< aux(87)*(4/11)+s(1432)*(1/11)+aux(94) s(1445) =< aux(87)*(4/11)+s(1432)*(1/11)+aux(94) s(1436) =< aux(87)*(4/11)+s(1432)*(1/11)+aux(94) s(1450) =< s(1443)*s(1447) s(1451) =< s(1440)*s(1448) s(1452) =< s(1437)*s(1449) s(1453) =< s(1436)*s(1447) s(1454) =< s(1436)*aux(86) s(1455) =< s(1454) s(1456) =< s(1453) s(1406) =< aux(77) s(1407) =< aux(77) s(1408) =< aux(77) s(1409) =< aux(77) s(1410) =< aux(77) s(1411) =< aux(77) s(1412) =< aux(77) s(1413) =< aux(77) s(1414) =< aux(77) s(1402) =< aux(77) s(1402) =< aux(78) s(1410) =< aux(79) s(1409) =< aux(80) s(1408) =< aux(81) s(1409) =< aux(81) s(1410) =< aux(81) s(1411) =< aux(81) s(1407) =< aux(83) s(1409) =< aux(83) s(1415) =< aux(84) s(1416) =< aux(85) s(1417) =< aux(77)-1 s(1418) =< aux(77)-2 s(1419) =< aux(77)-3 s(1408) =< aux(78)*(1/3)+aux(81) s(1409) =< aux(78)*(1/3)+aux(81) s(1410) =< aux(78)*(1/3)+aux(81) s(1411) =< aux(78)*(1/3)+aux(81) s(1412) =< aux(78)*(1/3)+aux(81) s(1413) =< aux(78)*(1/3)+aux(81) s(1410) =< aux(78)*(1/2)+aux(79) s(1411) =< aux(78)*(1/2)+aux(79) s(1412) =< aux(78)*(1/2)+aux(79) s(1413) =< aux(78)*(1/2)+aux(79) s(1409) =< aux(78)*(2/3)+s(1402)*(1/3)+aux(80) s(1410) =< aux(78)*(2/3)+s(1402)*(1/3)+aux(80) s(1411) =< aux(78)*(2/3)+s(1402)*(1/3)+aux(80) s(1412) =< aux(78)*(2/3)+s(1402)*(1/3)+aux(80) s(1413) =< aux(78)*(2/3)+s(1402)*(1/3)+aux(80) s(1407) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1408) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1409) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1410) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1411) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1412) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1413) =< aux(78)*(3/5)+s(1402)*(1/5)+aux(83) s(1415) =< aux(78)*(2/7)+aux(84) s(1406) =< aux(78)*(2/7)+aux(84) s(1416) =< aux(78)*(4/11)+s(1402)*(1/11)+aux(85) s(1415) =< aux(78)*(4/11)+s(1402)*(1/11)+aux(85) s(1406) =< aux(78)*(4/11)+s(1402)*(1/11)+aux(85) s(1420) =< s(1413)*s(1417) s(1421) =< s(1410)*s(1418) s(1422) =< s(1407)*s(1419) s(1423) =< s(1406)*s(1417) s(1424) =< s(1406)*aux(77) s(1425) =< s(1424) s(1426) =< s(1423) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [70]: 72*s(1670)+6*s(1671)+6*s(1672)+6*s(1673)+6*s(1674)+12*s(1675)+6*s(1676)+12*s(1678)+36*s(1679)+72*s(1680)+6*s(1684)+6*s(1685)+6*s(1686)+108*s(1689)+936*s(1690)+48*s(1700)+4*s(1701)+4*s(1702)+4*s(1703)+4*s(1704)+8*s(1705)+4*s(1706)+320*s(1708)+24*s(1709)+48*s(1710)+4*s(1714)+4*s(1715)+4*s(1716)+72*s(1719)+624*s(1720)+420*s(1723)+12 Such that:aux(99) =< 2 aux(100) =< V1 aux(101) =< 2*V1+1 aux(102) =< V1/2 aux(103) =< V1/3 aux(104) =< 2/3*V1 aux(105) =< 2/3*V1+1/3 aux(106) =< 2/5*V1 aux(107) =< 3/7*V1 aux(108) =< 3/11*V1 aux(109) =< V2 aux(110) =< 2*V2+1 aux(111) =< V2/2 aux(112) =< V2/3 aux(113) =< 2/3*V2 aux(114) =< 2/3*V2+1/3 aux(115) =< 2/5*V2 aux(116) =< 3/7*V2 aux(117) =< 3/11*V2 s(1666) =< aux(105) s(1696) =< aux(114) s(1723) =< aux(99) s(1708) =< aux(109) s(1700) =< aux(109) s(1701) =< aux(109) s(1702) =< aux(109) s(1703) =< aux(109) s(1704) =< aux(109) s(1705) =< aux(109) s(1706) =< aux(109) s(1707) =< aux(109) s(1696) =< aux(109) s(1696) =< aux(110) s(1704) =< aux(111) s(1703) =< aux(112) s(1702) =< aux(113) s(1703) =< aux(113) s(1704) =< aux(113) s(1705) =< aux(113) s(1701) =< aux(115) s(1703) =< aux(115) s(1709) =< aux(116) s(1710) =< aux(117) s(1711) =< aux(109)-1 s(1712) =< aux(109)-2 s(1713) =< aux(109)-3 s(1702) =< aux(110)*(1/3)+aux(113) s(1703) =< aux(110)*(1/3)+aux(113) s(1704) =< aux(110)*(1/3)+aux(113) s(1705) =< aux(110)*(1/3)+aux(113) s(1706) =< aux(110)*(1/3)+aux(113) s(1707) =< aux(110)*(1/3)+aux(113) s(1704) =< aux(110)*(1/2)+aux(111) s(1705) =< aux(110)*(1/2)+aux(111) s(1706) =< aux(110)*(1/2)+aux(111) s(1707) =< aux(110)*(1/2)+aux(111) s(1703) =< aux(110)*(2/3)+s(1696)*(1/3)+aux(112) s(1704) =< aux(110)*(2/3)+s(1696)*(1/3)+aux(112) s(1705) =< aux(110)*(2/3)+s(1696)*(1/3)+aux(112) s(1706) =< aux(110)*(2/3)+s(1696)*(1/3)+aux(112) s(1707) =< aux(110)*(2/3)+s(1696)*(1/3)+aux(112) s(1701) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1702) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1703) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1704) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1705) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1706) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1707) =< aux(110)*(3/5)+s(1696)*(1/5)+aux(115) s(1709) =< aux(110)*(2/7)+aux(116) s(1700) =< aux(110)*(2/7)+aux(116) s(1710) =< aux(110)*(4/11)+s(1696)*(1/11)+aux(117) s(1709) =< aux(110)*(4/11)+s(1696)*(1/11)+aux(117) s(1700) =< aux(110)*(4/11)+s(1696)*(1/11)+aux(117) s(1714) =< s(1707)*s(1711) s(1715) =< s(1704)*s(1712) s(1716) =< s(1701)*s(1713) s(1717) =< s(1700)*s(1711) s(1718) =< s(1700)*aux(109) s(1719) =< s(1718) s(1720) =< s(1717) s(1670) =< aux(100) s(1671) =< aux(100) s(1672) =< aux(100) s(1673) =< aux(100) s(1674) =< aux(100) s(1675) =< aux(100) s(1676) =< aux(100) s(1677) =< aux(100) s(1678) =< aux(100) s(1666) =< aux(100) s(1666) =< aux(101) s(1674) =< aux(102) s(1673) =< aux(103) s(1672) =< aux(104) s(1673) =< aux(104) s(1674) =< aux(104) s(1675) =< aux(104) s(1671) =< aux(106) s(1673) =< aux(106) s(1679) =< aux(107) s(1680) =< aux(108) s(1681) =< aux(100)-1 s(1682) =< aux(100)-2 s(1683) =< aux(100)-3 s(1672) =< aux(101)*(1/3)+aux(104) s(1673) =< aux(101)*(1/3)+aux(104) s(1674) =< aux(101)*(1/3)+aux(104) s(1675) =< aux(101)*(1/3)+aux(104) s(1676) =< aux(101)*(1/3)+aux(104) s(1677) =< aux(101)*(1/3)+aux(104) s(1674) =< aux(101)*(1/2)+aux(102) s(1675) =< aux(101)*(1/2)+aux(102) s(1676) =< aux(101)*(1/2)+aux(102) s(1677) =< aux(101)*(1/2)+aux(102) s(1673) =< aux(101)*(2/3)+s(1666)*(1/3)+aux(103) s(1674) =< aux(101)*(2/3)+s(1666)*(1/3)+aux(103) s(1675) =< aux(101)*(2/3)+s(1666)*(1/3)+aux(103) s(1676) =< aux(101)*(2/3)+s(1666)*(1/3)+aux(103) s(1677) =< aux(101)*(2/3)+s(1666)*(1/3)+aux(103) s(1671) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1672) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1673) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1674) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1675) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1676) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1677) =< aux(101)*(3/5)+s(1666)*(1/5)+aux(106) s(1679) =< aux(101)*(2/7)+aux(107) s(1670) =< aux(101)*(2/7)+aux(107) s(1680) =< aux(101)*(4/11)+s(1666)*(1/11)+aux(108) s(1679) =< aux(101)*(4/11)+s(1666)*(1/11)+aux(108) s(1670) =< aux(101)*(4/11)+s(1666)*(1/11)+aux(108) s(1684) =< s(1677)*s(1681) s(1685) =< s(1674)*s(1682) s(1686) =< s(1671)*s(1683) s(1687) =< s(1670)*s(1681) s(1688) =< s(1670)*aux(100) s(1689) =< s(1688) s(1690) =< s(1687) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun1(Out): * Chain [74]: 0 with precondition: [Out=0] * Chain [73]: 0 with precondition: [Out=2] #### Cost of chains of fun2(V1,V,Out): * Chain [80]: 24*s(2153)+2*s(2154)+2*s(2155)+2*s(2156)+2*s(2157)+4*s(2158)+2*s(2159)+4*s(2161)+12*s(2162)+24*s(2163)+2*s(2167)+2*s(2168)+2*s(2169)+36*s(2172)+312*s(2173)+36*s(2183)+3*s(2184)+3*s(2185)+3*s(2186)+3*s(2187)+6*s(2188)+3*s(2189)+6*s(2191)+18*s(2192)+36*s(2193)+3*s(2197)+3*s(2198)+3*s(2199)+54*s(2202)+468*s(2203)+0 Such that:aux(137) =< V1 aux(138) =< 2*V1+1 aux(139) =< V1/2 aux(140) =< V1/3 aux(141) =< 2/3*V1 aux(142) =< 2/3*V1+1/3 aux(143) =< 2/5*V1 aux(144) =< 3/7*V1 aux(145) =< 3/11*V1 aux(146) =< V aux(147) =< 2*V+1 aux(148) =< V/2 aux(149) =< V/3 aux(150) =< 2/3*V aux(151) =< 2/3*V+1/3 aux(152) =< 2/5*V aux(153) =< 3/7*V aux(154) =< 3/11*V s(2149) =< aux(142) s(2179) =< aux(151) s(2183) =< aux(146) s(2184) =< aux(146) s(2185) =< aux(146) s(2186) =< aux(146) s(2187) =< aux(146) s(2188) =< aux(146) s(2189) =< aux(146) s(2190) =< aux(146) s(2191) =< aux(146) s(2179) =< aux(146) s(2179) =< aux(147) s(2187) =< aux(148) s(2186) =< aux(149) s(2185) =< aux(150) s(2186) =< aux(150) s(2187) =< aux(150) s(2188) =< aux(150) s(2184) =< aux(152) s(2186) =< aux(152) s(2192) =< aux(153) s(2193) =< aux(154) s(2194) =< aux(146)-1 s(2195) =< aux(146)-2 s(2196) =< aux(146)-3 s(2185) =< aux(147)*(1/3)+aux(150) s(2186) =< aux(147)*(1/3)+aux(150) s(2187) =< aux(147)*(1/3)+aux(150) s(2188) =< aux(147)*(1/3)+aux(150) s(2189) =< aux(147)*(1/3)+aux(150) s(2190) =< aux(147)*(1/3)+aux(150) s(2187) =< aux(147)*(1/2)+aux(148) s(2188) =< aux(147)*(1/2)+aux(148) s(2189) =< aux(147)*(1/2)+aux(148) s(2190) =< aux(147)*(1/2)+aux(148) s(2186) =< aux(147)*(2/3)+s(2179)*(1/3)+aux(149) s(2187) =< aux(147)*(2/3)+s(2179)*(1/3)+aux(149) s(2188) =< aux(147)*(2/3)+s(2179)*(1/3)+aux(149) s(2189) =< aux(147)*(2/3)+s(2179)*(1/3)+aux(149) s(2190) =< aux(147)*(2/3)+s(2179)*(1/3)+aux(149) s(2184) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2185) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2186) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2187) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2188) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2189) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2190) =< aux(147)*(3/5)+s(2179)*(1/5)+aux(152) s(2192) =< aux(147)*(2/7)+aux(153) s(2183) =< aux(147)*(2/7)+aux(153) s(2193) =< aux(147)*(4/11)+s(2179)*(1/11)+aux(154) s(2192) =< aux(147)*(4/11)+s(2179)*(1/11)+aux(154) s(2183) =< aux(147)*(4/11)+s(2179)*(1/11)+aux(154) s(2197) =< s(2190)*s(2194) s(2198) =< s(2187)*s(2195) s(2199) =< s(2184)*s(2196) s(2200) =< s(2183)*s(2194) s(2201) =< s(2183)*aux(146) s(2202) =< s(2201) s(2203) =< s(2200) s(2153) =< aux(137) s(2154) =< aux(137) s(2155) =< aux(137) s(2156) =< aux(137) s(2157) =< aux(137) s(2158) =< aux(137) s(2159) =< aux(137) s(2160) =< aux(137) s(2161) =< aux(137) s(2149) =< aux(137) s(2149) =< aux(138) s(2157) =< aux(139) s(2156) =< aux(140) s(2155) =< aux(141) s(2156) =< aux(141) s(2157) =< aux(141) s(2158) =< aux(141) s(2154) =< aux(143) s(2156) =< aux(143) s(2162) =< aux(144) s(2163) =< aux(145) s(2164) =< aux(137)-1 s(2165) =< aux(137)-2 s(2166) =< aux(137)-3 s(2155) =< aux(138)*(1/3)+aux(141) s(2156) =< aux(138)*(1/3)+aux(141) s(2157) =< aux(138)*(1/3)+aux(141) s(2158) =< aux(138)*(1/3)+aux(141) s(2159) =< aux(138)*(1/3)+aux(141) s(2160) =< aux(138)*(1/3)+aux(141) s(2157) =< aux(138)*(1/2)+aux(139) s(2158) =< aux(138)*(1/2)+aux(139) s(2159) =< aux(138)*(1/2)+aux(139) s(2160) =< aux(138)*(1/2)+aux(139) s(2156) =< aux(138)*(2/3)+s(2149)*(1/3)+aux(140) s(2157) =< aux(138)*(2/3)+s(2149)*(1/3)+aux(140) s(2158) =< aux(138)*(2/3)+s(2149)*(1/3)+aux(140) s(2159) =< aux(138)*(2/3)+s(2149)*(1/3)+aux(140) s(2160) =< aux(138)*(2/3)+s(2149)*(1/3)+aux(140) s(2154) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2155) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2156) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2157) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2158) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2159) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2160) =< aux(138)*(3/5)+s(2149)*(1/5)+aux(143) s(2162) =< aux(138)*(2/7)+aux(144) s(2153) =< aux(138)*(2/7)+aux(144) s(2163) =< aux(138)*(4/11)+s(2149)*(1/11)+aux(145) s(2162) =< aux(138)*(4/11)+s(2149)*(1/11)+aux(145) s(2153) =< aux(138)*(4/11)+s(2149)*(1/11)+aux(145) s(2167) =< s(2160)*s(2164) s(2168) =< s(2157)*s(2165) s(2169) =< s(2154)*s(2166) s(2170) =< s(2153)*s(2164) s(2171) =< s(2153)*aux(137) s(2172) =< s(2171) s(2173) =< s(2170) with precondition: [Out=0,V1>=0,V>=0] * Chain [79]: 12*s(2303)+1*s(2304)+1*s(2305)+1*s(2306)+1*s(2307)+2*s(2308)+1*s(2309)+2*s(2311)+6*s(2312)+12*s(2313)+1*s(2317)+1*s(2318)+1*s(2319)+18*s(2322)+156*s(2323)+24*s(2333)+2*s(2334)+2*s(2335)+2*s(2336)+2*s(2337)+4*s(2338)+2*s(2339)+4*s(2341)+12*s(2342)+24*s(2343)+2*s(2347)+2*s(2348)+2*s(2349)+36*s(2352)+312*s(2353)+1 Such that:s(2294) =< V1 s(2295) =< 2*V1+1 s(2296) =< V1/2 s(2297) =< V1/3 s(2298) =< 2/3*V1 s(2299) =< 2/3*V1+1/3 s(2300) =< 2/5*V1 s(2301) =< 3/7*V1 s(2302) =< 3/11*V1 aux(155) =< V aux(156) =< 2*V+1 aux(157) =< V/2 aux(158) =< V/3 aux(159) =< 2/3*V aux(160) =< 2/3*V+1/3 aux(161) =< 2/5*V aux(162) =< 3/7*V aux(163) =< 3/11*V s(2329) =< aux(160) s(2333) =< aux(155) s(2334) =< aux(155) s(2335) =< aux(155) s(2336) =< aux(155) s(2337) =< aux(155) s(2338) =< aux(155) s(2339) =< aux(155) s(2340) =< aux(155) s(2341) =< aux(155) s(2329) =< aux(155) s(2329) =< aux(156) s(2337) =< aux(157) s(2336) =< aux(158) s(2335) =< aux(159) s(2336) =< aux(159) s(2337) =< aux(159) s(2338) =< aux(159) s(2334) =< aux(161) s(2336) =< aux(161) s(2342) =< aux(162) s(2343) =< aux(163) s(2344) =< aux(155)-1 s(2345) =< aux(155)-2 s(2346) =< aux(155)-3 s(2335) =< aux(156)*(1/3)+aux(159) s(2336) =< aux(156)*(1/3)+aux(159) s(2337) =< aux(156)*(1/3)+aux(159) s(2338) =< aux(156)*(1/3)+aux(159) s(2339) =< aux(156)*(1/3)+aux(159) s(2340) =< aux(156)*(1/3)+aux(159) s(2337) =< aux(156)*(1/2)+aux(157) s(2338) =< aux(156)*(1/2)+aux(157) s(2339) =< aux(156)*(1/2)+aux(157) s(2340) =< aux(156)*(1/2)+aux(157) s(2336) =< aux(156)*(2/3)+s(2329)*(1/3)+aux(158) s(2337) =< aux(156)*(2/3)+s(2329)*(1/3)+aux(158) s(2338) =< aux(156)*(2/3)+s(2329)*(1/3)+aux(158) s(2339) =< aux(156)*(2/3)+s(2329)*(1/3)+aux(158) s(2340) =< aux(156)*(2/3)+s(2329)*(1/3)+aux(158) s(2334) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2335) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2336) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2337) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2338) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2339) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2340) =< aux(156)*(3/5)+s(2329)*(1/5)+aux(161) s(2342) =< aux(156)*(2/7)+aux(162) s(2333) =< aux(156)*(2/7)+aux(162) s(2343) =< aux(156)*(4/11)+s(2329)*(1/11)+aux(163) s(2342) =< aux(156)*(4/11)+s(2329)*(1/11)+aux(163) s(2333) =< aux(156)*(4/11)+s(2329)*(1/11)+aux(163) s(2347) =< s(2340)*s(2344) s(2348) =< s(2337)*s(2345) s(2349) =< s(2334)*s(2346) s(2350) =< s(2333)*s(2344) s(2351) =< s(2333)*aux(155) s(2352) =< s(2351) s(2353) =< s(2350) s(2303) =< s(2294) s(2304) =< s(2294) s(2305) =< s(2294) s(2306) =< s(2294) s(2307) =< s(2294) s(2308) =< s(2294) s(2309) =< s(2294) s(2310) =< s(2294) s(2311) =< s(2294) s(2299) =< s(2294) s(2299) =< s(2295) s(2307) =< s(2296) s(2306) =< s(2297) s(2305) =< s(2298) s(2306) =< s(2298) s(2307) =< s(2298) s(2308) =< s(2298) s(2304) =< s(2300) s(2306) =< s(2300) s(2312) =< s(2301) s(2313) =< s(2302) s(2314) =< s(2294)-1 s(2315) =< s(2294)-2 s(2316) =< s(2294)-3 s(2305) =< s(2295)*(1/3)+s(2298) s(2306) =< s(2295)*(1/3)+s(2298) s(2307) =< s(2295)*(1/3)+s(2298) s(2308) =< s(2295)*(1/3)+s(2298) s(2309) =< s(2295)*(1/3)+s(2298) s(2310) =< s(2295)*(1/3)+s(2298) s(2307) =< s(2295)*(1/2)+s(2296) s(2308) =< s(2295)*(1/2)+s(2296) s(2309) =< s(2295)*(1/2)+s(2296) s(2310) =< s(2295)*(1/2)+s(2296) s(2306) =< s(2295)*(2/3)+s(2299)*(1/3)+s(2297) s(2307) =< s(2295)*(2/3)+s(2299)*(1/3)+s(2297) s(2308) =< s(2295)*(2/3)+s(2299)*(1/3)+s(2297) s(2309) =< s(2295)*(2/3)+s(2299)*(1/3)+s(2297) s(2310) =< s(2295)*(2/3)+s(2299)*(1/3)+s(2297) s(2304) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2305) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2306) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2307) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2308) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2309) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2310) =< s(2295)*(3/5)+s(2299)*(1/5)+s(2300) s(2312) =< s(2295)*(2/7)+s(2301) s(2303) =< s(2295)*(2/7)+s(2301) s(2313) =< s(2295)*(4/11)+s(2299)*(1/11)+s(2302) s(2312) =< s(2295)*(4/11)+s(2299)*(1/11)+s(2302) s(2303) =< s(2295)*(4/11)+s(2299)*(1/11)+s(2302) s(2317) =< s(2310)*s(2314) s(2318) =< s(2307)*s(2315) s(2319) =< s(2304)*s(2316) s(2320) =< s(2303)*s(2314) s(2321) =< s(2303)*s(2294) s(2322) =< s(2321) s(2323) =< s(2320) with precondition: [Out=2,V1>=2,V>=2] * Chain [78]: 24*s(2393)+2*s(2394)+2*s(2395)+2*s(2396)+2*s(2397)+4*s(2398)+2*s(2399)+4*s(2401)+12*s(2402)+24*s(2403)+2*s(2407)+2*s(2408)+2*s(2409)+36*s(2412)+312*s(2413)+48*s(2423)+4*s(2424)+4*s(2425)+4*s(2426)+4*s(2427)+8*s(2428)+4*s(2429)+8*s(2431)+24*s(2432)+48*s(2433)+4*s(2437)+4*s(2438)+4*s(2439)+72*s(2442)+624*s(2443)+1 Such that:aux(164) =< V1 aux(165) =< 2*V1+1 aux(166) =< V1/2 aux(167) =< V1/3 aux(168) =< 2/3*V1 aux(169) =< 2/3*V1+1/3 aux(170) =< 2/5*V1 aux(171) =< 3/7*V1 aux(172) =< 3/11*V1 aux(173) =< V aux(174) =< 2*V+1 aux(175) =< V/2 aux(176) =< V/3 aux(177) =< 2/3*V aux(178) =< 2/3*V+1/3 aux(179) =< 2/5*V aux(180) =< 3/7*V aux(181) =< 3/11*V s(2389) =< aux(169) s(2419) =< aux(178) s(2423) =< aux(173) s(2424) =< aux(173) s(2425) =< aux(173) s(2426) =< aux(173) s(2427) =< aux(173) s(2428) =< aux(173) s(2429) =< aux(173) s(2430) =< aux(173) s(2431) =< aux(173) s(2419) =< aux(173) s(2419) =< aux(174) s(2427) =< aux(175) s(2426) =< aux(176) s(2425) =< aux(177) s(2426) =< aux(177) s(2427) =< aux(177) s(2428) =< aux(177) s(2424) =< aux(179) s(2426) =< aux(179) s(2432) =< aux(180) s(2433) =< aux(181) s(2434) =< aux(173)-1 s(2435) =< aux(173)-2 s(2436) =< aux(173)-3 s(2425) =< aux(174)*(1/3)+aux(177) s(2426) =< aux(174)*(1/3)+aux(177) s(2427) =< aux(174)*(1/3)+aux(177) s(2428) =< aux(174)*(1/3)+aux(177) s(2429) =< aux(174)*(1/3)+aux(177) s(2430) =< aux(174)*(1/3)+aux(177) s(2427) =< aux(174)*(1/2)+aux(175) s(2428) =< aux(174)*(1/2)+aux(175) s(2429) =< aux(174)*(1/2)+aux(175) s(2430) =< aux(174)*(1/2)+aux(175) s(2426) =< aux(174)*(2/3)+s(2419)*(1/3)+aux(176) s(2427) =< aux(174)*(2/3)+s(2419)*(1/3)+aux(176) s(2428) =< aux(174)*(2/3)+s(2419)*(1/3)+aux(176) s(2429) =< aux(174)*(2/3)+s(2419)*(1/3)+aux(176) s(2430) =< aux(174)*(2/3)+s(2419)*(1/3)+aux(176) s(2424) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2425) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2426) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2427) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2428) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2429) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2430) =< aux(174)*(3/5)+s(2419)*(1/5)+aux(179) s(2432) =< aux(174)*(2/7)+aux(180) s(2423) =< aux(174)*(2/7)+aux(180) s(2433) =< aux(174)*(4/11)+s(2419)*(1/11)+aux(181) s(2432) =< aux(174)*(4/11)+s(2419)*(1/11)+aux(181) s(2423) =< aux(174)*(4/11)+s(2419)*(1/11)+aux(181) s(2437) =< s(2430)*s(2434) s(2438) =< s(2427)*s(2435) s(2439) =< s(2424)*s(2436) s(2440) =< s(2423)*s(2434) s(2441) =< s(2423)*aux(173) s(2442) =< s(2441) s(2443) =< s(2440) s(2393) =< aux(164) s(2394) =< aux(164) s(2395) =< aux(164) s(2396) =< aux(164) s(2397) =< aux(164) s(2398) =< aux(164) s(2399) =< aux(164) s(2400) =< aux(164) s(2401) =< aux(164) s(2389) =< aux(164) s(2389) =< aux(165) s(2397) =< aux(166) s(2396) =< aux(167) s(2395) =< aux(168) s(2396) =< aux(168) s(2397) =< aux(168) s(2398) =< aux(168) s(2394) =< aux(170) s(2396) =< aux(170) s(2402) =< aux(171) s(2403) =< aux(172) s(2404) =< aux(164)-1 s(2405) =< aux(164)-2 s(2406) =< aux(164)-3 s(2395) =< aux(165)*(1/3)+aux(168) s(2396) =< aux(165)*(1/3)+aux(168) s(2397) =< aux(165)*(1/3)+aux(168) s(2398) =< aux(165)*(1/3)+aux(168) s(2399) =< aux(165)*(1/3)+aux(168) s(2400) =< aux(165)*(1/3)+aux(168) s(2397) =< aux(165)*(1/2)+aux(166) s(2398) =< aux(165)*(1/2)+aux(166) s(2399) =< aux(165)*(1/2)+aux(166) s(2400) =< aux(165)*(1/2)+aux(166) s(2396) =< aux(165)*(2/3)+s(2389)*(1/3)+aux(167) s(2397) =< aux(165)*(2/3)+s(2389)*(1/3)+aux(167) s(2398) =< aux(165)*(2/3)+s(2389)*(1/3)+aux(167) s(2399) =< aux(165)*(2/3)+s(2389)*(1/3)+aux(167) s(2400) =< aux(165)*(2/3)+s(2389)*(1/3)+aux(167) s(2394) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2395) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2396) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2397) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2398) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2399) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2400) =< aux(165)*(3/5)+s(2389)*(1/5)+aux(170) s(2402) =< aux(165)*(2/7)+aux(171) s(2393) =< aux(165)*(2/7)+aux(171) s(2403) =< aux(165)*(4/11)+s(2389)*(1/11)+aux(172) s(2402) =< aux(165)*(4/11)+s(2389)*(1/11)+aux(172) s(2393) =< aux(165)*(4/11)+s(2389)*(1/11)+aux(172) s(2407) =< s(2400)*s(2404) s(2408) =< s(2397)*s(2405) s(2409) =< s(2394)*s(2406) s(2410) =< s(2393)*s(2404) s(2411) =< s(2393)*aux(164) s(2412) =< s(2411) s(2413) =< s(2410) with precondition: [Out=1,V1>=0,V>=1] * Chain [77]: 12*s(2573)+1*s(2574)+1*s(2575)+1*s(2576)+1*s(2577)+2*s(2578)+1*s(2579)+2*s(2581)+6*s(2582)+12*s(2583)+1*s(2587)+1*s(2588)+1*s(2589)+18*s(2592)+156*s(2593)+0 Such that:s(2564) =< V1 s(2565) =< 2*V1+1 s(2566) =< V1/2 s(2567) =< V1/3 s(2568) =< 2/3*V1 s(2569) =< 2/3*V1+1/3 s(2570) =< 2/5*V1 s(2571) =< 3/7*V1 s(2572) =< 3/11*V1 s(2573) =< s(2564) s(2574) =< s(2564) s(2575) =< s(2564) s(2576) =< s(2564) s(2577) =< s(2564) s(2578) =< s(2564) s(2579) =< s(2564) s(2580) =< s(2564) s(2581) =< s(2564) s(2569) =< s(2564) s(2569) =< s(2565) s(2577) =< s(2566) s(2576) =< s(2567) s(2575) =< s(2568) s(2576) =< s(2568) s(2577) =< s(2568) s(2578) =< s(2568) s(2574) =< s(2570) s(2576) =< s(2570) s(2582) =< s(2571) s(2583) =< s(2572) s(2584) =< s(2564)-1 s(2585) =< s(2564)-2 s(2586) =< s(2564)-3 s(2575) =< s(2565)*(1/3)+s(2568) s(2576) =< s(2565)*(1/3)+s(2568) s(2577) =< s(2565)*(1/3)+s(2568) s(2578) =< s(2565)*(1/3)+s(2568) s(2579) =< s(2565)*(1/3)+s(2568) s(2580) =< s(2565)*(1/3)+s(2568) s(2577) =< s(2565)*(1/2)+s(2566) s(2578) =< s(2565)*(1/2)+s(2566) s(2579) =< s(2565)*(1/2)+s(2566) s(2580) =< s(2565)*(1/2)+s(2566) s(2576) =< s(2565)*(2/3)+s(2569)*(1/3)+s(2567) s(2577) =< s(2565)*(2/3)+s(2569)*(1/3)+s(2567) s(2578) =< s(2565)*(2/3)+s(2569)*(1/3)+s(2567) s(2579) =< s(2565)*(2/3)+s(2569)*(1/3)+s(2567) s(2580) =< s(2565)*(2/3)+s(2569)*(1/3)+s(2567) s(2574) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2575) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2576) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2577) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2578) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2579) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2580) =< s(2565)*(3/5)+s(2569)*(1/5)+s(2570) s(2582) =< s(2565)*(2/7)+s(2571) s(2573) =< s(2565)*(2/7)+s(2571) s(2583) =< s(2565)*(4/11)+s(2569)*(1/11)+s(2572) s(2582) =< s(2565)*(4/11)+s(2569)*(1/11)+s(2572) s(2573) =< s(2565)*(4/11)+s(2569)*(1/11)+s(2572) s(2587) =< s(2580)*s(2584) s(2588) =< s(2577)*s(2585) s(2589) =< s(2574)*s(2586) s(2590) =< s(2573)*s(2584) s(2591) =< s(2573)*s(2564) s(2592) =< s(2591) s(2593) =< s(2590) with precondition: [V=2,Out=0,V1>=0] * Chain [76]: 24*s(2603)+2*s(2604)+2*s(2605)+2*s(2606)+2*s(2607)+4*s(2608)+2*s(2609)+4*s(2611)+12*s(2612)+24*s(2613)+2*s(2617)+2*s(2618)+2*s(2619)+36*s(2622)+312*s(2623)+1 Such that:aux(182) =< V1 aux(183) =< 2*V1+1 aux(184) =< V1/2 aux(185) =< V1/3 aux(186) =< 2/3*V1 aux(187) =< 2/3*V1+1/3 aux(188) =< 2/5*V1 aux(189) =< 3/7*V1 aux(190) =< 3/11*V1 s(2599) =< aux(187) s(2603) =< aux(182) s(2604) =< aux(182) s(2605) =< aux(182) s(2606) =< aux(182) s(2607) =< aux(182) s(2608) =< aux(182) s(2609) =< aux(182) s(2610) =< aux(182) s(2611) =< aux(182) s(2599) =< aux(182) s(2599) =< aux(183) s(2607) =< aux(184) s(2606) =< aux(185) s(2605) =< aux(186) s(2606) =< aux(186) s(2607) =< aux(186) s(2608) =< aux(186) s(2604) =< aux(188) s(2606) =< aux(188) s(2612) =< aux(189) s(2613) =< aux(190) s(2614) =< aux(182)-1 s(2615) =< aux(182)-2 s(2616) =< aux(182)-3 s(2605) =< aux(183)*(1/3)+aux(186) s(2606) =< aux(183)*(1/3)+aux(186) s(2607) =< aux(183)*(1/3)+aux(186) s(2608) =< aux(183)*(1/3)+aux(186) s(2609) =< aux(183)*(1/3)+aux(186) s(2610) =< aux(183)*(1/3)+aux(186) s(2607) =< aux(183)*(1/2)+aux(184) s(2608) =< aux(183)*(1/2)+aux(184) s(2609) =< aux(183)*(1/2)+aux(184) s(2610) =< aux(183)*(1/2)+aux(184) s(2606) =< aux(183)*(2/3)+s(2599)*(1/3)+aux(185) s(2607) =< aux(183)*(2/3)+s(2599)*(1/3)+aux(185) s(2608) =< aux(183)*(2/3)+s(2599)*(1/3)+aux(185) s(2609) =< aux(183)*(2/3)+s(2599)*(1/3)+aux(185) s(2610) =< aux(183)*(2/3)+s(2599)*(1/3)+aux(185) s(2604) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2605) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2606) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2607) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2608) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2609) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2610) =< aux(183)*(3/5)+s(2599)*(1/5)+aux(188) s(2612) =< aux(183)*(2/7)+aux(189) s(2603) =< aux(183)*(2/7)+aux(189) s(2613) =< aux(183)*(4/11)+s(2599)*(1/11)+aux(190) s(2612) =< aux(183)*(4/11)+s(2599)*(1/11)+aux(190) s(2603) =< aux(183)*(4/11)+s(2599)*(1/11)+aux(190) s(2617) =< s(2610)*s(2614) s(2618) =< s(2607)*s(2615) s(2619) =< s(2604)*s(2616) s(2620) =< s(2603)*s(2614) s(2621) =< s(2603)*aux(182) s(2622) =< s(2621) s(2623) =< s(2620) with precondition: [Out=1,V1>=1,V>=0] * Chain [75]: 12*s(2663)+1*s(2664)+1*s(2665)+1*s(2666)+1*s(2667)+2*s(2668)+1*s(2669)+2*s(2671)+6*s(2672)+12*s(2673)+1*s(2677)+1*s(2678)+1*s(2679)+18*s(2682)+156*s(2683)+1 Such that:s(2654) =< V1 s(2655) =< 2*V1+1 s(2656) =< V1/2 s(2657) =< V1/3 s(2658) =< 2/3*V1 s(2659) =< 2/3*V1+1/3 s(2660) =< 2/5*V1 s(2661) =< 3/7*V1 s(2662) =< 3/11*V1 s(2663) =< s(2654) s(2664) =< s(2654) s(2665) =< s(2654) s(2666) =< s(2654) s(2667) =< s(2654) s(2668) =< s(2654) s(2669) =< s(2654) s(2670) =< s(2654) s(2671) =< s(2654) s(2659) =< s(2654) s(2659) =< s(2655) s(2667) =< s(2656) s(2666) =< s(2657) s(2665) =< s(2658) s(2666) =< s(2658) s(2667) =< s(2658) s(2668) =< s(2658) s(2664) =< s(2660) s(2666) =< s(2660) s(2672) =< s(2661) s(2673) =< s(2662) s(2674) =< s(2654)-1 s(2675) =< s(2654)-2 s(2676) =< s(2654)-3 s(2665) =< s(2655)*(1/3)+s(2658) s(2666) =< s(2655)*(1/3)+s(2658) s(2667) =< s(2655)*(1/3)+s(2658) s(2668) =< s(2655)*(1/3)+s(2658) s(2669) =< s(2655)*(1/3)+s(2658) s(2670) =< s(2655)*(1/3)+s(2658) s(2667) =< s(2655)*(1/2)+s(2656) s(2668) =< s(2655)*(1/2)+s(2656) s(2669) =< s(2655)*(1/2)+s(2656) s(2670) =< s(2655)*(1/2)+s(2656) s(2666) =< s(2655)*(2/3)+s(2659)*(1/3)+s(2657) s(2667) =< s(2655)*(2/3)+s(2659)*(1/3)+s(2657) s(2668) =< s(2655)*(2/3)+s(2659)*(1/3)+s(2657) s(2669) =< s(2655)*(2/3)+s(2659)*(1/3)+s(2657) s(2670) =< s(2655)*(2/3)+s(2659)*(1/3)+s(2657) s(2664) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2665) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2666) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2667) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2668) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2669) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2670) =< s(2655)*(3/5)+s(2659)*(1/5)+s(2660) s(2672) =< s(2655)*(2/7)+s(2661) s(2663) =< s(2655)*(2/7)+s(2661) s(2673) =< s(2655)*(4/11)+s(2659)*(1/11)+s(2662) s(2672) =< s(2655)*(4/11)+s(2659)*(1/11)+s(2662) s(2663) =< s(2655)*(4/11)+s(2659)*(1/11)+s(2662) s(2677) =< s(2670)*s(2674) s(2678) =< s(2667)*s(2675) s(2679) =< s(2664)*s(2676) s(2680) =< s(2663)*s(2674) s(2681) =< s(2663)*s(2654) s(2682) =< s(2681) s(2683) =< s(2680) with precondition: [V=2,Out=2,V1>=2] #### Cost of chains of fun3(V1,V,Out): * Chain [86]: 24*s(2876)+2*s(2877)+2*s(2878)+2*s(2879)+2*s(2880)+4*s(2881)+2*s(2882)+4*s(2884)+12*s(2885)+24*s(2886)+2*s(2890)+2*s(2891)+2*s(2892)+36*s(2895)+312*s(2896)+36*s(2906)+3*s(2907)+3*s(2908)+3*s(2909)+3*s(2910)+6*s(2911)+3*s(2912)+9*s(2914)+18*s(2915)+36*s(2916)+3*s(2920)+3*s(2921)+3*s(2922)+54*s(2925)+468*s(2926)+1*s(2990)+0 Such that:s(2990) =< 2 aux(212) =< V1 aux(213) =< 2*V1+1 aux(214) =< V1/2 aux(215) =< V1/3 aux(216) =< 2/3*V1 aux(217) =< 2/3*V1+1/3 aux(218) =< 2/5*V1 aux(219) =< 3/7*V1 aux(220) =< 3/11*V1 aux(221) =< V aux(222) =< 2*V+1 aux(223) =< V/2 aux(224) =< V/3 aux(225) =< 2/3*V aux(226) =< 2/3*V+1/3 aux(227) =< 2/5*V aux(228) =< 3/7*V aux(229) =< 3/11*V s(2872) =< aux(217) s(2902) =< aux(226) s(2914) =< aux(221) s(2906) =< aux(221) s(2907) =< aux(221) s(2908) =< aux(221) s(2909) =< aux(221) s(2910) =< aux(221) s(2911) =< aux(221) s(2912) =< aux(221) s(2913) =< aux(221) s(2902) =< aux(221) s(2902) =< aux(222) s(2910) =< aux(223) s(2909) =< aux(224) s(2908) =< aux(225) s(2909) =< aux(225) s(2910) =< aux(225) s(2911) =< aux(225) s(2907) =< aux(227) s(2909) =< aux(227) s(2915) =< aux(228) s(2916) =< aux(229) s(2917) =< aux(221)-1 s(2918) =< aux(221)-2 s(2919) =< aux(221)-3 s(2908) =< aux(222)*(1/3)+aux(225) s(2909) =< aux(222)*(1/3)+aux(225) s(2910) =< aux(222)*(1/3)+aux(225) s(2911) =< aux(222)*(1/3)+aux(225) s(2912) =< aux(222)*(1/3)+aux(225) s(2913) =< aux(222)*(1/3)+aux(225) s(2910) =< aux(222)*(1/2)+aux(223) s(2911) =< aux(222)*(1/2)+aux(223) s(2912) =< aux(222)*(1/2)+aux(223) s(2913) =< aux(222)*(1/2)+aux(223) s(2909) =< aux(222)*(2/3)+s(2902)*(1/3)+aux(224) s(2910) =< aux(222)*(2/3)+s(2902)*(1/3)+aux(224) s(2911) =< aux(222)*(2/3)+s(2902)*(1/3)+aux(224) s(2912) =< aux(222)*(2/3)+s(2902)*(1/3)+aux(224) s(2913) =< aux(222)*(2/3)+s(2902)*(1/3)+aux(224) s(2907) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2908) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2909) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2910) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2911) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2912) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2913) =< aux(222)*(3/5)+s(2902)*(1/5)+aux(227) s(2915) =< aux(222)*(2/7)+aux(228) s(2906) =< aux(222)*(2/7)+aux(228) s(2916) =< aux(222)*(4/11)+s(2902)*(1/11)+aux(229) s(2915) =< aux(222)*(4/11)+s(2902)*(1/11)+aux(229) s(2906) =< aux(222)*(4/11)+s(2902)*(1/11)+aux(229) s(2920) =< s(2913)*s(2917) s(2921) =< s(2910)*s(2918) s(2922) =< s(2907)*s(2919) s(2923) =< s(2906)*s(2917) s(2924) =< s(2906)*aux(221) s(2925) =< s(2924) s(2926) =< s(2923) s(2876) =< aux(212) s(2877) =< aux(212) s(2878) =< aux(212) s(2879) =< aux(212) s(2880) =< aux(212) s(2881) =< aux(212) s(2882) =< aux(212) s(2883) =< aux(212) s(2884) =< aux(212) s(2872) =< aux(212) s(2872) =< aux(213) s(2880) =< aux(214) s(2879) =< aux(215) s(2878) =< aux(216) s(2879) =< aux(216) s(2880) =< aux(216) s(2881) =< aux(216) s(2877) =< aux(218) s(2879) =< aux(218) s(2885) =< aux(219) s(2886) =< aux(220) s(2887) =< aux(212)-1 s(2888) =< aux(212)-2 s(2889) =< aux(212)-3 s(2878) =< aux(213)*(1/3)+aux(216) s(2879) =< aux(213)*(1/3)+aux(216) s(2880) =< aux(213)*(1/3)+aux(216) s(2881) =< aux(213)*(1/3)+aux(216) s(2882) =< aux(213)*(1/3)+aux(216) s(2883) =< aux(213)*(1/3)+aux(216) s(2880) =< aux(213)*(1/2)+aux(214) s(2881) =< aux(213)*(1/2)+aux(214) s(2882) =< aux(213)*(1/2)+aux(214) s(2883) =< aux(213)*(1/2)+aux(214) s(2879) =< aux(213)*(2/3)+s(2872)*(1/3)+aux(215) s(2880) =< aux(213)*(2/3)+s(2872)*(1/3)+aux(215) s(2881) =< aux(213)*(2/3)+s(2872)*(1/3)+aux(215) s(2882) =< aux(213)*(2/3)+s(2872)*(1/3)+aux(215) s(2883) =< aux(213)*(2/3)+s(2872)*(1/3)+aux(215) s(2877) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2878) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2879) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2880) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2881) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2882) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2883) =< aux(213)*(3/5)+s(2872)*(1/5)+aux(218) s(2885) =< aux(213)*(2/7)+aux(219) s(2876) =< aux(213)*(2/7)+aux(219) s(2886) =< aux(213)*(4/11)+s(2872)*(1/11)+aux(220) s(2885) =< aux(213)*(4/11)+s(2872)*(1/11)+aux(220) s(2876) =< aux(213)*(4/11)+s(2872)*(1/11)+aux(220) s(2890) =< s(2883)*s(2887) s(2891) =< s(2880)*s(2888) s(2892) =< s(2877)*s(2889) s(2893) =< s(2876)*s(2887) s(2894) =< s(2876)*aux(212) s(2895) =< s(2894) s(2896) =< s(2893) with precondition: [Out=0,V1>=0,V>=0] * Chain [85]: 36*s(3033)+3*s(3034)+3*s(3035)+3*s(3036)+3*s(3037)+6*s(3038)+3*s(3039)+6*s(3041)+18*s(3042)+36*s(3043)+3*s(3047)+3*s(3048)+3*s(3049)+54*s(3052)+468*s(3053)+48*s(3063)+4*s(3064)+4*s(3065)+4*s(3066)+4*s(3067)+8*s(3068)+4*s(3069)+9*s(3071)+24*s(3072)+48*s(3073)+4*s(3077)+4*s(3078)+4*s(3079)+72*s(3082)+624*s(3083)+2*s(3205)+1 Such that:aux(231) =< 2 aux(232) =< V1 aux(233) =< 2*V1+1 aux(234) =< V1/2 aux(235) =< V1/3 aux(236) =< 2/3*V1 aux(237) =< 2/3*V1+1/3 aux(238) =< 2/5*V1 aux(239) =< 3/7*V1 aux(240) =< 3/11*V1 aux(241) =< V aux(242) =< 2*V+1 aux(243) =< V/2 aux(244) =< V/3 aux(245) =< 2/3*V aux(246) =< 2/3*V+1/3 aux(247) =< 2/5*V aux(248) =< 3/7*V aux(249) =< 3/11*V s(3205) =< aux(231) s(3029) =< aux(237) s(3059) =< aux(246) s(3063) =< aux(241) s(3064) =< aux(241) s(3065) =< aux(241) s(3066) =< aux(241) s(3067) =< aux(241) s(3068) =< aux(241) s(3069) =< aux(241) s(3070) =< aux(241) s(3071) =< aux(241) s(3059) =< aux(241) s(3059) =< aux(242) s(3067) =< aux(243) s(3066) =< aux(244) s(3065) =< aux(245) s(3066) =< aux(245) s(3067) =< aux(245) s(3068) =< aux(245) s(3064) =< aux(247) s(3066) =< aux(247) s(3072) =< aux(248) s(3073) =< aux(249) s(3074) =< aux(241)-1 s(3075) =< aux(241)-2 s(3076) =< aux(241)-3 s(3065) =< aux(242)*(1/3)+aux(245) s(3066) =< aux(242)*(1/3)+aux(245) s(3067) =< aux(242)*(1/3)+aux(245) s(3068) =< aux(242)*(1/3)+aux(245) s(3069) =< aux(242)*(1/3)+aux(245) s(3070) =< aux(242)*(1/3)+aux(245) s(3067) =< aux(242)*(1/2)+aux(243) s(3068) =< aux(242)*(1/2)+aux(243) s(3069) =< aux(242)*(1/2)+aux(243) s(3070) =< aux(242)*(1/2)+aux(243) s(3066) =< aux(242)*(2/3)+s(3059)*(1/3)+aux(244) s(3067) =< aux(242)*(2/3)+s(3059)*(1/3)+aux(244) s(3068) =< aux(242)*(2/3)+s(3059)*(1/3)+aux(244) s(3069) =< aux(242)*(2/3)+s(3059)*(1/3)+aux(244) s(3070) =< aux(242)*(2/3)+s(3059)*(1/3)+aux(244) s(3064) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3065) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3066) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3067) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3068) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3069) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3070) =< aux(242)*(3/5)+s(3059)*(1/5)+aux(247) s(3072) =< aux(242)*(2/7)+aux(248) s(3063) =< aux(242)*(2/7)+aux(248) s(3073) =< aux(242)*(4/11)+s(3059)*(1/11)+aux(249) s(3072) =< aux(242)*(4/11)+s(3059)*(1/11)+aux(249) s(3063) =< aux(242)*(4/11)+s(3059)*(1/11)+aux(249) s(3077) =< s(3070)*s(3074) s(3078) =< s(3067)*s(3075) s(3079) =< s(3064)*s(3076) s(3080) =< s(3063)*s(3074) s(3081) =< s(3063)*aux(241) s(3082) =< s(3081) s(3083) =< s(3080) s(3033) =< aux(232) s(3034) =< aux(232) s(3035) =< aux(232) s(3036) =< aux(232) s(3037) =< aux(232) s(3038) =< aux(232) s(3039) =< aux(232) s(3040) =< aux(232) s(3041) =< aux(232) s(3029) =< aux(232) s(3029) =< aux(233) s(3037) =< aux(234) s(3036) =< aux(235) s(3035) =< aux(236) s(3036) =< aux(236) s(3037) =< aux(236) s(3038) =< aux(236) s(3034) =< aux(238) s(3036) =< aux(238) s(3042) =< aux(239) s(3043) =< aux(240) s(3044) =< aux(232)-1 s(3045) =< aux(232)-2 s(3046) =< aux(232)-3 s(3035) =< aux(233)*(1/3)+aux(236) s(3036) =< aux(233)*(1/3)+aux(236) s(3037) =< aux(233)*(1/3)+aux(236) s(3038) =< aux(233)*(1/3)+aux(236) s(3039) =< aux(233)*(1/3)+aux(236) s(3040) =< aux(233)*(1/3)+aux(236) s(3037) =< aux(233)*(1/2)+aux(234) s(3038) =< aux(233)*(1/2)+aux(234) s(3039) =< aux(233)*(1/2)+aux(234) s(3040) =< aux(233)*(1/2)+aux(234) s(3036) =< aux(233)*(2/3)+s(3029)*(1/3)+aux(235) s(3037) =< aux(233)*(2/3)+s(3029)*(1/3)+aux(235) s(3038) =< aux(233)*(2/3)+s(3029)*(1/3)+aux(235) s(3039) =< aux(233)*(2/3)+s(3029)*(1/3)+aux(235) s(3040) =< aux(233)*(2/3)+s(3029)*(1/3)+aux(235) s(3034) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3035) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3036) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3037) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3038) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3039) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3040) =< aux(233)*(3/5)+s(3029)*(1/5)+aux(238) s(3042) =< aux(233)*(2/7)+aux(239) s(3033) =< aux(233)*(2/7)+aux(239) s(3043) =< aux(233)*(4/11)+s(3029)*(1/11)+aux(240) s(3042) =< aux(233)*(4/11)+s(3029)*(1/11)+aux(240) s(3033) =< aux(233)*(4/11)+s(3029)*(1/11)+aux(240) s(3047) =< s(3040)*s(3044) s(3048) =< s(3037)*s(3045) s(3049) =< s(3034)*s(3046) s(3050) =< s(3033)*s(3044) s(3051) =< s(3033)*aux(232) s(3052) =< s(3051) s(3053) =< s(3050) with precondition: [Out=1,V1>=0,V>=0] * Chain [84]: 36*s(3246)+3*s(3247)+3*s(3248)+3*s(3249)+3*s(3250)+6*s(3251)+3*s(3252)+6*s(3254)+18*s(3255)+36*s(3256)+3*s(3260)+3*s(3261)+3*s(3262)+54*s(3265)+468*s(3266)+48*s(3276)+4*s(3277)+4*s(3278)+4*s(3279)+4*s(3280)+8*s(3281)+4*s(3282)+9*s(3284)+24*s(3285)+48*s(3286)+4*s(3290)+4*s(3291)+4*s(3292)+72*s(3295)+624*s(3296)+1*s(3448)+1 Such that:s(3448) =< 1 aux(251) =< V1 aux(252) =< 2*V1+1 aux(253) =< V1/2 aux(254) =< V1/3 aux(255) =< 2/3*V1 aux(256) =< 2/3*V1+1/3 aux(257) =< 2/5*V1 aux(258) =< 3/7*V1 aux(259) =< 3/11*V1 aux(260) =< V aux(261) =< 2*V+1 aux(262) =< V/2 aux(263) =< V/3 aux(264) =< 2/3*V aux(265) =< 2/3*V+1/3 aux(266) =< 2/5*V aux(267) =< 3/7*V aux(268) =< 3/11*V s(3242) =< aux(256) s(3272) =< aux(265) s(3276) =< aux(260) s(3277) =< aux(260) s(3278) =< aux(260) s(3279) =< aux(260) s(3280) =< aux(260) s(3281) =< aux(260) s(3282) =< aux(260) s(3283) =< aux(260) s(3284) =< aux(260) s(3272) =< aux(260) s(3272) =< aux(261) s(3280) =< aux(262) s(3279) =< aux(263) s(3278) =< aux(264) s(3279) =< aux(264) s(3280) =< aux(264) s(3281) =< aux(264) s(3277) =< aux(266) s(3279) =< aux(266) s(3285) =< aux(267) s(3286) =< aux(268) s(3287) =< aux(260)-1 s(3288) =< aux(260)-2 s(3289) =< aux(260)-3 s(3278) =< aux(261)*(1/3)+aux(264) s(3279) =< aux(261)*(1/3)+aux(264) s(3280) =< aux(261)*(1/3)+aux(264) s(3281) =< aux(261)*(1/3)+aux(264) s(3282) =< aux(261)*(1/3)+aux(264) s(3283) =< aux(261)*(1/3)+aux(264) s(3280) =< aux(261)*(1/2)+aux(262) s(3281) =< aux(261)*(1/2)+aux(262) s(3282) =< aux(261)*(1/2)+aux(262) s(3283) =< aux(261)*(1/2)+aux(262) s(3279) =< aux(261)*(2/3)+s(3272)*(1/3)+aux(263) s(3280) =< aux(261)*(2/3)+s(3272)*(1/3)+aux(263) s(3281) =< aux(261)*(2/3)+s(3272)*(1/3)+aux(263) s(3282) =< aux(261)*(2/3)+s(3272)*(1/3)+aux(263) s(3283) =< aux(261)*(2/3)+s(3272)*(1/3)+aux(263) s(3277) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3278) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3279) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3280) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3281) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3282) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3283) =< aux(261)*(3/5)+s(3272)*(1/5)+aux(266) s(3285) =< aux(261)*(2/7)+aux(267) s(3276) =< aux(261)*(2/7)+aux(267) s(3286) =< aux(261)*(4/11)+s(3272)*(1/11)+aux(268) s(3285) =< aux(261)*(4/11)+s(3272)*(1/11)+aux(268) s(3276) =< aux(261)*(4/11)+s(3272)*(1/11)+aux(268) s(3290) =< s(3283)*s(3287) s(3291) =< s(3280)*s(3288) s(3292) =< s(3277)*s(3289) s(3293) =< s(3276)*s(3287) s(3294) =< s(3276)*aux(260) s(3295) =< s(3294) s(3296) =< s(3293) s(3246) =< aux(251) s(3247) =< aux(251) s(3248) =< aux(251) s(3249) =< aux(251) s(3250) =< aux(251) s(3251) =< aux(251) s(3252) =< aux(251) s(3253) =< aux(251) s(3254) =< aux(251) s(3242) =< aux(251) s(3242) =< aux(252) s(3250) =< aux(253) s(3249) =< aux(254) s(3248) =< aux(255) s(3249) =< aux(255) s(3250) =< aux(255) s(3251) =< aux(255) s(3247) =< aux(257) s(3249) =< aux(257) s(3255) =< aux(258) s(3256) =< aux(259) s(3257) =< aux(251)-1 s(3258) =< aux(251)-2 s(3259) =< aux(251)-3 s(3248) =< aux(252)*(1/3)+aux(255) s(3249) =< aux(252)*(1/3)+aux(255) s(3250) =< aux(252)*(1/3)+aux(255) s(3251) =< aux(252)*(1/3)+aux(255) s(3252) =< aux(252)*(1/3)+aux(255) s(3253) =< aux(252)*(1/3)+aux(255) s(3250) =< aux(252)*(1/2)+aux(253) s(3251) =< aux(252)*(1/2)+aux(253) s(3252) =< aux(252)*(1/2)+aux(253) s(3253) =< aux(252)*(1/2)+aux(253) s(3249) =< aux(252)*(2/3)+s(3242)*(1/3)+aux(254) s(3250) =< aux(252)*(2/3)+s(3242)*(1/3)+aux(254) s(3251) =< aux(252)*(2/3)+s(3242)*(1/3)+aux(254) s(3252) =< aux(252)*(2/3)+s(3242)*(1/3)+aux(254) s(3253) =< aux(252)*(2/3)+s(3242)*(1/3)+aux(254) s(3247) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3248) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3249) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3250) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3251) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3252) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3253) =< aux(252)*(3/5)+s(3242)*(1/5)+aux(257) s(3255) =< aux(252)*(2/7)+aux(258) s(3246) =< aux(252)*(2/7)+aux(258) s(3256) =< aux(252)*(4/11)+s(3242)*(1/11)+aux(259) s(3255) =< aux(252)*(4/11)+s(3242)*(1/11)+aux(259) s(3246) =< aux(252)*(4/11)+s(3242)*(1/11)+aux(259) s(3260) =< s(3253)*s(3257) s(3261) =< s(3250)*s(3258) s(3262) =< s(3247)*s(3259) s(3263) =< s(3246)*s(3257) s(3264) =< s(3246)*aux(251) s(3265) =< s(3264) s(3266) =< s(3263) with precondition: [Out=2,V1>=1,V>=0] * Chain [83]: 12*s(3458)+1*s(3459)+1*s(3460)+1*s(3461)+1*s(3462)+2*s(3463)+1*s(3464)+2*s(3466)+6*s(3467)+12*s(3468)+1*s(3472)+1*s(3473)+1*s(3474)+18*s(3477)+156*s(3478)+2*s(3479)+0 Such that:s(3449) =< V1 s(3450) =< 2*V1+1 s(3451) =< V1/2 s(3452) =< V1/3 s(3453) =< 2/3*V1 s(3454) =< 2/3*V1+1/3 s(3455) =< 2/5*V1 s(3456) =< 3/7*V1 s(3457) =< 3/11*V1 aux(269) =< 2 s(3479) =< aux(269) s(3458) =< s(3449) s(3459) =< s(3449) s(3460) =< s(3449) s(3461) =< s(3449) s(3462) =< s(3449) s(3463) =< s(3449) s(3464) =< s(3449) s(3465) =< s(3449) s(3466) =< s(3449) s(3454) =< s(3449) s(3454) =< s(3450) s(3462) =< s(3451) s(3461) =< s(3452) s(3460) =< s(3453) s(3461) =< s(3453) s(3462) =< s(3453) s(3463) =< s(3453) s(3459) =< s(3455) s(3461) =< s(3455) s(3467) =< s(3456) s(3468) =< s(3457) s(3469) =< s(3449)-1 s(3470) =< s(3449)-2 s(3471) =< s(3449)-3 s(3460) =< s(3450)*(1/3)+s(3453) s(3461) =< s(3450)*(1/3)+s(3453) s(3462) =< s(3450)*(1/3)+s(3453) s(3463) =< s(3450)*(1/3)+s(3453) s(3464) =< s(3450)*(1/3)+s(3453) s(3465) =< s(3450)*(1/3)+s(3453) s(3462) =< s(3450)*(1/2)+s(3451) s(3463) =< s(3450)*(1/2)+s(3451) s(3464) =< s(3450)*(1/2)+s(3451) s(3465) =< s(3450)*(1/2)+s(3451) s(3461) =< s(3450)*(2/3)+s(3454)*(1/3)+s(3452) s(3462) =< s(3450)*(2/3)+s(3454)*(1/3)+s(3452) s(3463) =< s(3450)*(2/3)+s(3454)*(1/3)+s(3452) s(3464) =< s(3450)*(2/3)+s(3454)*(1/3)+s(3452) s(3465) =< s(3450)*(2/3)+s(3454)*(1/3)+s(3452) s(3459) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3460) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3461) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3462) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3463) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3464) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3465) =< s(3450)*(3/5)+s(3454)*(1/5)+s(3455) s(3467) =< s(3450)*(2/7)+s(3456) s(3458) =< s(3450)*(2/7)+s(3456) s(3468) =< s(3450)*(4/11)+s(3454)*(1/11)+s(3457) s(3467) =< s(3450)*(4/11)+s(3454)*(1/11)+s(3457) s(3458) =< s(3450)*(4/11)+s(3454)*(1/11)+s(3457) s(3472) =< s(3465)*s(3469) s(3473) =< s(3462)*s(3470) s(3474) =< s(3459)*s(3471) s(3475) =< s(3458)*s(3469) s(3476) =< s(3458)*s(3449) s(3477) =< s(3476) s(3478) =< s(3475) with precondition: [V=2,Out=0,V1>=0] * Chain [82]: 24*s(3490)+2*s(3491)+2*s(3492)+2*s(3493)+2*s(3494)+4*s(3495)+2*s(3496)+5*s(3498)+12*s(3499)+24*s(3500)+2*s(3504)+2*s(3505)+2*s(3506)+36*s(3509)+312*s(3510)+1 Such that:aux(271) =< V1 aux(272) =< 2*V1+1 aux(273) =< V1/2 aux(274) =< V1/3 aux(275) =< 2/3*V1 aux(276) =< 2/3*V1+1/3 aux(277) =< 2/5*V1 aux(278) =< 3/7*V1 aux(279) =< 3/11*V1 s(3486) =< aux(276) s(3490) =< aux(271) s(3491) =< aux(271) s(3492) =< aux(271) s(3493) =< aux(271) s(3494) =< aux(271) s(3495) =< aux(271) s(3496) =< aux(271) s(3497) =< aux(271) s(3498) =< aux(271) s(3486) =< aux(271) s(3486) =< aux(272) s(3494) =< aux(273) s(3493) =< aux(274) s(3492) =< aux(275) s(3493) =< aux(275) s(3494) =< aux(275) s(3495) =< aux(275) s(3491) =< aux(277) s(3493) =< aux(277) s(3499) =< aux(278) s(3500) =< aux(279) s(3501) =< aux(271)-1 s(3502) =< aux(271)-2 s(3503) =< aux(271)-3 s(3492) =< aux(272)*(1/3)+aux(275) s(3493) =< aux(272)*(1/3)+aux(275) s(3494) =< aux(272)*(1/3)+aux(275) s(3495) =< aux(272)*(1/3)+aux(275) s(3496) =< aux(272)*(1/3)+aux(275) s(3497) =< aux(272)*(1/3)+aux(275) s(3494) =< aux(272)*(1/2)+aux(273) s(3495) =< aux(272)*(1/2)+aux(273) s(3496) =< aux(272)*(1/2)+aux(273) s(3497) =< aux(272)*(1/2)+aux(273) s(3493) =< aux(272)*(2/3)+s(3486)*(1/3)+aux(274) s(3494) =< aux(272)*(2/3)+s(3486)*(1/3)+aux(274) s(3495) =< aux(272)*(2/3)+s(3486)*(1/3)+aux(274) s(3496) =< aux(272)*(2/3)+s(3486)*(1/3)+aux(274) s(3497) =< aux(272)*(2/3)+s(3486)*(1/3)+aux(274) s(3491) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3492) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3493) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3494) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3495) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3496) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3497) =< aux(272)*(3/5)+s(3486)*(1/5)+aux(277) s(3499) =< aux(272)*(2/7)+aux(278) s(3490) =< aux(272)*(2/7)+aux(278) s(3500) =< aux(272)*(4/11)+s(3486)*(1/11)+aux(279) s(3499) =< aux(272)*(4/11)+s(3486)*(1/11)+aux(279) s(3490) =< aux(272)*(4/11)+s(3486)*(1/11)+aux(279) s(3504) =< s(3497)*s(3501) s(3505) =< s(3494)*s(3502) s(3506) =< s(3491)*s(3503) s(3507) =< s(3490)*s(3501) s(3508) =< s(3490)*aux(271) s(3509) =< s(3508) s(3510) =< s(3507) with precondition: [V=2,Out=1,V1>=0] * Chain [81]: 12*s(3551)+1*s(3552)+1*s(3553)+1*s(3554)+1*s(3555)+2*s(3556)+1*s(3557)+2*s(3559)+6*s(3560)+12*s(3561)+1*s(3565)+1*s(3566)+1*s(3567)+18*s(3570)+156*s(3571)+1*s(3572)+1 Such that:s(3572) =< 2 s(3542) =< V1 s(3543) =< 2*V1+1 s(3544) =< V1/2 s(3545) =< V1/3 s(3546) =< 2/3*V1 s(3547) =< 2/3*V1+1/3 s(3548) =< 2/5*V1 s(3549) =< 3/7*V1 s(3550) =< 3/11*V1 s(3551) =< s(3542) s(3552) =< s(3542) s(3553) =< s(3542) s(3554) =< s(3542) s(3555) =< s(3542) s(3556) =< s(3542) s(3557) =< s(3542) s(3558) =< s(3542) s(3559) =< s(3542) s(3547) =< s(3542) s(3547) =< s(3543) s(3555) =< s(3544) s(3554) =< s(3545) s(3553) =< s(3546) s(3554) =< s(3546) s(3555) =< s(3546) s(3556) =< s(3546) s(3552) =< s(3548) s(3554) =< s(3548) s(3560) =< s(3549) s(3561) =< s(3550) s(3562) =< s(3542)-1 s(3563) =< s(3542)-2 s(3564) =< s(3542)-3 s(3553) =< s(3543)*(1/3)+s(3546) s(3554) =< s(3543)*(1/3)+s(3546) s(3555) =< s(3543)*(1/3)+s(3546) s(3556) =< s(3543)*(1/3)+s(3546) s(3557) =< s(3543)*(1/3)+s(3546) s(3558) =< s(3543)*(1/3)+s(3546) s(3555) =< s(3543)*(1/2)+s(3544) s(3556) =< s(3543)*(1/2)+s(3544) s(3557) =< s(3543)*(1/2)+s(3544) s(3558) =< s(3543)*(1/2)+s(3544) s(3554) =< s(3543)*(2/3)+s(3547)*(1/3)+s(3545) s(3555) =< s(3543)*(2/3)+s(3547)*(1/3)+s(3545) s(3556) =< s(3543)*(2/3)+s(3547)*(1/3)+s(3545) s(3557) =< s(3543)*(2/3)+s(3547)*(1/3)+s(3545) s(3558) =< s(3543)*(2/3)+s(3547)*(1/3)+s(3545) s(3552) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3553) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3554) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3555) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3556) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3557) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3558) =< s(3543)*(3/5)+s(3547)*(1/5)+s(3548) s(3560) =< s(3543)*(2/7)+s(3549) s(3551) =< s(3543)*(2/7)+s(3549) s(3561) =< s(3543)*(4/11)+s(3547)*(1/11)+s(3550) s(3560) =< s(3543)*(4/11)+s(3547)*(1/11)+s(3550) s(3551) =< s(3543)*(4/11)+s(3547)*(1/11)+s(3550) s(3565) =< s(3558)*s(3562) s(3566) =< s(3555)*s(3563) s(3567) =< s(3552)*s(3564) s(3568) =< s(3551)*s(3562) s(3569) =< s(3551)*s(3542) s(3570) =< s(3569) s(3571) =< s(3568) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun5(V1,Out): * Chain [88]: 12*s(3866)+1*s(3867)+1*s(3868)+1*s(3869)+1*s(3870)+2*s(3871)+1*s(3872)+2*s(3874)+6*s(3875)+12*s(3876)+1*s(3880)+1*s(3881)+1*s(3882)+18*s(3885)+156*s(3886)+1 Such that:s(3857) =< V1 s(3858) =< 2*V1+1 s(3859) =< V1/2 s(3860) =< V1/3 s(3861) =< 2/3*V1 s(3862) =< 2/3*V1+1/3 s(3863) =< 2/5*V1 s(3864) =< 3/7*V1 s(3865) =< 3/11*V1 s(3866) =< s(3857) s(3867) =< s(3857) s(3868) =< s(3857) s(3869) =< s(3857) s(3870) =< s(3857) s(3871) =< s(3857) s(3872) =< s(3857) s(3873) =< s(3857) s(3874) =< s(3857) s(3862) =< s(3857) s(3862) =< s(3858) s(3870) =< s(3859) s(3869) =< s(3860) s(3868) =< s(3861) s(3869) =< s(3861) s(3870) =< s(3861) s(3871) =< s(3861) s(3867) =< s(3863) s(3869) =< s(3863) s(3875) =< s(3864) s(3876) =< s(3865) s(3877) =< s(3857)-1 s(3878) =< s(3857)-2 s(3879) =< s(3857)-3 s(3868) =< s(3858)*(1/3)+s(3861) s(3869) =< s(3858)*(1/3)+s(3861) s(3870) =< s(3858)*(1/3)+s(3861) s(3871) =< s(3858)*(1/3)+s(3861) s(3872) =< s(3858)*(1/3)+s(3861) s(3873) =< s(3858)*(1/3)+s(3861) s(3870) =< s(3858)*(1/2)+s(3859) s(3871) =< s(3858)*(1/2)+s(3859) s(3872) =< s(3858)*(1/2)+s(3859) s(3873) =< s(3858)*(1/2)+s(3859) s(3869) =< s(3858)*(2/3)+s(3862)*(1/3)+s(3860) s(3870) =< s(3858)*(2/3)+s(3862)*(1/3)+s(3860) s(3871) =< s(3858)*(2/3)+s(3862)*(1/3)+s(3860) s(3872) =< s(3858)*(2/3)+s(3862)*(1/3)+s(3860) s(3873) =< s(3858)*(2/3)+s(3862)*(1/3)+s(3860) s(3867) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3868) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3869) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3870) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3871) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3872) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3873) =< s(3858)*(3/5)+s(3862)*(1/5)+s(3863) s(3875) =< s(3858)*(2/7)+s(3864) s(3866) =< s(3858)*(2/7)+s(3864) s(3876) =< s(3858)*(4/11)+s(3862)*(1/11)+s(3865) s(3875) =< s(3858)*(4/11)+s(3862)*(1/11)+s(3865) s(3866) =< s(3858)*(4/11)+s(3862)*(1/11)+s(3865) s(3880) =< s(3873)*s(3877) s(3881) =< s(3870)*s(3878) s(3882) =< s(3867)*s(3879) s(3883) =< s(3866)*s(3877) s(3884) =< s(3866)*s(3857) s(3885) =< s(3884) s(3886) =< s(3883) with precondition: [Out=0,V1>=0] * Chain [87]: 12*s(3896)+1*s(3897)+1*s(3898)+1*s(3899)+1*s(3900)+2*s(3901)+1*s(3902)+2*s(3904)+6*s(3905)+12*s(3906)+1*s(3910)+1*s(3911)+1*s(3912)+18*s(3915)+156*s(3916)+1 Such that:s(3887) =< V1 s(3888) =< 2*V1+1 s(3889) =< V1/2 s(3890) =< V1/3 s(3891) =< 2/3*V1 s(3892) =< 2/3*V1+1/3 s(3893) =< 2/5*V1 s(3894) =< 3/7*V1 s(3895) =< 3/11*V1 s(3896) =< s(3887) s(3897) =< s(3887) s(3898) =< s(3887) s(3899) =< s(3887) s(3900) =< s(3887) s(3901) =< s(3887) s(3902) =< s(3887) s(3903) =< s(3887) s(3904) =< s(3887) s(3892) =< s(3887) s(3892) =< s(3888) s(3900) =< s(3889) s(3899) =< s(3890) s(3898) =< s(3891) s(3899) =< s(3891) s(3900) =< s(3891) s(3901) =< s(3891) s(3897) =< s(3893) s(3899) =< s(3893) s(3905) =< s(3894) s(3906) =< s(3895) s(3907) =< s(3887)-1 s(3908) =< s(3887)-2 s(3909) =< s(3887)-3 s(3898) =< s(3888)*(1/3)+s(3891) s(3899) =< s(3888)*(1/3)+s(3891) s(3900) =< s(3888)*(1/3)+s(3891) s(3901) =< s(3888)*(1/3)+s(3891) s(3902) =< s(3888)*(1/3)+s(3891) s(3903) =< s(3888)*(1/3)+s(3891) s(3900) =< s(3888)*(1/2)+s(3889) s(3901) =< s(3888)*(1/2)+s(3889) s(3902) =< s(3888)*(1/2)+s(3889) s(3903) =< s(3888)*(1/2)+s(3889) s(3899) =< s(3888)*(2/3)+s(3892)*(1/3)+s(3890) s(3900) =< s(3888)*(2/3)+s(3892)*(1/3)+s(3890) s(3901) =< s(3888)*(2/3)+s(3892)*(1/3)+s(3890) s(3902) =< s(3888)*(2/3)+s(3892)*(1/3)+s(3890) s(3903) =< s(3888)*(2/3)+s(3892)*(1/3)+s(3890) s(3897) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3898) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3899) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3900) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3901) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3902) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3903) =< s(3888)*(3/5)+s(3892)*(1/5)+s(3893) s(3905) =< s(3888)*(2/7)+s(3894) s(3896) =< s(3888)*(2/7)+s(3894) s(3906) =< s(3888)*(4/11)+s(3892)*(1/11)+s(3895) s(3905) =< s(3888)*(4/11)+s(3892)*(1/11)+s(3895) s(3896) =< s(3888)*(4/11)+s(3892)*(1/11)+s(3895) s(3910) =< s(3903)*s(3907) s(3911) =< s(3900)*s(3908) s(3912) =< s(3897)*s(3909) s(3913) =< s(3896)*s(3907) s(3914) =< s(3896)*s(3887) s(3915) =< s(3914) s(3916) =< s(3913) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun6(Out): * Chain [90]: 0 with precondition: [Out=0] * Chain [89]: 0 with precondition: [Out=1] #### Cost of chains of fun7(V1,Out): * Chain [93]: 12*s(3926)+1*s(3927)+1*s(3928)+1*s(3929)+1*s(3930)+2*s(3931)+1*s(3932)+2*s(3934)+6*s(3935)+12*s(3936)+1*s(3940)+1*s(3941)+1*s(3942)+18*s(3945)+156*s(3946)+0 Such that:s(3917) =< V1 s(3918) =< 2*V1+1 s(3919) =< V1/2 s(3920) =< V1/3 s(3921) =< 2/3*V1 s(3922) =< 2/3*V1+1/3 s(3923) =< 2/5*V1 s(3924) =< 3/7*V1 s(3925) =< 3/11*V1 s(3926) =< s(3917) s(3927) =< s(3917) s(3928) =< s(3917) s(3929) =< s(3917) s(3930) =< s(3917) s(3931) =< s(3917) s(3932) =< s(3917) s(3933) =< s(3917) s(3934) =< s(3917) s(3922) =< s(3917) s(3922) =< s(3918) s(3930) =< s(3919) s(3929) =< s(3920) s(3928) =< s(3921) s(3929) =< s(3921) s(3930) =< s(3921) s(3931) =< s(3921) s(3927) =< s(3923) s(3929) =< s(3923) s(3935) =< s(3924) s(3936) =< s(3925) s(3937) =< s(3917)-1 s(3938) =< s(3917)-2 s(3939) =< s(3917)-3 s(3928) =< s(3918)*(1/3)+s(3921) s(3929) =< s(3918)*(1/3)+s(3921) s(3930) =< s(3918)*(1/3)+s(3921) s(3931) =< s(3918)*(1/3)+s(3921) s(3932) =< s(3918)*(1/3)+s(3921) s(3933) =< s(3918)*(1/3)+s(3921) s(3930) =< s(3918)*(1/2)+s(3919) s(3931) =< s(3918)*(1/2)+s(3919) s(3932) =< s(3918)*(1/2)+s(3919) s(3933) =< s(3918)*(1/2)+s(3919) s(3929) =< s(3918)*(2/3)+s(3922)*(1/3)+s(3920) s(3930) =< s(3918)*(2/3)+s(3922)*(1/3)+s(3920) s(3931) =< s(3918)*(2/3)+s(3922)*(1/3)+s(3920) s(3932) =< s(3918)*(2/3)+s(3922)*(1/3)+s(3920) s(3933) =< s(3918)*(2/3)+s(3922)*(1/3)+s(3920) s(3927) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3928) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3929) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3930) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3931) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3932) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3933) =< s(3918)*(3/5)+s(3922)*(1/5)+s(3923) s(3935) =< s(3918)*(2/7)+s(3924) s(3926) =< s(3918)*(2/7)+s(3924) s(3936) =< s(3918)*(4/11)+s(3922)*(1/11)+s(3925) s(3935) =< s(3918)*(4/11)+s(3922)*(1/11)+s(3925) s(3926) =< s(3918)*(4/11)+s(3922)*(1/11)+s(3925) s(3940) =< s(3933)*s(3937) s(3941) =< s(3930)*s(3938) s(3942) =< s(3927)*s(3939) s(3943) =< s(3926)*s(3937) s(3944) =< s(3926)*s(3917) s(3945) =< s(3944) s(3946) =< s(3943) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [92]: 0 with precondition: [Out=0,V1>=0] * Chain [91]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of start(V1,V,V2): * Chain [94]: 265*s(3949)+1602*s(3950)+90*s(3952)+528*s(3963)+44*s(3964)+44*s(3965)+44*s(3966)+44*s(3967)+88*s(3968)+44*s(3969)+264*s(3972)+528*s(3973)+44*s(3977)+44*s(3978)+44*s(3979)+792*s(3982)+6864*s(3983)+1572*s(4014)+252*s(4016)+21*s(4017)+21*s(4018)+21*s(4019)+21*s(4020)+42*s(4021)+21*s(4022)+126*s(4024)+252*s(4025)+21*s(4029)+21*s(4030)+21*s(4031)+378*s(4034)+3276*s(4035)+468*s(4059)+39*s(4060)+39*s(4061)+39*s(4062)+39*s(4063)+78*s(4064)+39*s(4065)+234*s(4067)+468*s(4068)+39*s(4072)+39*s(4073)+39*s(4074)+702*s(4077)+6084*s(4078)+1*s(4488)+12 Such that:s(4488) =< 1 s(4004) =< 2*V2+1 s(4005) =< V2/2 s(4006) =< V2/3 s(4007) =< 2/3*V2 s(4008) =< 2/3*V2+1/3 s(4009) =< 2/5*V2 s(4010) =< 3/7*V2 s(4011) =< 3/11*V2 aux(308) =< 2 aux(309) =< V1 aux(310) =< 2*V1+1 aux(311) =< V1/2 aux(312) =< V1/3 aux(313) =< 2/3*V1 aux(314) =< 2/3*V1+1/3 aux(315) =< 2/5*V1 aux(316) =< 3/7*V1 aux(317) =< 3/11*V1 aux(318) =< V aux(319) =< 2*V+1 aux(320) =< V/2 aux(321) =< V/3 aux(322) =< 2/3*V aux(323) =< 2/3*V+1/3 aux(324) =< 2/5*V aux(325) =< 3/7*V aux(326) =< 3/11*V aux(327) =< V2 s(4014) =< aux(308) s(3952) =< aux(309) s(3959) =< aux(314) s(3949) =< aux(318) s(4057) =< aux(323) s(4059) =< aux(318) s(4060) =< aux(318) s(4061) =< aux(318) s(4062) =< aux(318) s(4063) =< aux(318) s(4064) =< aux(318) s(4065) =< aux(318) s(4066) =< aux(318) s(4057) =< aux(318) s(4057) =< aux(319) s(4063) =< aux(320) s(4062) =< aux(321) s(4061) =< aux(322) s(4062) =< aux(322) s(4063) =< aux(322) s(4064) =< aux(322) s(4060) =< aux(324) s(4062) =< aux(324) s(4067) =< aux(325) s(4068) =< aux(326) s(4069) =< aux(318)-1 s(4070) =< aux(318)-2 s(4071) =< aux(318)-3 s(4061) =< aux(319)*(1/3)+aux(322) s(4062) =< aux(319)*(1/3)+aux(322) s(4063) =< aux(319)*(1/3)+aux(322) s(4064) =< aux(319)*(1/3)+aux(322) s(4065) =< aux(319)*(1/3)+aux(322) s(4066) =< aux(319)*(1/3)+aux(322) s(4063) =< aux(319)*(1/2)+aux(320) s(4064) =< aux(319)*(1/2)+aux(320) s(4065) =< aux(319)*(1/2)+aux(320) s(4066) =< aux(319)*(1/2)+aux(320) s(4062) =< aux(319)*(2/3)+s(4057)*(1/3)+aux(321) s(4063) =< aux(319)*(2/3)+s(4057)*(1/3)+aux(321) s(4064) =< aux(319)*(2/3)+s(4057)*(1/3)+aux(321) s(4065) =< aux(319)*(2/3)+s(4057)*(1/3)+aux(321) s(4066) =< aux(319)*(2/3)+s(4057)*(1/3)+aux(321) s(4060) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4061) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4062) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4063) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4064) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4065) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4066) =< aux(319)*(3/5)+s(4057)*(1/5)+aux(324) s(4067) =< aux(319)*(2/7)+aux(325) s(4059) =< aux(319)*(2/7)+aux(325) s(4068) =< aux(319)*(4/11)+s(4057)*(1/11)+aux(326) s(4067) =< aux(319)*(4/11)+s(4057)*(1/11)+aux(326) s(4059) =< aux(319)*(4/11)+s(4057)*(1/11)+aux(326) s(4072) =< s(4066)*s(4069) s(4073) =< s(4063)*s(4070) s(4074) =< s(4060)*s(4071) s(4075) =< s(4059)*s(4069) s(4076) =< s(4059)*aux(318) s(4077) =< s(4076) s(4078) =< s(4075) s(3963) =< aux(309) s(3964) =< aux(309) s(3965) =< aux(309) s(3966) =< aux(309) s(3967) =< aux(309) s(3968) =< aux(309) s(3969) =< aux(309) s(3970) =< aux(309) s(3959) =< aux(309) s(3959) =< aux(310) s(3967) =< aux(311) s(3966) =< aux(312) s(3965) =< aux(313) s(3966) =< aux(313) s(3967) =< aux(313) s(3968) =< aux(313) s(3964) =< aux(315) s(3966) =< aux(315) s(3972) =< aux(316) s(3973) =< aux(317) s(3974) =< aux(309)-1 s(3975) =< aux(309)-2 s(3976) =< aux(309)-3 s(3965) =< aux(310)*(1/3)+aux(313) s(3966) =< aux(310)*(1/3)+aux(313) s(3967) =< aux(310)*(1/3)+aux(313) s(3968) =< aux(310)*(1/3)+aux(313) s(3969) =< aux(310)*(1/3)+aux(313) s(3970) =< aux(310)*(1/3)+aux(313) s(3967) =< aux(310)*(1/2)+aux(311) s(3968) =< aux(310)*(1/2)+aux(311) s(3969) =< aux(310)*(1/2)+aux(311) s(3970) =< aux(310)*(1/2)+aux(311) s(3966) =< aux(310)*(2/3)+s(3959)*(1/3)+aux(312) s(3967) =< aux(310)*(2/3)+s(3959)*(1/3)+aux(312) s(3968) =< aux(310)*(2/3)+s(3959)*(1/3)+aux(312) s(3969) =< aux(310)*(2/3)+s(3959)*(1/3)+aux(312) s(3970) =< aux(310)*(2/3)+s(3959)*(1/3)+aux(312) s(3964) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3965) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3966) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3967) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3968) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3969) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3970) =< aux(310)*(3/5)+s(3959)*(1/5)+aux(315) s(3972) =< aux(310)*(2/7)+aux(316) s(3963) =< aux(310)*(2/7)+aux(316) s(3973) =< aux(310)*(4/11)+s(3959)*(1/11)+aux(317) s(3972) =< aux(310)*(4/11)+s(3959)*(1/11)+aux(317) s(3963) =< aux(310)*(4/11)+s(3959)*(1/11)+aux(317) s(3977) =< s(3970)*s(3974) s(3978) =< s(3967)*s(3975) s(3979) =< s(3964)*s(3976) s(3980) =< s(3963)*s(3974) s(3981) =< s(3963)*aux(309) s(3982) =< s(3981) s(3983) =< s(3980) s(4013) =< s(4008) s(3950) =< aux(327) s(4016) =< aux(327) s(4017) =< aux(327) s(4018) =< aux(327) s(4019) =< aux(327) s(4020) =< aux(327) s(4021) =< aux(327) s(4022) =< aux(327) s(4023) =< aux(327) s(4013) =< aux(327) s(4013) =< s(4004) s(4020) =< s(4005) s(4019) =< s(4006) s(4018) =< s(4007) s(4019) =< s(4007) s(4020) =< s(4007) s(4021) =< s(4007) s(4017) =< s(4009) s(4019) =< s(4009) s(4024) =< s(4010) s(4025) =< s(4011) s(4026) =< aux(327)-1 s(4027) =< aux(327)-2 s(4028) =< aux(327)-3 s(4018) =< s(4004)*(1/3)+s(4007) s(4019) =< s(4004)*(1/3)+s(4007) s(4020) =< s(4004)*(1/3)+s(4007) s(4021) =< s(4004)*(1/3)+s(4007) s(4022) =< s(4004)*(1/3)+s(4007) s(4023) =< s(4004)*(1/3)+s(4007) s(4020) =< s(4004)*(1/2)+s(4005) s(4021) =< s(4004)*(1/2)+s(4005) s(4022) =< s(4004)*(1/2)+s(4005) s(4023) =< s(4004)*(1/2)+s(4005) s(4019) =< s(4004)*(2/3)+s(4013)*(1/3)+s(4006) s(4020) =< s(4004)*(2/3)+s(4013)*(1/3)+s(4006) s(4021) =< s(4004)*(2/3)+s(4013)*(1/3)+s(4006) s(4022) =< s(4004)*(2/3)+s(4013)*(1/3)+s(4006) s(4023) =< s(4004)*(2/3)+s(4013)*(1/3)+s(4006) s(4017) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4018) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4019) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4020) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4021) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4022) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4023) =< s(4004)*(3/5)+s(4013)*(1/5)+s(4009) s(4024) =< s(4004)*(2/7)+s(4010) s(4016) =< s(4004)*(2/7)+s(4010) s(4025) =< s(4004)*(4/11)+s(4013)*(1/11)+s(4011) s(4024) =< s(4004)*(4/11)+s(4013)*(1/11)+s(4011) s(4016) =< s(4004)*(4/11)+s(4013)*(1/11)+s(4011) s(4029) =< s(4023)*s(4026) s(4030) =< s(4020)*s(4027) s(4031) =< s(4017)*s(4028) s(4032) =< s(4016)*s(4026) s(4033) =< s(4016)*aux(327) s(4034) =< s(4033) s(4035) =< s(4032) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [94] with precondition: [] - Upper bound: nat(V1)*926+3157+nat(V1)*792*nat(V1)+nat(V1)*44*nat(nat(V1)+ -3)+nat(V1)*44*nat(nat(V1)+ -2)+nat(V1)*6908*nat(nat(V1)+ -1)+nat(V)*1006+nat(V)*702*nat(V)+nat(V)*39*nat(nat(V)+ -3)+nat(V)*39*nat(nat(V)+ -2)+nat(V)*6123*nat(nat(V)+ -1)+nat(V2)*2001+nat(V2)*378*nat(V2)+nat(V2)*21*nat(nat(V2)+ -3)+nat(V2)*21*nat(nat(V2)+ -2)+nat(V2)*3297*nat(nat(V2)+ -1)+nat(3/7*V1)*264+nat(3/7*V)*234+nat(3/7*V2)*126+nat(3/11*V1)*528+nat(3/11*V)*468+nat(3/11*V2)*252 - Complexity: n^2 ### Maximum cost of start(V1,V,V2): nat(V1)*926+3157+nat(V1)*792*nat(V1)+nat(V1)*44*nat(nat(V1)+ -3)+nat(V1)*44*nat(nat(V1)+ -2)+nat(V1)*6908*nat(nat(V1)+ -1)+nat(V)*1006+nat(V)*702*nat(V)+nat(V)*39*nat(nat(V)+ -3)+nat(V)*39*nat(nat(V)+ -2)+nat(V)*6123*nat(nat(V)+ -1)+nat(V2)*2001+nat(V2)*378*nat(V2)+nat(V2)*21*nat(nat(V2)+ -3)+nat(V2)*21*nat(nat(V2)+ -2)+nat(V2)*3297*nat(nat(V2)+ -1)+nat(3/7*V1)*264+nat(3/7*V)*234+nat(3/7*V2)*126+nat(3/11*V1)*528+nat(3/11*V)*468+nat(3/11*V2)*252 Asymptotic class: n^2 * Total analysis performed in 19558 ms. ---------------------------------------- (14) BOUNDS(1, n^2) ---------------------------------------- (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(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Types: cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p 0' :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p hole_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_and: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(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Types: cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p 0' :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p hole_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p Generator Equations: gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond:cons_and: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:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, 0)), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, 0))) Induction Step: gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, +(n4_4, 1))), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond:cons_and: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(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Types: cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p 0' :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p hole_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p Generator Equations: gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond:cons_and: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(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Types: cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p 0' :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p hole_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p Lemmas: gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond:cons_and: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: cond(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4)) -> *3_4, rt in Omega(n1589_4) Induction Base: cond(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0)) Induction Step: cond(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1)), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1))) ->_R^Omega(1) cond(and(gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1)), 0'), gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1)), 0')), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1))), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n1589_4, 1)))) ->_R^Omega(1) cond(and(true, gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4)), 0')), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4))), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4)))) ->_R^Omega(1) cond(and(true, true), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4))), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4)))) ->_R^Omega(1) cond(true, p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4))), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4)))) ->_R^Omega(1) cond(true, gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4), p(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n1589_4)))) ->_R^Omega(1) cond(true, gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4)) ->_IH *3_4 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: cond(true, x, y) -> cond(and(gr(x, 0'), gr(y, 0')), p(x), p(y)) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0', 0') -> false gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) 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_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_s(x_1) -> s(encArg(x_1)) Types: cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p 0' :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encArg :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_cond :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_and :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p hole_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond:cons_and:cons_gr:cons_p gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond:cons_and:cons_gr:cons_p Lemmas: gr(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) cond(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4), gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n1589_4)) -> *3_4, rt in Omega(n1589_4) Generator Equations: gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: encArg ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n3159_4)) -> gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n3159_4), rt in Omega(0) Induction Base: encArg(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(0)) ->_R^Omega(0) true Induction Step: encArg(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(+(n3159_4, 1))) ->_R^Omega(0) s(encArg(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(n3159_4))) ->_IH s(gen_true:0':false:s:cons_cond:cons_and:cons_gr:cons_p2_4(c3160_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (30) BOUNDS(1, INF)