/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 211 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), 5 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 25.4 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 515 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), 163 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 314 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(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(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0) -> 0 encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) [1] cond2(true, x, y) -> cond1(y, y) [1] cond2(false, x, y) -> cond1(p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) [1] cond2(true, x, y) -> cond1(y, y) [1] cond2(false, x, y) -> cond1(p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] The TRS has the following type information: cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_cond1(v0, v1) -> null_encode_cond1 [0] encode_s(v0) -> null_encode_s [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_neq(v0, v1) -> null_encode_neq [0] cond1(v0, v1) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] neq(v0, v1) -> null_neq [0] p(v0) -> null_p [0] And the following fresh constants: null_encArg, null_encode_cond1, null_encode_s, null_encode_cond2, null_encode_gr, null_encode_true, null_encode_false, null_encode_p, null_encode_0, null_encode_neq, null_cond1, null_cond2, null_gr, null_neq, null_p ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) [1] cond2(true, x, y) -> cond1(y, y) [1] cond2(false, x, y) -> cond1(p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(v0) -> null_encArg [0] encode_cond1(v0, v1) -> null_encode_cond1 [0] encode_s(v0) -> null_encode_s [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_neq(v0, v1) -> null_encode_neq [0] cond1(v0, v1) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] neq(v0, v1) -> null_neq [0] p(v0) -> null_p [0] The TRS has the following type information: cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p s :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p true :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p false :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p 0 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encArg :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cons_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cons_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cons_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cons_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p cons_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_s :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_true :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_false :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_0 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p encode_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p -> s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encArg :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_s :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_true :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_false :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_0 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_cond1 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_cond2 :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_gr :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_neq :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p null_p :: s:true:false:0:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_s:null_encode_cond2:null_encode_gr:null_encode_true:null_encode_false:null_encode_p:null_encode_0:null_encode_neq:null_cond1:null_cond2:null_gr:null_neq:null_p Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: true => 2 false => 1 0 => 0 null_encArg => 0 null_encode_cond1 => 0 null_encode_s => 0 null_encode_cond2 => 0 null_encode_gr => 0 null_encode_true => 0 null_encode_false => 0 null_encode_p => 0 null_encode_0 => 0 null_encode_neq => 0 null_cond1 => 0 null_cond2 => 0 null_gr => 0 null_neq => 0 null_p => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond1(z, z') -{ 1 }-> cond2(gr(1 + x, y), 1 + x, y) :|: x >= 0, y >= 0, z = 1 + x, z' = y cond1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond2(z, z', z'') -{ 1 }-> cond1(y, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond2(z, z', z'') -{ 1 }-> cond1(p(x), y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> neq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2)) :|: 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_cond1(z, z') -{ 0 }-> cond1(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_cond1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_neq(z, z') -{ 0 }-> neq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_neq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0 gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 neq(z, z') -{ 1 }-> neq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x neq(z, z') -{ 1 }-> 2 :|: z' = 1 + x, x >= 0, z = 0 neq(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 neq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0 neq(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, V5),0,[cond1(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[cond2(V1, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[gr(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[neq(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[p(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun1(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun2(V1, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[fun3(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun4(Out)],[]). eq(start(V1, V, V5),0,[fun5(Out)],[]). eq(start(V1, V, V5),0,[fun6(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun7(Out)],[]). eq(start(V1, V, V5),0,[fun8(V1, V, Out)],[V1 >= 0,V >= 0]). eq(cond1(V1, V, Out),1,[gr(1 + V3, V2, Ret0),cond2(Ret0, 1 + V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = 1 + V3,V = V2]). eq(cond2(V1, V, V5, Out),1,[cond1(V6, V6, Ret1)],[Out = Ret1,V1 = 2,V = V4,V5 = V6,V4 >= 0,V6 >= 0]). eq(cond2(V1, V, V5, Out),1,[p(V8, Ret01),cond1(Ret01, V7, Ret2)],[Out = Ret2,V = V8,V5 = V7,V1 = 1,V8 >= 0,V7 >= 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V = V9,V9 >= 0,V1 = 0]). eq(gr(V1, V, Out),1,[],[Out = 2,V10 >= 0,V1 = 1 + V10,V = 0]). eq(gr(V1, V, Out),1,[gr(V12, V11, Ret3)],[Out = Ret3,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]). eq(neq(V1, V, Out),1,[],[Out = 1,V1 = 0,V = 0]). eq(neq(V1, V, Out),1,[],[Out = 2,V = 1 + V13,V13 >= 0,V1 = 0]). eq(neq(V1, V, Out),1,[],[Out = 2,V14 >= 0,V1 = 1 + V14,V = 0]). eq(neq(V1, V, Out),1,[neq(V16, V15, Ret4)],[Out = Ret4,V = 1 + V15,V16 >= 0,V15 >= 0,V1 = 1 + V16]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V17,V17 >= 0,V1 = 1 + V17]). eq(encArg(V1, Out),0,[encArg(V18, Ret11)],[Out = 1 + Ret11,V1 = 1 + V18,V18 >= 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[encArg(V19, Ret02),encArg(V20, Ret12),cond1(Ret02, Ret12, Ret5)],[Out = Ret5,V19 >= 0,V1 = 1 + V19 + V20,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret03),encArg(V23, Ret13),encArg(V21, Ret21),cond2(Ret03, Ret13, Ret21, Ret6)],[Out = Ret6,V22 >= 0,V1 = 1 + V21 + V22 + V23,V21 >= 0,V23 >= 0]). eq(encArg(V1, Out),0,[encArg(V25, Ret04),encArg(V24, Ret14),gr(Ret04, Ret14, Ret7)],[Out = Ret7,V25 >= 0,V1 = 1 + V24 + V25,V24 >= 0]). eq(encArg(V1, Out),0,[encArg(V27, Ret05),encArg(V26, Ret15),neq(Ret05, Ret15, Ret8)],[Out = Ret8,V27 >= 0,V1 = 1 + V26 + V27,V26 >= 0]). eq(encArg(V1, Out),0,[encArg(V28, Ret06),p(Ret06, Ret9)],[Out = Ret9,V1 = 1 + V28,V28 >= 0]). eq(fun(V1, V, Out),0,[encArg(V29, Ret07),encArg(V30, Ret16),cond1(Ret07, Ret16, Ret10)],[Out = Ret10,V29 >= 0,V30 >= 0,V1 = V29,V = V30]). eq(fun1(V1, Out),0,[encArg(V31, Ret17)],[Out = 1 + Ret17,V31 >= 0,V1 = V31]). eq(fun2(V1, V, V5, Out),0,[encArg(V34, Ret08),encArg(V33, Ret18),encArg(V32, Ret22),cond2(Ret08, Ret18, Ret22, Ret19)],[Out = Ret19,V34 >= 0,V32 >= 0,V33 >= 0,V1 = V34,V = V33,V5 = V32]). eq(fun3(V1, V, Out),0,[encArg(V35, Ret09),encArg(V36, Ret110),gr(Ret09, Ret110, Ret20)],[Out = Ret20,V35 >= 0,V36 >= 0,V1 = V35,V = V36]). eq(fun4(Out),0,[],[Out = 2]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V1, Out),0,[encArg(V37, Ret010),p(Ret010, Ret23)],[Out = Ret23,V37 >= 0,V1 = V37]). eq(fun7(Out),0,[],[Out = 0]). eq(fun8(V1, V, Out),0,[encArg(V38, Ret011),encArg(V39, Ret111),neq(Ret011, Ret111, Ret24)],[Out = Ret24,V38 >= 0,V39 >= 0,V1 = V38,V = V39]). eq(encArg(V1, Out),0,[],[Out = 0,V40 >= 0,V1 = V40]). eq(fun(V1, V, Out),0,[],[Out = 0,V42 >= 0,V41 >= 0,V1 = V42,V = V41]). eq(fun1(V1, Out),0,[],[Out = 0,V43 >= 0,V1 = V43]). eq(fun2(V1, V, V5, Out),0,[],[Out = 0,V44 >= 0,V5 = V46,V45 >= 0,V1 = V44,V = V45,V46 >= 0]). eq(fun3(V1, V, Out),0,[],[Out = 0,V47 >= 0,V48 >= 0,V1 = V47,V = V48]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V1, Out),0,[],[Out = 0,V49 >= 0,V1 = V49]). eq(fun8(V1, V, Out),0,[],[Out = 0,V50 >= 0,V51 >= 0,V1 = V50,V = V51]). eq(cond1(V1, V, Out),0,[],[Out = 0,V52 >= 0,V53 >= 0,V1 = V52,V = V53]). eq(cond2(V1, V, V5, Out),0,[],[Out = 0,V54 >= 0,V5 = V56,V55 >= 0,V1 = V54,V = V55,V56 >= 0]). eq(gr(V1, V, Out),0,[],[Out = 0,V58 >= 0,V57 >= 0,V1 = V58,V = V57]). eq(neq(V1, V, Out),0,[],[Out = 0,V60 >= 0,V59 >= 0,V1 = V60,V = V59]). eq(p(V1, Out),0,[],[Out = 0,V61 >= 0,V1 = V61]). input_output_vars(cond1(V1,V,Out),[V1,V],[Out]). input_output_vars(cond2(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(gr(V1,V,Out),[V1,V],[Out]). input_output_vars(neq(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,Out),[V1,V],[Out]). input_output_vars(fun1(V1,Out),[V1],[Out]). input_output_vars(fun2(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(fun3(V1,V,Out),[V1,V],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V1,Out),[V1],[Out]). input_output_vars(fun7(Out),[],[Out]). input_output_vars(fun8(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [p/2] 1. recursive : [gr/3] 2. recursive : [cond1/3,cond2/4] 3. recursive : [neq/3] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/3] 6. non_recursive : [fun1/2] 7. non_recursive : [fun2/4] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/1] 10. non_recursive : [fun5/1] 11. non_recursive : [fun6/2] 12. non_recursive : [fun7/1] 13. non_recursive : [fun8/3] 14. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into p/2 1. SCC is partially evaluated into gr/3 2. SCC is partially evaluated into cond1/3 3. SCC is partially evaluated into neq/3 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/3 6. SCC is partially evaluated into fun1/2 7. SCC is partially evaluated into fun2/4 8. SCC is partially evaluated into fun3/3 9. SCC is partially evaluated into fun4/1 10. SCC is partially evaluated into fun5/1 11. SCC is partially evaluated into fun6/2 12. SCC is completely evaluated into other SCCs 13. SCC is partially evaluated into fun8/3 14. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations p/2 * CE 18 is refined into CE [62] * CE 17 is refined into CE [63] * CE 19 is refined into CE [64] ### Cost equations --> "Loop" of p/2 * CEs [62] --> Loop 33 * CEs [63,64] --> Loop 34 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations gr/3 * CE 27 is refined into CE [65] * CE 25 is refined into CE [66] * CE 24 is refined into CE [67] * CE 26 is refined into CE [68] ### Cost equations --> "Loop" of gr/3 * CEs [68] --> Loop 35 * CEs [65] --> Loop 36 * CEs [66] --> Loop 37 * CEs [67] --> Loop 38 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [35]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [35]: - RF of loop [35:1]: V V1 ### Specialization of cost equations cond1/3 * CE 20 is refined into CE [69,70,71,72] * CE 23 is refined into CE [73] * CE 21 is refined into CE [74,75] * CE 22 is refined into CE [76,77] ### Cost equations --> "Loop" of cond1/3 * CEs [77] --> Loop 39 * CEs [75] --> Loop 40 * CEs [74] --> Loop 41 * CEs [76] --> Loop 42 * CEs [69,70,71,72,73] --> Loop 43 ### Ranking functions of CR cond1(V1,V,Out) * RF of phase [40]: [V1] #### Partial ranking functions of CR cond1(V1,V,Out) * Partial RF of phase [40]: - RF of loop [40:1]: V1 ### Specialization of cost equations neq/3 * CE 32 is refined into CE [78] * CE 30 is refined into CE [79] * CE 29 is refined into CE [80] * CE 28 is refined into CE [81] * CE 31 is refined into CE [82] ### Cost equations --> "Loop" of neq/3 * CEs [82] --> Loop 44 * CEs [78] --> Loop 45 * CEs [79] --> Loop 46 * CEs [80] --> Loop 47 * CEs [81] --> Loop 48 ### Ranking functions of CR neq(V1,V,Out) * RF of phase [44]: [V,V1] #### Partial ranking functions of CR neq(V1,V,Out) * Partial RF of phase [44]: - RF of loop [44:1]: V V1 ### Specialization of cost equations encArg/2 * CE 39 is refined into CE [83] * CE 37 is refined into CE [84] * CE 38 is refined into CE [85] * CE 36 is refined into CE [86] * CE 43 is refined into CE [87,88] * CE 40 is refined into CE [89] * CE 41 is refined into CE [90,91,92,93,94] * CE 42 is refined into CE [95,96,97,98,99,100,101] * CE 35 is refined into CE [102] * CE 34 is refined into CE [103,104] * CE 33 is refined into CE [105] ### Cost equations --> "Loop" of encArg/2 * CEs [102] --> Loop 49 * CEs [103,104,105] --> Loop 50 * CEs [94,101] --> Loop 51 * CEs [100] --> Loop 52 * CEs [91,97] --> Loop 53 * CEs [96] --> Loop 54 * CEs [93,99] --> Loop 55 * CEs [90,95] --> Loop 56 * CEs [89,92,98] --> Loop 57 * CEs [86] --> Loop 58 * CEs [88] --> Loop 59 * CEs [87] --> Loop 60 * CEs [83] --> Loop 61 * CEs [84] --> Loop 62 * CEs [85] --> Loop 63 ### Ranking functions of CR encArg(V1,Out) * RF of phase [49,50,51,52,53,54,55,56,57,58,59,60]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [49,50,51,52,53,54,55,56,57,58,59,60]: - RF of loop [49:1,49:2,49:3,50:1,50:2,50:3,51:1,51:2,52:1,52:2,53:1,53:2,54:1,54:2,55:1,55:2,56:1,56:2,57:1,57:2,58:1,59:1,60:1]: V1 ### Specialization of cost equations fun/3 * CE 44 is refined into CE [106,107,108,109,110,111,112,113,114] * CE 45 is refined into CE [115] ### Cost equations --> "Loop" of fun/3 * CEs [107,113] --> Loop 64 * CEs [106,108,109,110,111,112,114,115] --> Loop 65 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun1/2 * CE 46 is refined into CE [116,117,118] * CE 47 is refined into CE [119] ### Cost equations --> "Loop" of fun1/2 * CEs [118] --> Loop 66 * CEs [119] --> Loop 67 * CEs [116,117] --> Loop 68 ### Ranking functions of CR fun1(V1,Out) #### Partial ranking functions of CR fun1(V1,Out) ### Specialization of cost equations fun2/4 * CE 48 is refined into CE [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] * CE 49 is refined into CE [147,148,149,150,151,152,153,154,155,156,157,158,159,160,161] * CE 50 is refined into CE [162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179] * CE 51 is refined into CE [180] ### Cost equations --> "Loop" of fun2/4 * CEs [123,124,125,141,142,143,153,154,155,156,157,158,165,166,167] --> Loop 69 * CEs [121,127,130,136,139,145,149,150,160,163,169,172,178] --> Loop 70 * CEs [120,122,126,128,129,131,132,133,134,135,137,138,140,144,146,147,148,151,152,159,161,162,164,168,170,171,173,174,175,176,177,179,180] --> Loop 71 ### Ranking functions of CR fun2(V1,V,V5,Out) #### Partial ranking functions of CR fun2(V1,V,V5,Out) ### Specialization of cost equations fun3/3 * CE 52 is refined into CE [181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206] * CE 53 is refined into CE [207] ### Cost equations --> "Loop" of fun3/3 * CEs [189] --> Loop 72 * CEs [186,188,203] --> Loop 73 * CEs [187,204] --> Loop 74 * CEs [182,185,191,193,196,199] --> Loop 75 * CEs [181,184,190,195,198,201,205] --> Loop 76 * CEs [183,192,194,197,200,202,206,207] --> Loop 77 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun4/1 * CE 54 is refined into CE [208] * CE 55 is refined into CE [209] ### Cost equations --> "Loop" of fun4/1 * CEs [208] --> Loop 78 * CEs [209] --> Loop 79 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/1 * CE 56 is refined into CE [210] * CE 57 is refined into CE [211] ### Cost equations --> "Loop" of fun5/1 * CEs [210] --> Loop 80 * CEs [211] --> Loop 81 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/2 * CE 58 is refined into CE [212,213,214,215,216] * CE 59 is refined into CE [217] ### Cost equations --> "Loop" of fun6/2 * CEs [213,215] --> Loop 82 * CEs [212,214,216,217] --> Loop 83 ### Ranking functions of CR fun6(V1,Out) #### Partial ranking functions of CR fun6(V1,Out) ### Specialization of cost equations fun8/3 * CE 60 is refined into CE [218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248] * CE 61 is refined into CE [249] ### Cost equations --> "Loop" of fun8/3 * CEs [225,228,229,243,245] --> Loop 84 * CEs [227] --> Loop 85 * CEs [226,246] --> Loop 86 * CEs [219,220,223,224,231,233,236,237,240] --> Loop 87 * CEs [218,222,230,235,239,242,247] --> Loop 88 * CEs [221,232,234,238,241,244,248,249] --> Loop 89 ### Ranking functions of CR fun8(V1,V,Out) #### Partial ranking functions of CR fun8(V1,V,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [250] * CE 2 is refined into CE [251,252] * CE 3 is refined into CE [253] * CE 4 is refined into CE [254] * CE 5 is refined into CE [255,256,257,258,259] * CE 6 is refined into CE [260,261,262,263,264,265,266] * CE 7 is refined into CE [267,268] * CE 8 is refined into CE [269,270,271] * CE 9 is refined into CE [272] * CE 10 is refined into CE [273,274,275] * CE 11 is refined into CE [276,277] * CE 12 is refined into CE [278,279,280] * CE 13 is refined into CE [281,282] * CE 14 is refined into CE [283,284] * CE 15 is refined into CE [285,286] * CE 16 is refined into CE [287,288,289,290] ### Cost equations --> "Loop" of start/3 * CEs [250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290] --> Loop 90 ### Ranking functions of CR start(V1,V,V5) #### Partial ranking functions of CR start(V1,V,V5) Computing Bounds ===================================== #### Cost of chains of p(V1,Out): * Chain [34]: 1 with precondition: [Out=0,V1>=0] * Chain [33]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of gr(V1,V,Out): * Chain [[35],38]: 1*it(35)+1 Such that:it(35) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[35],37]: 1*it(35)+1 Such that:it(35) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[35],36]: 1*it(35)+0 Such that:it(35) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [38]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [37]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [36]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of cond1(V1,V,Out): * Chain [[40],43]: 5*it(40)+2*s(2)+1*s(7)+2 Such that:aux(1) =< V aux(4) =< V1 it(40) =< aux(4) s(2) =< aux(1) s(7) =< it(40)*aux(4) with precondition: [Out=0,V1>=1,V>=V1] * Chain [[40],41,43]: 5*it(40)+2*s(2)+1*s(7)+6 Such that:aux(1) =< V aux(5) =< V1 it(40) =< aux(5) s(2) =< aux(1) s(7) =< it(40)*aux(5) with precondition: [Out=0,V1>=2,V>=V1] * Chain [43]: 2*s(2)+1*s(3)+2 Such that:s(3) =< V1 aux(1) =< V s(2) =< aux(1) with precondition: [Out=0,V1>=0,V>=0] * Chain [42,43]: 5 with precondition: [V=0,Out=0,V1>=1] * Chain [41,43]: 2*s(2)+1*s(8)+6 Such that:s(8) =< V1 aux(1) =< V s(2) =< aux(1) with precondition: [Out=0,V1>=1,V>=V1] * Chain [39,[40],43]: 8*it(40)+1*s(7)+5 Such that:aux(7) =< V it(40) =< aux(7) s(7) =< it(40)*aux(7) with precondition: [Out=0,V>=1,V1>=V+1] * Chain [39,[40],41,43]: 8*it(40)+1*s(7)+9 Such that:aux(8) =< V it(40) =< aux(8) s(7) =< it(40)*aux(8) with precondition: [Out=0,V>=2,V1>=V+1] * Chain [39,43]: 4*s(2)+5 Such that:aux(9) =< V s(2) =< aux(9) with precondition: [Out=0,V>=1,V1>=V+1] * Chain [39,41,43]: 4*s(2)+9 Such that:aux(10) =< V s(2) =< aux(10) with precondition: [Out=0,V>=1,V1>=V+1] #### Cost of chains of neq(V1,V,Out): * Chain [[44],48]: 1*it(44)+1 Such that:it(44) =< V1 with precondition: [Out=1,V1=V,V1>=1] * Chain [[44],47]: 1*it(44)+1 Such that:it(44) =< V1 with precondition: [Out=2,V1>=1,V>=V1+1] * Chain [[44],46]: 1*it(44)+1 Such that:it(44) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[44],45]: 1*it(44)+0 Such that:it(44) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [48]: 1 with precondition: [V1=0,V=0,Out=1] * Chain [47]: 1 with precondition: [V1=0,Out=2,V>=1] * Chain [46]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [45]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of encArg(V1,Out): * Chain [63]: 0 with precondition: [V1=1,Out=1] * Chain [62]: 0 with precondition: [V1=2,Out=2] * Chain [61]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([49,50,51,52,53,54,55,56,57,58,59,60],[[63],[62],[61]])]: 10*it(49)+11*it(50)+2*it(51)+2*it(53)+1*it(55)+10*it(56)+2*it(59)+44*s(90)+4*s(91)+76*s(93)+6*s(94)+2*s(99)+1*s(101)+2*s(102)+14*s(104)+32*s(105)+2*s(106)+2*s(107)+0 Such that:it([63]) =< 2/3*V1+1/3 aux(33) =< V1 aux(34) =< 2*V1+1 aux(35) =< V1/2 aux(36) =< 2/3*V1 aux(37) =< 2/5*V1 aux(38) =< 3/7*V1 it(50) =< aux(33) it(51) =< aux(33) it(53) =< aux(33) it(55) =< aux(33) it(56) =< aux(33) it(59) =< aux(33) it([63]) =< aux(33) it([61]) =< aux(34) it([63]) =< aux(34) it(55) =< aux(35) it(53) =< aux(36) it(55) =< aux(36) it(51) =< aux(37) it(49) =< aux(38) aux(20) =< aux(33)+2 aux(30) =< aux(33)+3 aux(25) =< aux(33)+1 aux(19) =< aux(33) it(55) =< it([61])*(1/2)+aux(35) it(56) =< it([61])*(1/2)+aux(35) it(53) =< it([61])*(1/3)+aux(36) it(55) =< it([61])*(1/3)+aux(36) it(56) =< it([61])*(1/3)+aux(36) it(51) =< it([61])*(3/5)+it([63])*(1/5)+aux(37) it(53) =< it([61])*(3/5)+it([63])*(1/5)+aux(37) it(55) =< it([61])*(3/5)+it([63])*(1/5)+aux(37) it(56) =< it([61])*(3/5)+it([63])*(1/5)+aux(37) it(49) =< it([61])*(2/7)+aux(38) it(50) =< it([61])*(2/7)+aux(38) s(110) =< it(56)*aux(20) s(109) =< it(56)*aux(30) s(103) =< it(55)*aux(25) s(101) =< it(51)*aux(25) s(100) =< it(51)*aux(19) s(97) =< it(50)*aux(20) s(92) =< it(49)*aux(19) s(104) =< s(110) s(105) =< s(109) s(106) =< s(105)*aux(30) s(107) =< s(104)*aux(20) s(102) =< s(103) s(99) =< s(100) s(93) =< s(97) s(94) =< s(93)*aux(20) s(90) =< s(92) s(91) =< s(90)*aux(33) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [65]: 22*s(155)+4*s(156)+4*s(157)+2*s(158)+20*s(159)+28*s(160)+20*s(161)+2*s(169)+28*s(173)+64*s(174)+4*s(175)+4*s(176)+4*s(177)+4*s(178)+152*s(179)+12*s(180)+88*s(181)+8*s(182)+33*s(190)+6*s(191)+6*s(192)+3*s(193)+30*s(194)+102*s(195)+30*s(196)+3*s(204)+42*s(208)+96*s(209)+6*s(210)+6*s(211)+6*s(212)+6*s(213)+228*s(214)+18*s(215)+132*s(216)+12*s(217)+6*s(222)+4*s(223)+68*s(302)+8*s(305)+9 Such that:aux(46) =< 2 aux(47) =< V1 aux(48) =< 2*V1+1 aux(49) =< V1/2 aux(50) =< 2/3*V1 aux(51) =< 2/3*V1+1/3 aux(52) =< 2/5*V1 aux(53) =< 3/7*V1 aux(54) =< V aux(55) =< 2*V+1 aux(56) =< V/2 aux(57) =< 2/3*V aux(58) =< 2/3*V+1/3 aux(59) =< 2/5*V aux(60) =< 3/7*V s(152) =< aux(51) s(187) =< aux(58) s(302) =< aux(46) s(305) =< s(302)*aux(46) s(195) =< aux(54) s(222) =< s(195)*aux(54) s(190) =< aux(54) s(191) =< aux(54) s(192) =< aux(54) s(193) =< aux(54) s(194) =< aux(54) s(187) =< aux(54) s(187) =< aux(55) s(193) =< aux(56) s(192) =< aux(57) s(193) =< aux(57) s(191) =< aux(59) s(196) =< aux(60) s(197) =< aux(54)+2 s(198) =< aux(54)+3 s(199) =< aux(54)+1 s(200) =< aux(54) s(193) =< aux(55)*(1/2)+aux(56) s(194) =< aux(55)*(1/2)+aux(56) s(192) =< aux(55)*(1/3)+aux(57) s(193) =< aux(55)*(1/3)+aux(57) s(194) =< aux(55)*(1/3)+aux(57) s(191) =< aux(55)*(3/5)+s(187)*(1/5)+aux(59) s(192) =< aux(55)*(3/5)+s(187)*(1/5)+aux(59) s(193) =< aux(55)*(3/5)+s(187)*(1/5)+aux(59) s(194) =< aux(55)*(3/5)+s(187)*(1/5)+aux(59) s(196) =< aux(55)*(2/7)+aux(60) s(190) =< aux(55)*(2/7)+aux(60) s(201) =< s(194)*s(197) s(202) =< s(194)*s(198) s(203) =< s(193)*s(199) s(204) =< s(191)*s(199) s(205) =< s(191)*s(200) s(206) =< s(190)*s(197) s(207) =< s(196)*s(200) s(208) =< s(201) s(209) =< s(202) s(210) =< s(209)*s(198) s(211) =< s(208)*s(197) s(212) =< s(203) s(213) =< s(205) s(214) =< s(206) s(215) =< s(214)*s(197) s(216) =< s(207) s(217) =< s(216)*aux(54) s(160) =< aux(47) s(223) =< s(160)*aux(47) s(155) =< aux(47) s(156) =< aux(47) s(157) =< aux(47) s(158) =< aux(47) s(159) =< aux(47) s(152) =< aux(47) s(152) =< aux(48) s(158) =< aux(49) s(157) =< aux(50) s(158) =< aux(50) s(156) =< aux(52) s(161) =< aux(53) s(162) =< aux(47)+2 s(163) =< aux(47)+3 s(164) =< aux(47)+1 s(165) =< aux(47) s(158) =< aux(48)*(1/2)+aux(49) s(159) =< aux(48)*(1/2)+aux(49) s(157) =< aux(48)*(1/3)+aux(50) s(158) =< aux(48)*(1/3)+aux(50) s(159) =< aux(48)*(1/3)+aux(50) s(156) =< aux(48)*(3/5)+s(152)*(1/5)+aux(52) s(157) =< aux(48)*(3/5)+s(152)*(1/5)+aux(52) s(158) =< aux(48)*(3/5)+s(152)*(1/5)+aux(52) s(159) =< aux(48)*(3/5)+s(152)*(1/5)+aux(52) s(161) =< aux(48)*(2/7)+aux(53) s(155) =< aux(48)*(2/7)+aux(53) s(166) =< s(159)*s(162) s(167) =< s(159)*s(163) s(168) =< s(158)*s(164) s(169) =< s(156)*s(164) s(170) =< s(156)*s(165) s(171) =< s(155)*s(162) s(172) =< s(161)*s(165) s(173) =< s(166) s(174) =< s(167) s(175) =< s(174)*s(163) s(176) =< s(173)*s(162) s(177) =< s(168) s(178) =< s(170) s(179) =< s(171) s(180) =< s(179)*s(162) s(181) =< s(172) s(182) =< s(181)*aux(47) with precondition: [Out=0,V1>=0,V>=0] * Chain [64]: 11*s(372)+2*s(373)+2*s(374)+1*s(375)+10*s(376)+14*s(377)+10*s(378)+1*s(386)+14*s(390)+32*s(391)+2*s(392)+2*s(393)+2*s(394)+2*s(395)+76*s(396)+6*s(397)+44*s(398)+4*s(399)+64*s(403)+4*s(404)+2*s(405)+9 Such that:aux(61) =< V1 s(366) =< 2*V1+1 s(367) =< V1/2 s(368) =< 2/3*V1 s(369) =< 2/3*V1+1/3 s(370) =< 2/5*V1 s(371) =< 3/7*V1 aux(62) =< 2 s(377) =< aux(61) s(403) =< aux(62) s(404) =< s(403)*aux(62) s(405) =< s(377)*aux(61) s(372) =< aux(61) s(373) =< aux(61) s(374) =< aux(61) s(375) =< aux(61) s(376) =< aux(61) s(369) =< aux(61) s(369) =< s(366) s(375) =< s(367) s(374) =< s(368) s(375) =< s(368) s(373) =< s(370) s(378) =< s(371) s(379) =< aux(61)+2 s(380) =< aux(61)+3 s(381) =< aux(61)+1 s(382) =< aux(61) s(375) =< s(366)*(1/2)+s(367) s(376) =< s(366)*(1/2)+s(367) s(374) =< s(366)*(1/3)+s(368) s(375) =< s(366)*(1/3)+s(368) s(376) =< s(366)*(1/3)+s(368) s(373) =< s(366)*(3/5)+s(369)*(1/5)+s(370) s(374) =< s(366)*(3/5)+s(369)*(1/5)+s(370) s(375) =< s(366)*(3/5)+s(369)*(1/5)+s(370) s(376) =< s(366)*(3/5)+s(369)*(1/5)+s(370) s(378) =< s(366)*(2/7)+s(371) s(372) =< s(366)*(2/7)+s(371) s(383) =< s(376)*s(379) s(384) =< s(376)*s(380) s(385) =< s(375)*s(381) s(386) =< s(373)*s(381) s(387) =< s(373)*s(382) s(388) =< s(372)*s(379) s(389) =< s(378)*s(382) s(390) =< s(383) s(391) =< s(384) s(392) =< s(391)*s(380) s(393) =< s(390)*s(379) s(394) =< s(385) s(395) =< s(387) s(396) =< s(388) s(397) =< s(396)*s(379) s(398) =< s(389) s(399) =< s(398)*aux(61) with precondition: [V=2,Out=0,V1>=0] #### Cost of chains of fun1(V1,Out): * Chain [68]: 11*s(535)+2*s(536)+2*s(537)+1*s(538)+10*s(539)+2*s(540)+10*s(541)+1*s(549)+14*s(553)+32*s(554)+2*s(555)+2*s(556)+2*s(557)+2*s(558)+76*s(559)+6*s(560)+44*s(561)+4*s(562)+0 Such that:s(528) =< V1 s(529) =< 2*V1+1 s(530) =< V1/2 s(531) =< 2/3*V1 s(532) =< 2/3*V1+1/3 s(533) =< 2/5*V1 s(534) =< 3/7*V1 s(535) =< s(528) s(536) =< s(528) s(537) =< s(528) s(538) =< s(528) s(539) =< s(528) s(540) =< s(528) s(532) =< s(528) s(532) =< s(529) s(538) =< s(530) s(537) =< s(531) s(538) =< s(531) s(536) =< s(533) s(541) =< s(534) s(542) =< s(528)+2 s(543) =< s(528)+3 s(544) =< s(528)+1 s(545) =< s(528) s(538) =< s(529)*(1/2)+s(530) s(539) =< s(529)*(1/2)+s(530) s(537) =< s(529)*(1/3)+s(531) s(538) =< s(529)*(1/3)+s(531) s(539) =< s(529)*(1/3)+s(531) s(536) =< s(529)*(3/5)+s(532)*(1/5)+s(533) s(537) =< s(529)*(3/5)+s(532)*(1/5)+s(533) s(538) =< s(529)*(3/5)+s(532)*(1/5)+s(533) s(539) =< s(529)*(3/5)+s(532)*(1/5)+s(533) s(541) =< s(529)*(2/7)+s(534) s(535) =< s(529)*(2/7)+s(534) s(546) =< s(539)*s(542) s(547) =< s(539)*s(543) s(548) =< s(538)*s(544) s(549) =< s(536)*s(544) s(550) =< s(536)*s(545) s(551) =< s(535)*s(542) s(552) =< s(541)*s(545) s(553) =< s(546) s(554) =< s(547) s(555) =< s(554)*s(543) s(556) =< s(553)*s(542) s(557) =< s(548) s(558) =< s(550) s(559) =< s(551) s(560) =< s(559)*s(542) s(561) =< s(552) s(562) =< s(561)*s(528) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [67]: 0 with precondition: [Out=0,V1>=0] * Chain [66]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun2(V1,V,V5,Out): * Chain [71]: 154*s(570)+28*s(571)+28*s(572)+14*s(573)+140*s(574)+28*s(575)+140*s(576)+14*s(584)+196*s(588)+448*s(589)+28*s(590)+28*s(591)+28*s(592)+28*s(593)+1064*s(594)+84*s(595)+616*s(596)+56*s(597)+154*s(605)+28*s(606)+28*s(607)+14*s(608)+140*s(609)+52*s(610)+140*s(611)+14*s(619)+196*s(623)+448*s(624)+28*s(625)+28*s(626)+28*s(627)+28*s(628)+1064*s(629)+84*s(630)+616*s(631)+56*s(632)+165*s(640)+30*s(641)+30*s(642)+15*s(643)+150*s(644)+346*s(645)+150*s(646)+15*s(654)+210*s(658)+480*s(659)+30*s(660)+30*s(661)+30*s(662)+30*s(663)+1140*s(664)+90*s(665)+660*s(666)+60*s(667)+26*s(1267)+4*s(1379)+44*s(2113)+4*s(2115)+11 Such that:aux(85) =< 2 aux(89) =< V1 aux(90) =< 2*V1+1 aux(91) =< V1/2 aux(92) =< 2/3*V1 aux(93) =< 2/3*V1+1/3 aux(94) =< 2/5*V1 aux(95) =< 3/7*V1 aux(96) =< V aux(97) =< 2*V+1 aux(98) =< V/2 aux(99) =< 2/3*V aux(100) =< 2/3*V+1/3 aux(101) =< 2/5*V aux(102) =< 3/7*V aux(103) =< V5 aux(104) =< 2*V5+1 aux(105) =< V5/2 aux(106) =< 2/3*V5 aux(107) =< 2/3*V5+1/3 aux(108) =< 2/5*V5 aux(109) =< 3/7*V5 s(567) =< aux(93) s(602) =< aux(100) s(637) =< aux(107) s(2113) =< aux(85) s(2115) =< s(2113)*aux(85) s(640) =< aux(103) s(641) =< aux(103) s(642) =< aux(103) s(643) =< aux(103) s(644) =< aux(103) s(645) =< aux(103) s(637) =< aux(103) s(637) =< aux(104) s(643) =< aux(105) s(642) =< aux(106) s(643) =< aux(106) s(641) =< aux(108) s(646) =< aux(109) s(647) =< aux(103)+2 s(648) =< aux(103)+3 s(649) =< aux(103)+1 s(650) =< aux(103) s(643) =< aux(104)*(1/2)+aux(105) s(644) =< aux(104)*(1/2)+aux(105) s(642) =< aux(104)*(1/3)+aux(106) s(643) =< aux(104)*(1/3)+aux(106) s(644) =< aux(104)*(1/3)+aux(106) s(641) =< aux(104)*(3/5)+s(637)*(1/5)+aux(108) s(642) =< aux(104)*(3/5)+s(637)*(1/5)+aux(108) s(643) =< aux(104)*(3/5)+s(637)*(1/5)+aux(108) s(644) =< aux(104)*(3/5)+s(637)*(1/5)+aux(108) s(646) =< aux(104)*(2/7)+aux(109) s(640) =< aux(104)*(2/7)+aux(109) s(651) =< s(644)*s(647) s(652) =< s(644)*s(648) s(653) =< s(643)*s(649) s(654) =< s(641)*s(649) s(655) =< s(641)*s(650) s(656) =< s(640)*s(647) s(657) =< s(646)*s(650) s(658) =< s(651) s(659) =< s(652) s(660) =< s(659)*s(648) s(661) =< s(658)*s(647) s(662) =< s(653) s(663) =< s(655) s(664) =< s(656) s(665) =< s(664)*s(647) s(666) =< s(657) s(667) =< s(666)*aux(103) s(605) =< aux(96) s(606) =< aux(96) s(607) =< aux(96) s(608) =< aux(96) s(609) =< aux(96) s(610) =< aux(96) s(602) =< aux(96) s(602) =< aux(97) s(608) =< aux(98) s(607) =< aux(99) s(608) =< aux(99) s(606) =< aux(101) s(611) =< aux(102) s(612) =< aux(96)+2 s(613) =< aux(96)+3 s(614) =< aux(96)+1 s(615) =< aux(96) s(608) =< aux(97)*(1/2)+aux(98) s(609) =< aux(97)*(1/2)+aux(98) s(607) =< aux(97)*(1/3)+aux(99) s(608) =< aux(97)*(1/3)+aux(99) s(609) =< aux(97)*(1/3)+aux(99) s(606) =< aux(97)*(3/5)+s(602)*(1/5)+aux(101) s(607) =< aux(97)*(3/5)+s(602)*(1/5)+aux(101) s(608) =< aux(97)*(3/5)+s(602)*(1/5)+aux(101) s(609) =< aux(97)*(3/5)+s(602)*(1/5)+aux(101) s(611) =< aux(97)*(2/7)+aux(102) s(605) =< aux(97)*(2/7)+aux(102) s(616) =< s(609)*s(612) s(617) =< s(609)*s(613) s(618) =< s(608)*s(614) s(619) =< s(606)*s(614) s(620) =< s(606)*s(615) s(621) =< s(605)*s(612) s(622) =< s(611)*s(615) s(623) =< s(616) s(624) =< s(617) s(625) =< s(624)*s(613) s(626) =< s(623)*s(612) s(627) =< s(618) s(628) =< s(620) s(629) =< s(621) s(630) =< s(629)*s(612) s(631) =< s(622) s(632) =< s(631)*aux(96) s(570) =< aux(89) s(571) =< aux(89) s(572) =< aux(89) s(573) =< aux(89) s(574) =< aux(89) s(575) =< aux(89) s(567) =< aux(89) s(567) =< aux(90) s(573) =< aux(91) s(572) =< aux(92) s(573) =< aux(92) s(571) =< aux(94) s(576) =< aux(95) s(577) =< aux(89)+2 s(578) =< aux(89)+3 s(579) =< aux(89)+1 s(580) =< aux(89) s(573) =< aux(90)*(1/2)+aux(91) s(574) =< aux(90)*(1/2)+aux(91) s(572) =< aux(90)*(1/3)+aux(92) s(573) =< aux(90)*(1/3)+aux(92) s(574) =< aux(90)*(1/3)+aux(92) s(571) =< aux(90)*(3/5)+s(567)*(1/5)+aux(94) s(572) =< aux(90)*(3/5)+s(567)*(1/5)+aux(94) s(573) =< aux(90)*(3/5)+s(567)*(1/5)+aux(94) s(574) =< aux(90)*(3/5)+s(567)*(1/5)+aux(94) s(576) =< aux(90)*(2/7)+aux(95) s(570) =< aux(90)*(2/7)+aux(95) s(581) =< s(574)*s(577) s(582) =< s(574)*s(578) s(583) =< s(573)*s(579) s(584) =< s(571)*s(579) s(585) =< s(571)*s(580) s(586) =< s(570)*s(577) s(587) =< s(576)*s(580) s(588) =< s(581) s(589) =< s(582) s(590) =< s(589)*s(578) s(591) =< s(588)*s(577) s(592) =< s(583) s(593) =< s(585) s(594) =< s(586) s(595) =< s(594)*s(577) s(596) =< s(587) s(597) =< s(596)*aux(89) s(1267) =< s(645)*aux(103) s(1379) =< s(610)*aux(96) with precondition: [Out=0,V1>=0,V>=0,V5>=0] * Chain [70]: 77*s(2177)+14*s(2178)+14*s(2179)+7*s(2180)+70*s(2181)+14*s(2182)+70*s(2183)+7*s(2191)+98*s(2195)+224*s(2196)+14*s(2197)+14*s(2198)+14*s(2199)+14*s(2200)+532*s(2201)+42*s(2202)+308*s(2203)+28*s(2204)+77*s(2212)+14*s(2213)+14*s(2214)+7*s(2215)+70*s(2216)+26*s(2217)+70*s(2218)+7*s(2226)+98*s(2230)+224*s(2231)+14*s(2232)+14*s(2233)+14*s(2234)+14*s(2235)+532*s(2236)+42*s(2237)+308*s(2238)+28*s(2239)+272*s(2418)+22*s(2419)+2*s(2496)+11 Such that:aux(115) =< 2 aux(116) =< V1 aux(117) =< 2*V1+1 aux(118) =< V1/2 aux(119) =< 2/3*V1 aux(120) =< 2/3*V1+1/3 aux(121) =< 2/5*V1 aux(122) =< 3/7*V1 aux(123) =< V aux(124) =< 2*V+1 aux(125) =< V/2 aux(126) =< 2/3*V aux(127) =< 2/3*V+1/3 aux(128) =< 2/5*V aux(129) =< 3/7*V s(2174) =< aux(120) s(2209) =< aux(127) s(2418) =< aux(115) s(2419) =< s(2418)*aux(115) s(2212) =< aux(123) s(2213) =< aux(123) s(2214) =< aux(123) s(2215) =< aux(123) s(2216) =< aux(123) s(2217) =< aux(123) s(2209) =< aux(123) s(2209) =< aux(124) s(2215) =< aux(125) s(2214) =< aux(126) s(2215) =< aux(126) s(2213) =< aux(128) s(2218) =< aux(129) s(2219) =< aux(123)+2 s(2220) =< aux(123)+3 s(2221) =< aux(123)+1 s(2222) =< aux(123) s(2215) =< aux(124)*(1/2)+aux(125) s(2216) =< aux(124)*(1/2)+aux(125) s(2214) =< aux(124)*(1/3)+aux(126) s(2215) =< aux(124)*(1/3)+aux(126) s(2216) =< aux(124)*(1/3)+aux(126) s(2213) =< aux(124)*(3/5)+s(2209)*(1/5)+aux(128) s(2214) =< aux(124)*(3/5)+s(2209)*(1/5)+aux(128) s(2215) =< aux(124)*(3/5)+s(2209)*(1/5)+aux(128) s(2216) =< aux(124)*(3/5)+s(2209)*(1/5)+aux(128) s(2218) =< aux(124)*(2/7)+aux(129) s(2212) =< aux(124)*(2/7)+aux(129) s(2223) =< s(2216)*s(2219) s(2224) =< s(2216)*s(2220) s(2225) =< s(2215)*s(2221) s(2226) =< s(2213)*s(2221) s(2227) =< s(2213)*s(2222) s(2228) =< s(2212)*s(2219) s(2229) =< s(2218)*s(2222) s(2230) =< s(2223) s(2231) =< s(2224) s(2232) =< s(2231)*s(2220) s(2233) =< s(2230)*s(2219) s(2234) =< s(2225) s(2235) =< s(2227) s(2236) =< s(2228) s(2237) =< s(2236)*s(2219) s(2238) =< s(2229) s(2239) =< s(2238)*aux(123) s(2177) =< aux(116) s(2178) =< aux(116) s(2179) =< aux(116) s(2180) =< aux(116) s(2181) =< aux(116) s(2182) =< aux(116) s(2174) =< aux(116) s(2174) =< aux(117) s(2180) =< aux(118) s(2179) =< aux(119) s(2180) =< aux(119) s(2178) =< aux(121) s(2183) =< aux(122) s(2184) =< aux(116)+2 s(2185) =< aux(116)+3 s(2186) =< aux(116)+1 s(2187) =< aux(116) s(2180) =< aux(117)*(1/2)+aux(118) s(2181) =< aux(117)*(1/2)+aux(118) s(2179) =< aux(117)*(1/3)+aux(119) s(2180) =< aux(117)*(1/3)+aux(119) s(2181) =< aux(117)*(1/3)+aux(119) s(2178) =< aux(117)*(3/5)+s(2174)*(1/5)+aux(121) s(2179) =< aux(117)*(3/5)+s(2174)*(1/5)+aux(121) s(2180) =< aux(117)*(3/5)+s(2174)*(1/5)+aux(121) s(2181) =< aux(117)*(3/5)+s(2174)*(1/5)+aux(121) s(2183) =< aux(117)*(2/7)+aux(122) s(2177) =< aux(117)*(2/7)+aux(122) s(2188) =< s(2181)*s(2184) s(2189) =< s(2181)*s(2185) s(2190) =< s(2180)*s(2186) s(2191) =< s(2178)*s(2186) s(2192) =< s(2178)*s(2187) s(2193) =< s(2177)*s(2184) s(2194) =< s(2183)*s(2187) s(2195) =< s(2188) s(2196) =< s(2189) s(2197) =< s(2196)*s(2185) s(2198) =< s(2195)*s(2184) s(2199) =< s(2190) s(2200) =< s(2192) s(2201) =< s(2193) s(2202) =< s(2201)*s(2184) s(2203) =< s(2194) s(2204) =< s(2203)*aux(116) s(2496) =< s(2217)*aux(123) with precondition: [V5=2,Out=0,V1>=0,V>=0] * Chain [69]: 132*s(2709)+24*s(2710)+24*s(2711)+12*s(2712)+120*s(2713)+24*s(2714)+120*s(2715)+12*s(2723)+168*s(2727)+384*s(2728)+24*s(2729)+24*s(2730)+24*s(2731)+24*s(2732)+912*s(2733)+72*s(2734)+528*s(2735)+48*s(2736)+55*s(2744)+10*s(2745)+10*s(2746)+5*s(2747)+50*s(2748)+118*s(2749)+50*s(2750)+5*s(2758)+70*s(2762)+160*s(2763)+10*s(2764)+10*s(2765)+10*s(2766)+10*s(2767)+380*s(2768)+30*s(2769)+220*s(2770)+20*s(2771)+8*s(2951)+36*s(3025)+6*s(3028)+108*s(3067)+8*s(3068)+11 Such that:aux(136) =< 1 aux(137) =< 2 aux(138) =< V1 aux(139) =< 2*V1+1 aux(140) =< V1/2 aux(141) =< 2/3*V1 aux(142) =< 2/3*V1+1/3 aux(143) =< 2/5*V1 aux(144) =< 3/7*V1 aux(145) =< V5 aux(146) =< 2*V5+1 aux(147) =< V5/2 aux(148) =< 2/3*V5 aux(149) =< 2/3*V5+1/3 aux(150) =< 2/5*V5 aux(151) =< 3/7*V5 s(2706) =< aux(142) s(2741) =< aux(149) s(3025) =< aux(136) s(2749) =< aux(145) s(2951) =< s(2749)*aux(145) s(3028) =< s(3025)*aux(136) s(2744) =< aux(145) s(2745) =< aux(145) s(2746) =< aux(145) s(2747) =< aux(145) s(2748) =< aux(145) s(2741) =< aux(145) s(2741) =< aux(146) s(2747) =< aux(147) s(2746) =< aux(148) s(2747) =< aux(148) s(2745) =< aux(150) s(2750) =< aux(151) s(2751) =< aux(145)+2 s(2752) =< aux(145)+3 s(2753) =< aux(145)+1 s(2754) =< aux(145) s(2747) =< aux(146)*(1/2)+aux(147) s(2748) =< aux(146)*(1/2)+aux(147) s(2746) =< aux(146)*(1/3)+aux(148) s(2747) =< aux(146)*(1/3)+aux(148) s(2748) =< aux(146)*(1/3)+aux(148) s(2745) =< aux(146)*(3/5)+s(2741)*(1/5)+aux(150) s(2746) =< aux(146)*(3/5)+s(2741)*(1/5)+aux(150) s(2747) =< aux(146)*(3/5)+s(2741)*(1/5)+aux(150) s(2748) =< aux(146)*(3/5)+s(2741)*(1/5)+aux(150) s(2750) =< aux(146)*(2/7)+aux(151) s(2744) =< aux(146)*(2/7)+aux(151) s(2755) =< s(2748)*s(2751) s(2756) =< s(2748)*s(2752) s(2757) =< s(2747)*s(2753) s(2758) =< s(2745)*s(2753) s(2759) =< s(2745)*s(2754) s(2760) =< s(2744)*s(2751) s(2761) =< s(2750)*s(2754) s(2762) =< s(2755) s(2763) =< s(2756) s(2764) =< s(2763)*s(2752) s(2765) =< s(2762)*s(2751) s(2766) =< s(2757) s(2767) =< s(2759) s(2768) =< s(2760) s(2769) =< s(2768)*s(2751) s(2770) =< s(2761) s(2771) =< s(2770)*aux(145) s(2709) =< aux(138) s(2710) =< aux(138) s(2711) =< aux(138) s(2712) =< aux(138) s(2713) =< aux(138) s(2714) =< aux(138) s(2706) =< aux(138) s(2706) =< aux(139) s(2712) =< aux(140) s(2711) =< aux(141) s(2712) =< aux(141) s(2710) =< aux(143) s(2715) =< aux(144) s(2716) =< aux(138)+2 s(2717) =< aux(138)+3 s(2718) =< aux(138)+1 s(2719) =< aux(138) s(2712) =< aux(139)*(1/2)+aux(140) s(2713) =< aux(139)*(1/2)+aux(140) s(2711) =< aux(139)*(1/3)+aux(141) s(2712) =< aux(139)*(1/3)+aux(141) s(2713) =< aux(139)*(1/3)+aux(141) s(2710) =< aux(139)*(3/5)+s(2706)*(1/5)+aux(143) s(2711) =< aux(139)*(3/5)+s(2706)*(1/5)+aux(143) s(2712) =< aux(139)*(3/5)+s(2706)*(1/5)+aux(143) s(2713) =< aux(139)*(3/5)+s(2706)*(1/5)+aux(143) s(2715) =< aux(139)*(2/7)+aux(144) s(2709) =< aux(139)*(2/7)+aux(144) s(2720) =< s(2713)*s(2716) s(2721) =< s(2713)*s(2717) s(2722) =< s(2712)*s(2718) s(2723) =< s(2710)*s(2718) s(2724) =< s(2710)*s(2719) s(2725) =< s(2709)*s(2716) s(2726) =< s(2715)*s(2719) s(2727) =< s(2720) s(2728) =< s(2721) s(2729) =< s(2728)*s(2717) s(2730) =< s(2727)*s(2716) s(2731) =< s(2722) s(2732) =< s(2724) s(2733) =< s(2725) s(2734) =< s(2733)*s(2716) s(2735) =< s(2726) s(2736) =< s(2735)*aux(138) s(3067) =< aux(137) s(3068) =< s(3067)*aux(137) with precondition: [V=2,Out=0,V1>=0,V5>=0] #### Cost of chains of fun3(V1,V,Out): * Chain [77]: 22*s(3550)+4*s(3551)+4*s(3552)+2*s(3553)+20*s(3554)+4*s(3555)+20*s(3556)+2*s(3564)+28*s(3568)+64*s(3569)+4*s(3570)+4*s(3571)+4*s(3572)+4*s(3573)+152*s(3574)+12*s(3575)+88*s(3576)+8*s(3577)+33*s(3585)+6*s(3586)+6*s(3587)+3*s(3588)+30*s(3589)+9*s(3590)+30*s(3591)+3*s(3599)+42*s(3603)+96*s(3604)+6*s(3605)+6*s(3606)+6*s(3607)+6*s(3608)+228*s(3609)+18*s(3610)+132*s(3611)+12*s(3612)+1*s(3686)+0 Such that:s(3686) =< 2 aux(170) =< V1 aux(171) =< 2*V1+1 aux(172) =< V1/2 aux(173) =< 2/3*V1 aux(174) =< 2/3*V1+1/3 aux(175) =< 2/5*V1 aux(176) =< 3/7*V1 aux(177) =< V aux(178) =< 2*V+1 aux(179) =< V/2 aux(180) =< 2/3*V aux(181) =< 2/3*V+1/3 aux(182) =< 2/5*V aux(183) =< 3/7*V s(3547) =< aux(174) s(3582) =< aux(181) s(3590) =< aux(177) s(3585) =< aux(177) s(3586) =< aux(177) s(3587) =< aux(177) s(3588) =< aux(177) s(3589) =< aux(177) s(3582) =< aux(177) s(3582) =< aux(178) s(3588) =< aux(179) s(3587) =< aux(180) s(3588) =< aux(180) s(3586) =< aux(182) s(3591) =< aux(183) s(3592) =< aux(177)+2 s(3593) =< aux(177)+3 s(3594) =< aux(177)+1 s(3595) =< aux(177) s(3588) =< aux(178)*(1/2)+aux(179) s(3589) =< aux(178)*(1/2)+aux(179) s(3587) =< aux(178)*(1/3)+aux(180) s(3588) =< aux(178)*(1/3)+aux(180) s(3589) =< aux(178)*(1/3)+aux(180) s(3586) =< aux(178)*(3/5)+s(3582)*(1/5)+aux(182) s(3587) =< aux(178)*(3/5)+s(3582)*(1/5)+aux(182) s(3588) =< aux(178)*(3/5)+s(3582)*(1/5)+aux(182) s(3589) =< aux(178)*(3/5)+s(3582)*(1/5)+aux(182) s(3591) =< aux(178)*(2/7)+aux(183) s(3585) =< aux(178)*(2/7)+aux(183) s(3596) =< s(3589)*s(3592) s(3597) =< s(3589)*s(3593) s(3598) =< s(3588)*s(3594) s(3599) =< s(3586)*s(3594) s(3600) =< s(3586)*s(3595) s(3601) =< s(3585)*s(3592) s(3602) =< s(3591)*s(3595) s(3603) =< s(3596) s(3604) =< s(3597) s(3605) =< s(3604)*s(3593) s(3606) =< s(3603)*s(3592) s(3607) =< s(3598) s(3608) =< s(3600) s(3609) =< s(3601) s(3610) =< s(3609)*s(3592) s(3611) =< s(3602) s(3612) =< s(3611)*aux(177) s(3550) =< aux(170) s(3551) =< aux(170) s(3552) =< aux(170) s(3553) =< aux(170) s(3554) =< aux(170) s(3555) =< aux(170) s(3547) =< aux(170) s(3547) =< aux(171) s(3553) =< aux(172) s(3552) =< aux(173) s(3553) =< aux(173) s(3551) =< aux(175) s(3556) =< aux(176) s(3557) =< aux(170)+2 s(3558) =< aux(170)+3 s(3559) =< aux(170)+1 s(3560) =< aux(170) s(3553) =< aux(171)*(1/2)+aux(172) s(3554) =< aux(171)*(1/2)+aux(172) s(3552) =< aux(171)*(1/3)+aux(173) s(3553) =< aux(171)*(1/3)+aux(173) s(3554) =< aux(171)*(1/3)+aux(173) s(3551) =< aux(171)*(3/5)+s(3547)*(1/5)+aux(175) s(3552) =< aux(171)*(3/5)+s(3547)*(1/5)+aux(175) s(3553) =< aux(171)*(3/5)+s(3547)*(1/5)+aux(175) s(3554) =< aux(171)*(3/5)+s(3547)*(1/5)+aux(175) s(3556) =< aux(171)*(2/7)+aux(176) s(3550) =< aux(171)*(2/7)+aux(176) s(3561) =< s(3554)*s(3557) s(3562) =< s(3554)*s(3558) s(3563) =< s(3553)*s(3559) s(3564) =< s(3551)*s(3559) s(3565) =< s(3551)*s(3560) s(3566) =< s(3550)*s(3557) s(3567) =< s(3556)*s(3560) s(3568) =< s(3561) s(3569) =< s(3562) s(3570) =< s(3569)*s(3558) s(3571) =< s(3568)*s(3557) s(3572) =< s(3563) s(3573) =< s(3565) s(3574) =< s(3566) s(3575) =< s(3574)*s(3557) s(3576) =< s(3567) s(3577) =< s(3576)*aux(170) with precondition: [Out=0,V1>=0,V>=0] * Chain [76]: 33*s(3732)+6*s(3733)+6*s(3734)+3*s(3735)+30*s(3736)+6*s(3737)+30*s(3738)+3*s(3746)+42*s(3750)+96*s(3751)+6*s(3752)+6*s(3753)+6*s(3754)+6*s(3755)+228*s(3756)+18*s(3757)+132*s(3758)+12*s(3759)+44*s(3767)+8*s(3768)+8*s(3769)+4*s(3770)+40*s(3771)+9*s(3772)+40*s(3773)+4*s(3781)+56*s(3785)+128*s(3786)+8*s(3787)+8*s(3788)+8*s(3789)+8*s(3790)+304*s(3791)+24*s(3792)+176*s(3793)+16*s(3794)+2*s(3936)+1 Such that:aux(185) =< 2 aux(186) =< V1 aux(187) =< 2*V1+1 aux(188) =< V1/2 aux(189) =< 2/3*V1 aux(190) =< 2/3*V1+1/3 aux(191) =< 2/5*V1 aux(192) =< 3/7*V1 aux(193) =< V aux(194) =< 2*V+1 aux(195) =< V/2 aux(196) =< 2/3*V aux(197) =< 2/3*V+1/3 aux(198) =< 2/5*V aux(199) =< 3/7*V s(3936) =< aux(185) s(3729) =< aux(190) s(3764) =< aux(197) s(3767) =< aux(193) s(3768) =< aux(193) s(3769) =< aux(193) s(3770) =< aux(193) s(3771) =< aux(193) s(3772) =< aux(193) s(3764) =< aux(193) s(3764) =< aux(194) s(3770) =< aux(195) s(3769) =< aux(196) s(3770) =< aux(196) s(3768) =< aux(198) s(3773) =< aux(199) s(3774) =< aux(193)+2 s(3775) =< aux(193)+3 s(3776) =< aux(193)+1 s(3777) =< aux(193) s(3770) =< aux(194)*(1/2)+aux(195) s(3771) =< aux(194)*(1/2)+aux(195) s(3769) =< aux(194)*(1/3)+aux(196) s(3770) =< aux(194)*(1/3)+aux(196) s(3771) =< aux(194)*(1/3)+aux(196) s(3768) =< aux(194)*(3/5)+s(3764)*(1/5)+aux(198) s(3769) =< aux(194)*(3/5)+s(3764)*(1/5)+aux(198) s(3770) =< aux(194)*(3/5)+s(3764)*(1/5)+aux(198) s(3771) =< aux(194)*(3/5)+s(3764)*(1/5)+aux(198) s(3773) =< aux(194)*(2/7)+aux(199) s(3767) =< aux(194)*(2/7)+aux(199) s(3778) =< s(3771)*s(3774) s(3779) =< s(3771)*s(3775) s(3780) =< s(3770)*s(3776) s(3781) =< s(3768)*s(3776) s(3782) =< s(3768)*s(3777) s(3783) =< s(3767)*s(3774) s(3784) =< s(3773)*s(3777) s(3785) =< s(3778) s(3786) =< s(3779) s(3787) =< s(3786)*s(3775) s(3788) =< s(3785)*s(3774) s(3789) =< s(3780) s(3790) =< s(3782) s(3791) =< s(3783) s(3792) =< s(3791)*s(3774) s(3793) =< s(3784) s(3794) =< s(3793)*aux(193) s(3732) =< aux(186) s(3733) =< aux(186) s(3734) =< aux(186) s(3735) =< aux(186) s(3736) =< aux(186) s(3737) =< aux(186) s(3729) =< aux(186) s(3729) =< aux(187) s(3735) =< aux(188) s(3734) =< aux(189) s(3735) =< aux(189) s(3733) =< aux(191) s(3738) =< aux(192) s(3739) =< aux(186)+2 s(3740) =< aux(186)+3 s(3741) =< aux(186)+1 s(3742) =< aux(186) s(3735) =< aux(187)*(1/2)+aux(188) s(3736) =< aux(187)*(1/2)+aux(188) s(3734) =< aux(187)*(1/3)+aux(189) s(3735) =< aux(187)*(1/3)+aux(189) s(3736) =< aux(187)*(1/3)+aux(189) s(3733) =< aux(187)*(3/5)+s(3729)*(1/5)+aux(191) s(3734) =< aux(187)*(3/5)+s(3729)*(1/5)+aux(191) s(3735) =< aux(187)*(3/5)+s(3729)*(1/5)+aux(191) s(3736) =< aux(187)*(3/5)+s(3729)*(1/5)+aux(191) s(3738) =< aux(187)*(2/7)+aux(192) s(3732) =< aux(187)*(2/7)+aux(192) s(3743) =< s(3736)*s(3739) s(3744) =< s(3736)*s(3740) s(3745) =< s(3735)*s(3741) s(3746) =< s(3733)*s(3741) s(3747) =< s(3733)*s(3742) s(3748) =< s(3732)*s(3739) s(3749) =< s(3738)*s(3742) s(3750) =< s(3743) s(3751) =< s(3744) s(3752) =< s(3751)*s(3740) s(3753) =< s(3750)*s(3739) s(3754) =< s(3745) s(3755) =< s(3747) s(3756) =< s(3748) s(3757) =< s(3756)*s(3739) s(3758) =< s(3749) s(3759) =< s(3758)*aux(186) with precondition: [Out=1,V1>=0,V>=0] * Chain [75]: 33*s(3980)+6*s(3981)+6*s(3982)+3*s(3983)+30*s(3984)+6*s(3985)+30*s(3986)+3*s(3994)+42*s(3998)+96*s(3999)+6*s(4000)+6*s(4001)+6*s(4002)+6*s(4003)+228*s(4004)+18*s(4005)+132*s(4006)+12*s(4007)+44*s(4015)+8*s(4016)+8*s(4017)+4*s(4018)+40*s(4019)+9*s(4020)+40*s(4021)+4*s(4029)+56*s(4033)+128*s(4034)+8*s(4035)+8*s(4036)+8*s(4037)+8*s(4038)+304*s(4039)+24*s(4040)+176*s(4041)+16*s(4042)+1*s(4219)+1 Such that:s(4219) =< 1 aux(201) =< V1 aux(202) =< 2*V1+1 aux(203) =< V1/2 aux(204) =< 2/3*V1 aux(205) =< 2/3*V1+1/3 aux(206) =< 2/5*V1 aux(207) =< 3/7*V1 aux(208) =< V aux(209) =< 2*V+1 aux(210) =< V/2 aux(211) =< 2/3*V aux(212) =< 2/3*V+1/3 aux(213) =< 2/5*V aux(214) =< 3/7*V s(3977) =< aux(205) s(4012) =< aux(212) s(4015) =< aux(208) s(4016) =< aux(208) s(4017) =< aux(208) s(4018) =< aux(208) s(4019) =< aux(208) s(4020) =< aux(208) s(4012) =< aux(208) s(4012) =< aux(209) s(4018) =< aux(210) s(4017) =< aux(211) s(4018) =< aux(211) s(4016) =< aux(213) s(4021) =< aux(214) s(4022) =< aux(208)+2 s(4023) =< aux(208)+3 s(4024) =< aux(208)+1 s(4025) =< aux(208) s(4018) =< aux(209)*(1/2)+aux(210) s(4019) =< aux(209)*(1/2)+aux(210) s(4017) =< aux(209)*(1/3)+aux(211) s(4018) =< aux(209)*(1/3)+aux(211) s(4019) =< aux(209)*(1/3)+aux(211) s(4016) =< aux(209)*(3/5)+s(4012)*(1/5)+aux(213) s(4017) =< aux(209)*(3/5)+s(4012)*(1/5)+aux(213) s(4018) =< aux(209)*(3/5)+s(4012)*(1/5)+aux(213) s(4019) =< aux(209)*(3/5)+s(4012)*(1/5)+aux(213) s(4021) =< aux(209)*(2/7)+aux(214) s(4015) =< aux(209)*(2/7)+aux(214) s(4026) =< s(4019)*s(4022) s(4027) =< s(4019)*s(4023) s(4028) =< s(4018)*s(4024) s(4029) =< s(4016)*s(4024) s(4030) =< s(4016)*s(4025) s(4031) =< s(4015)*s(4022) s(4032) =< s(4021)*s(4025) s(4033) =< s(4026) s(4034) =< s(4027) s(4035) =< s(4034)*s(4023) s(4036) =< s(4033)*s(4022) s(4037) =< s(4028) s(4038) =< s(4030) s(4039) =< s(4031) s(4040) =< s(4039)*s(4022) s(4041) =< s(4032) s(4042) =< s(4041)*aux(208) s(3980) =< aux(201) s(3981) =< aux(201) s(3982) =< aux(201) s(3983) =< aux(201) s(3984) =< aux(201) s(3985) =< aux(201) s(3977) =< aux(201) s(3977) =< aux(202) s(3983) =< aux(203) s(3982) =< aux(204) s(3983) =< aux(204) s(3981) =< aux(206) s(3986) =< aux(207) s(3987) =< aux(201)+2 s(3988) =< aux(201)+3 s(3989) =< aux(201)+1 s(3990) =< aux(201) s(3983) =< aux(202)*(1/2)+aux(203) s(3984) =< aux(202)*(1/2)+aux(203) s(3982) =< aux(202)*(1/3)+aux(204) s(3983) =< aux(202)*(1/3)+aux(204) s(3984) =< aux(202)*(1/3)+aux(204) s(3981) =< aux(202)*(3/5)+s(3977)*(1/5)+aux(206) s(3982) =< aux(202)*(3/5)+s(3977)*(1/5)+aux(206) s(3983) =< aux(202)*(3/5)+s(3977)*(1/5)+aux(206) s(3984) =< aux(202)*(3/5)+s(3977)*(1/5)+aux(206) s(3986) =< aux(202)*(2/7)+aux(207) s(3980) =< aux(202)*(2/7)+aux(207) s(3991) =< s(3984)*s(3987) s(3992) =< s(3984)*s(3988) s(3993) =< s(3983)*s(3989) s(3994) =< s(3981)*s(3989) s(3995) =< s(3981)*s(3990) s(3996) =< s(3980)*s(3987) s(3997) =< s(3986)*s(3990) s(3998) =< s(3991) s(3999) =< s(3992) s(4000) =< s(3999)*s(3988) s(4001) =< s(3998)*s(3987) s(4002) =< s(3993) s(4003) =< s(3995) s(4004) =< s(3996) s(4005) =< s(4004)*s(3987) s(4006) =< s(3997) s(4007) =< s(4006)*aux(201) with precondition: [Out=2,V1>=1,V>=0] * Chain [74]: 11*s(4227)+2*s(4228)+2*s(4229)+1*s(4230)+10*s(4231)+2*s(4232)+10*s(4233)+1*s(4241)+14*s(4245)+32*s(4246)+2*s(4247)+2*s(4248)+2*s(4249)+2*s(4250)+76*s(4251)+6*s(4252)+44*s(4253)+4*s(4254)+2*s(4255)+0 Such that:s(4220) =< V1 s(4221) =< 2*V1+1 s(4222) =< V1/2 s(4223) =< 2/3*V1 s(4224) =< 2/3*V1+1/3 s(4225) =< 2/5*V1 s(4226) =< 3/7*V1 aux(215) =< 2 s(4255) =< aux(215) s(4227) =< s(4220) s(4228) =< s(4220) s(4229) =< s(4220) s(4230) =< s(4220) s(4231) =< s(4220) s(4232) =< s(4220) s(4224) =< s(4220) s(4224) =< s(4221) s(4230) =< s(4222) s(4229) =< s(4223) s(4230) =< s(4223) s(4228) =< s(4225) s(4233) =< s(4226) s(4234) =< s(4220)+2 s(4235) =< s(4220)+3 s(4236) =< s(4220)+1 s(4237) =< s(4220) s(4230) =< s(4221)*(1/2)+s(4222) s(4231) =< s(4221)*(1/2)+s(4222) s(4229) =< s(4221)*(1/3)+s(4223) s(4230) =< s(4221)*(1/3)+s(4223) s(4231) =< s(4221)*(1/3)+s(4223) s(4228) =< s(4221)*(3/5)+s(4224)*(1/5)+s(4225) s(4229) =< s(4221)*(3/5)+s(4224)*(1/5)+s(4225) s(4230) =< s(4221)*(3/5)+s(4224)*(1/5)+s(4225) s(4231) =< s(4221)*(3/5)+s(4224)*(1/5)+s(4225) s(4233) =< s(4221)*(2/7)+s(4226) s(4227) =< s(4221)*(2/7)+s(4226) s(4238) =< s(4231)*s(4234) s(4239) =< s(4231)*s(4235) s(4240) =< s(4230)*s(4236) s(4241) =< s(4228)*s(4236) s(4242) =< s(4228)*s(4237) s(4243) =< s(4227)*s(4234) s(4244) =< s(4233)*s(4237) s(4245) =< s(4238) s(4246) =< s(4239) s(4247) =< s(4246)*s(4235) s(4248) =< s(4245)*s(4234) s(4249) =< s(4240) s(4250) =< s(4242) s(4251) =< s(4243) s(4252) =< s(4251)*s(4234) s(4253) =< s(4244) s(4254) =< s(4253)*s(4220) with precondition: [V=2,Out=0,V1>=0] * Chain [73]: 22*s(4264)+4*s(4265)+4*s(4266)+2*s(4267)+20*s(4268)+5*s(4269)+20*s(4270)+2*s(4278)+28*s(4282)+64*s(4283)+4*s(4284)+4*s(4285)+4*s(4286)+4*s(4287)+152*s(4288)+12*s(4289)+88*s(4290)+8*s(4291)+1 Such that:aux(217) =< V1 aux(218) =< 2*V1+1 aux(219) =< V1/2 aux(220) =< 2/3*V1 aux(221) =< 2/3*V1+1/3 aux(222) =< 2/5*V1 aux(223) =< 3/7*V1 s(4261) =< aux(221) s(4264) =< aux(217) s(4265) =< aux(217) s(4266) =< aux(217) s(4267) =< aux(217) s(4268) =< aux(217) s(4269) =< aux(217) s(4261) =< aux(217) s(4261) =< aux(218) s(4267) =< aux(219) s(4266) =< aux(220) s(4267) =< aux(220) s(4265) =< aux(222) s(4270) =< aux(223) s(4271) =< aux(217)+2 s(4272) =< aux(217)+3 s(4273) =< aux(217)+1 s(4274) =< aux(217) s(4267) =< aux(218)*(1/2)+aux(219) s(4268) =< aux(218)*(1/2)+aux(219) s(4266) =< aux(218)*(1/3)+aux(220) s(4267) =< aux(218)*(1/3)+aux(220) s(4268) =< aux(218)*(1/3)+aux(220) s(4265) =< aux(218)*(3/5)+s(4261)*(1/5)+aux(222) s(4266) =< aux(218)*(3/5)+s(4261)*(1/5)+aux(222) s(4267) =< aux(218)*(3/5)+s(4261)*(1/5)+aux(222) s(4268) =< aux(218)*(3/5)+s(4261)*(1/5)+aux(222) s(4270) =< aux(218)*(2/7)+aux(223) s(4264) =< aux(218)*(2/7)+aux(223) s(4275) =< s(4268)*s(4271) s(4276) =< s(4268)*s(4272) s(4277) =< s(4267)*s(4273) s(4278) =< s(4265)*s(4273) s(4279) =< s(4265)*s(4274) s(4280) =< s(4264)*s(4271) s(4281) =< s(4270)*s(4274) s(4282) =< s(4275) s(4283) =< s(4276) s(4284) =< s(4283)*s(4272) s(4285) =< s(4282)*s(4271) s(4286) =< s(4277) s(4287) =< s(4279) s(4288) =< s(4280) s(4289) =< s(4288)*s(4271) s(4290) =< s(4281) s(4291) =< s(4290)*aux(217) with precondition: [V=2,Out=1,V1>=0] * Chain [72]: 11*s(4335)+2*s(4336)+2*s(4337)+1*s(4338)+10*s(4339)+2*s(4340)+10*s(4341)+1*s(4349)+14*s(4353)+32*s(4354)+2*s(4355)+2*s(4356)+2*s(4357)+2*s(4358)+76*s(4359)+6*s(4360)+44*s(4361)+4*s(4362)+1*s(4363)+1 Such that:s(4363) =< 2 s(4328) =< V1 s(4329) =< 2*V1+1 s(4330) =< V1/2 s(4331) =< 2/3*V1 s(4332) =< 2/3*V1+1/3 s(4333) =< 2/5*V1 s(4334) =< 3/7*V1 s(4335) =< s(4328) s(4336) =< s(4328) s(4337) =< s(4328) s(4338) =< s(4328) s(4339) =< s(4328) s(4340) =< s(4328) s(4332) =< s(4328) s(4332) =< s(4329) s(4338) =< s(4330) s(4337) =< s(4331) s(4338) =< s(4331) s(4336) =< s(4333) s(4341) =< s(4334) s(4342) =< s(4328)+2 s(4343) =< s(4328)+3 s(4344) =< s(4328)+1 s(4345) =< s(4328) s(4338) =< s(4329)*(1/2)+s(4330) s(4339) =< s(4329)*(1/2)+s(4330) s(4337) =< s(4329)*(1/3)+s(4331) s(4338) =< s(4329)*(1/3)+s(4331) s(4339) =< s(4329)*(1/3)+s(4331) s(4336) =< s(4329)*(3/5)+s(4332)*(1/5)+s(4333) s(4337) =< s(4329)*(3/5)+s(4332)*(1/5)+s(4333) s(4338) =< s(4329)*(3/5)+s(4332)*(1/5)+s(4333) s(4339) =< s(4329)*(3/5)+s(4332)*(1/5)+s(4333) s(4341) =< s(4329)*(2/7)+s(4334) s(4335) =< s(4329)*(2/7)+s(4334) s(4346) =< s(4339)*s(4342) s(4347) =< s(4339)*s(4343) s(4348) =< s(4338)*s(4344) s(4349) =< s(4336)*s(4344) s(4350) =< s(4336)*s(4345) s(4351) =< s(4335)*s(4342) s(4352) =< s(4341)*s(4345) s(4353) =< s(4346) s(4354) =< s(4347) s(4355) =< s(4354)*s(4343) s(4356) =< s(4353)*s(4342) s(4357) =< s(4348) s(4358) =< s(4350) s(4359) =< s(4351) s(4360) =< s(4359)*s(4342) s(4361) =< s(4352) s(4362) =< s(4361)*s(4328) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun4(Out): * Chain [79]: 0 with precondition: [Out=0] * Chain [78]: 0 with precondition: [Out=2] #### Cost of chains of fun5(Out): * Chain [81]: 0 with precondition: [Out=0] * Chain [80]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V1,Out): * Chain [83]: 11*s(4700)+2*s(4701)+2*s(4702)+1*s(4703)+10*s(4704)+2*s(4705)+10*s(4706)+1*s(4714)+14*s(4718)+32*s(4719)+2*s(4720)+2*s(4721)+2*s(4722)+2*s(4723)+76*s(4724)+6*s(4725)+44*s(4726)+4*s(4727)+1 Such that:s(4693) =< V1 s(4694) =< 2*V1+1 s(4695) =< V1/2 s(4696) =< 2/3*V1 s(4697) =< 2/3*V1+1/3 s(4698) =< 2/5*V1 s(4699) =< 3/7*V1 s(4700) =< s(4693) s(4701) =< s(4693) s(4702) =< s(4693) s(4703) =< s(4693) s(4704) =< s(4693) s(4705) =< s(4693) s(4697) =< s(4693) s(4697) =< s(4694) s(4703) =< s(4695) s(4702) =< s(4696) s(4703) =< s(4696) s(4701) =< s(4698) s(4706) =< s(4699) s(4707) =< s(4693)+2 s(4708) =< s(4693)+3 s(4709) =< s(4693)+1 s(4710) =< s(4693) s(4703) =< s(4694)*(1/2)+s(4695) s(4704) =< s(4694)*(1/2)+s(4695) s(4702) =< s(4694)*(1/3)+s(4696) s(4703) =< s(4694)*(1/3)+s(4696) s(4704) =< s(4694)*(1/3)+s(4696) s(4701) =< s(4694)*(3/5)+s(4697)*(1/5)+s(4698) s(4702) =< s(4694)*(3/5)+s(4697)*(1/5)+s(4698) s(4703) =< s(4694)*(3/5)+s(4697)*(1/5)+s(4698) s(4704) =< s(4694)*(3/5)+s(4697)*(1/5)+s(4698) s(4706) =< s(4694)*(2/7)+s(4699) s(4700) =< s(4694)*(2/7)+s(4699) s(4711) =< s(4704)*s(4707) s(4712) =< s(4704)*s(4708) s(4713) =< s(4703)*s(4709) s(4714) =< s(4701)*s(4709) s(4715) =< s(4701)*s(4710) s(4716) =< s(4700)*s(4707) s(4717) =< s(4706)*s(4710) s(4718) =< s(4711) s(4719) =< s(4712) s(4720) =< s(4719)*s(4708) s(4721) =< s(4718)*s(4707) s(4722) =< s(4713) s(4723) =< s(4715) s(4724) =< s(4716) s(4725) =< s(4724)*s(4707) s(4726) =< s(4717) s(4727) =< s(4726)*s(4693) with precondition: [Out=0,V1>=0] * Chain [82]: 11*s(4735)+2*s(4736)+2*s(4737)+1*s(4738)+10*s(4739)+2*s(4740)+10*s(4741)+1*s(4749)+14*s(4753)+32*s(4754)+2*s(4755)+2*s(4756)+2*s(4757)+2*s(4758)+76*s(4759)+6*s(4760)+44*s(4761)+4*s(4762)+1 Such that:s(4728) =< V1 s(4729) =< 2*V1+1 s(4730) =< V1/2 s(4731) =< 2/3*V1 s(4732) =< 2/3*V1+1/3 s(4733) =< 2/5*V1 s(4734) =< 3/7*V1 s(4735) =< s(4728) s(4736) =< s(4728) s(4737) =< s(4728) s(4738) =< s(4728) s(4739) =< s(4728) s(4740) =< s(4728) s(4732) =< s(4728) s(4732) =< s(4729) s(4738) =< s(4730) s(4737) =< s(4731) s(4738) =< s(4731) s(4736) =< s(4733) s(4741) =< s(4734) s(4742) =< s(4728)+2 s(4743) =< s(4728)+3 s(4744) =< s(4728)+1 s(4745) =< s(4728) s(4738) =< s(4729)*(1/2)+s(4730) s(4739) =< s(4729)*(1/2)+s(4730) s(4737) =< s(4729)*(1/3)+s(4731) s(4738) =< s(4729)*(1/3)+s(4731) s(4739) =< s(4729)*(1/3)+s(4731) s(4736) =< s(4729)*(3/5)+s(4732)*(1/5)+s(4733) s(4737) =< s(4729)*(3/5)+s(4732)*(1/5)+s(4733) s(4738) =< s(4729)*(3/5)+s(4732)*(1/5)+s(4733) s(4739) =< s(4729)*(3/5)+s(4732)*(1/5)+s(4733) s(4741) =< s(4729)*(2/7)+s(4734) s(4735) =< s(4729)*(2/7)+s(4734) s(4746) =< s(4739)*s(4742) s(4747) =< s(4739)*s(4743) s(4748) =< s(4738)*s(4744) s(4749) =< s(4736)*s(4744) s(4750) =< s(4736)*s(4745) s(4751) =< s(4735)*s(4742) s(4752) =< s(4741)*s(4745) s(4753) =< s(4746) s(4754) =< s(4747) s(4755) =< s(4754)*s(4743) s(4756) =< s(4753)*s(4742) s(4757) =< s(4748) s(4758) =< s(4750) s(4759) =< s(4751) s(4760) =< s(4759)*s(4742) s(4761) =< s(4752) s(4762) =< s(4761)*s(4728) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun8(V1,V,Out): * Chain [89]: 22*s(4770)+4*s(4771)+4*s(4772)+2*s(4773)+20*s(4774)+4*s(4775)+20*s(4776)+2*s(4784)+28*s(4788)+64*s(4789)+4*s(4790)+4*s(4791)+4*s(4792)+4*s(4793)+152*s(4794)+12*s(4795)+88*s(4796)+8*s(4797)+33*s(4805)+6*s(4806)+6*s(4807)+3*s(4808)+30*s(4809)+9*s(4810)+30*s(4811)+3*s(4819)+42*s(4823)+96*s(4824)+6*s(4825)+6*s(4826)+6*s(4827)+6*s(4828)+228*s(4829)+18*s(4830)+132*s(4831)+12*s(4832)+1*s(4906)+0 Such that:s(4906) =< 2 aux(249) =< V1 aux(250) =< 2*V1+1 aux(251) =< V1/2 aux(252) =< 2/3*V1 aux(253) =< 2/3*V1+1/3 aux(254) =< 2/5*V1 aux(255) =< 3/7*V1 aux(256) =< V aux(257) =< 2*V+1 aux(258) =< V/2 aux(259) =< 2/3*V aux(260) =< 2/3*V+1/3 aux(261) =< 2/5*V aux(262) =< 3/7*V s(4767) =< aux(253) s(4802) =< aux(260) s(4810) =< aux(256) s(4805) =< aux(256) s(4806) =< aux(256) s(4807) =< aux(256) s(4808) =< aux(256) s(4809) =< aux(256) s(4802) =< aux(256) s(4802) =< aux(257) s(4808) =< aux(258) s(4807) =< aux(259) s(4808) =< aux(259) s(4806) =< aux(261) s(4811) =< aux(262) s(4812) =< aux(256)+2 s(4813) =< aux(256)+3 s(4814) =< aux(256)+1 s(4815) =< aux(256) s(4808) =< aux(257)*(1/2)+aux(258) s(4809) =< aux(257)*(1/2)+aux(258) s(4807) =< aux(257)*(1/3)+aux(259) s(4808) =< aux(257)*(1/3)+aux(259) s(4809) =< aux(257)*(1/3)+aux(259) s(4806) =< aux(257)*(3/5)+s(4802)*(1/5)+aux(261) s(4807) =< aux(257)*(3/5)+s(4802)*(1/5)+aux(261) s(4808) =< aux(257)*(3/5)+s(4802)*(1/5)+aux(261) s(4809) =< aux(257)*(3/5)+s(4802)*(1/5)+aux(261) s(4811) =< aux(257)*(2/7)+aux(262) s(4805) =< aux(257)*(2/7)+aux(262) s(4816) =< s(4809)*s(4812) s(4817) =< s(4809)*s(4813) s(4818) =< s(4808)*s(4814) s(4819) =< s(4806)*s(4814) s(4820) =< s(4806)*s(4815) s(4821) =< s(4805)*s(4812) s(4822) =< s(4811)*s(4815) s(4823) =< s(4816) s(4824) =< s(4817) s(4825) =< s(4824)*s(4813) s(4826) =< s(4823)*s(4812) s(4827) =< s(4818) s(4828) =< s(4820) s(4829) =< s(4821) s(4830) =< s(4829)*s(4812) s(4831) =< s(4822) s(4832) =< s(4831)*aux(256) s(4770) =< aux(249) s(4771) =< aux(249) s(4772) =< aux(249) s(4773) =< aux(249) s(4774) =< aux(249) s(4775) =< aux(249) s(4767) =< aux(249) s(4767) =< aux(250) s(4773) =< aux(251) s(4772) =< aux(252) s(4773) =< aux(252) s(4771) =< aux(254) s(4776) =< aux(255) s(4777) =< aux(249)+2 s(4778) =< aux(249)+3 s(4779) =< aux(249)+1 s(4780) =< aux(249) s(4773) =< aux(250)*(1/2)+aux(251) s(4774) =< aux(250)*(1/2)+aux(251) s(4772) =< aux(250)*(1/3)+aux(252) s(4773) =< aux(250)*(1/3)+aux(252) s(4774) =< aux(250)*(1/3)+aux(252) s(4771) =< aux(250)*(3/5)+s(4767)*(1/5)+aux(254) s(4772) =< aux(250)*(3/5)+s(4767)*(1/5)+aux(254) s(4773) =< aux(250)*(3/5)+s(4767)*(1/5)+aux(254) s(4774) =< aux(250)*(3/5)+s(4767)*(1/5)+aux(254) s(4776) =< aux(250)*(2/7)+aux(255) s(4770) =< aux(250)*(2/7)+aux(255) s(4781) =< s(4774)*s(4777) s(4782) =< s(4774)*s(4778) s(4783) =< s(4773)*s(4779) s(4784) =< s(4771)*s(4779) s(4785) =< s(4771)*s(4780) s(4786) =< s(4770)*s(4777) s(4787) =< s(4776)*s(4780) s(4788) =< s(4781) s(4789) =< s(4782) s(4790) =< s(4789)*s(4778) s(4791) =< s(4788)*s(4777) s(4792) =< s(4783) s(4793) =< s(4785) s(4794) =< s(4786) s(4795) =< s(4794)*s(4777) s(4796) =< s(4787) s(4797) =< s(4796)*aux(249) with precondition: [Out=0,V1>=0,V>=0] * Chain [88]: 33*s(4952)+6*s(4953)+6*s(4954)+3*s(4955)+30*s(4956)+6*s(4957)+30*s(4958)+3*s(4966)+42*s(4970)+96*s(4971)+6*s(4972)+6*s(4973)+6*s(4974)+6*s(4975)+228*s(4976)+18*s(4977)+132*s(4978)+12*s(4979)+44*s(4987)+8*s(4988)+8*s(4989)+4*s(4990)+40*s(4991)+9*s(4992)+40*s(4993)+4*s(5001)+56*s(5005)+128*s(5006)+8*s(5007)+8*s(5008)+8*s(5009)+8*s(5010)+304*s(5011)+24*s(5012)+176*s(5013)+16*s(5014)+2*s(5156)+1 Such that:aux(264) =< 2 aux(265) =< V1 aux(266) =< 2*V1+1 aux(267) =< V1/2 aux(268) =< 2/3*V1 aux(269) =< 2/3*V1+1/3 aux(270) =< 2/5*V1 aux(271) =< 3/7*V1 aux(272) =< V aux(273) =< 2*V+1 aux(274) =< V/2 aux(275) =< 2/3*V aux(276) =< 2/3*V+1/3 aux(277) =< 2/5*V aux(278) =< 3/7*V s(5156) =< aux(264) s(4949) =< aux(269) s(4984) =< aux(276) s(4987) =< aux(272) s(4988) =< aux(272) s(4989) =< aux(272) s(4990) =< aux(272) s(4991) =< aux(272) s(4992) =< aux(272) s(4984) =< aux(272) s(4984) =< aux(273) s(4990) =< aux(274) s(4989) =< aux(275) s(4990) =< aux(275) s(4988) =< aux(277) s(4993) =< aux(278) s(4994) =< aux(272)+2 s(4995) =< aux(272)+3 s(4996) =< aux(272)+1 s(4997) =< aux(272) s(4990) =< aux(273)*(1/2)+aux(274) s(4991) =< aux(273)*(1/2)+aux(274) s(4989) =< aux(273)*(1/3)+aux(275) s(4990) =< aux(273)*(1/3)+aux(275) s(4991) =< aux(273)*(1/3)+aux(275) s(4988) =< aux(273)*(3/5)+s(4984)*(1/5)+aux(277) s(4989) =< aux(273)*(3/5)+s(4984)*(1/5)+aux(277) s(4990) =< aux(273)*(3/5)+s(4984)*(1/5)+aux(277) s(4991) =< aux(273)*(3/5)+s(4984)*(1/5)+aux(277) s(4993) =< aux(273)*(2/7)+aux(278) s(4987) =< aux(273)*(2/7)+aux(278) s(4998) =< s(4991)*s(4994) s(4999) =< s(4991)*s(4995) s(5000) =< s(4990)*s(4996) s(5001) =< s(4988)*s(4996) s(5002) =< s(4988)*s(4997) s(5003) =< s(4987)*s(4994) s(5004) =< s(4993)*s(4997) s(5005) =< s(4998) s(5006) =< s(4999) s(5007) =< s(5006)*s(4995) s(5008) =< s(5005)*s(4994) s(5009) =< s(5000) s(5010) =< s(5002) s(5011) =< s(5003) s(5012) =< s(5011)*s(4994) s(5013) =< s(5004) s(5014) =< s(5013)*aux(272) s(4952) =< aux(265) s(4953) =< aux(265) s(4954) =< aux(265) s(4955) =< aux(265) s(4956) =< aux(265) s(4957) =< aux(265) s(4949) =< aux(265) s(4949) =< aux(266) s(4955) =< aux(267) s(4954) =< aux(268) s(4955) =< aux(268) s(4953) =< aux(270) s(4958) =< aux(271) s(4959) =< aux(265)+2 s(4960) =< aux(265)+3 s(4961) =< aux(265)+1 s(4962) =< aux(265) s(4955) =< aux(266)*(1/2)+aux(267) s(4956) =< aux(266)*(1/2)+aux(267) s(4954) =< aux(266)*(1/3)+aux(268) s(4955) =< aux(266)*(1/3)+aux(268) s(4956) =< aux(266)*(1/3)+aux(268) s(4953) =< aux(266)*(3/5)+s(4949)*(1/5)+aux(270) s(4954) =< aux(266)*(3/5)+s(4949)*(1/5)+aux(270) s(4955) =< aux(266)*(3/5)+s(4949)*(1/5)+aux(270) s(4956) =< aux(266)*(3/5)+s(4949)*(1/5)+aux(270) s(4958) =< aux(266)*(2/7)+aux(271) s(4952) =< aux(266)*(2/7)+aux(271) s(4963) =< s(4956)*s(4959) s(4964) =< s(4956)*s(4960) s(4965) =< s(4955)*s(4961) s(4966) =< s(4953)*s(4961) s(4967) =< s(4953)*s(4962) s(4968) =< s(4952)*s(4959) s(4969) =< s(4958)*s(4962) s(4970) =< s(4963) s(4971) =< s(4964) s(4972) =< s(4971)*s(4960) s(4973) =< s(4970)*s(4959) s(4974) =< s(4965) s(4975) =< s(4967) s(4976) =< s(4968) s(4977) =< s(4976)*s(4959) s(4978) =< s(4969) s(4979) =< s(4978)*aux(265) with precondition: [Out=1,V1>=0,V>=0] * Chain [87]: 55*s(5200)+10*s(5201)+10*s(5202)+5*s(5203)+50*s(5204)+10*s(5205)+50*s(5206)+5*s(5214)+70*s(5218)+160*s(5219)+10*s(5220)+10*s(5221)+10*s(5222)+10*s(5223)+380*s(5224)+30*s(5225)+220*s(5226)+20*s(5227)+77*s(5235)+14*s(5236)+14*s(5237)+7*s(5238)+70*s(5239)+16*s(5240)+70*s(5241)+7*s(5249)+98*s(5253)+224*s(5254)+14*s(5255)+14*s(5256)+14*s(5257)+14*s(5258)+532*s(5259)+42*s(5260)+308*s(5261)+28*s(5262)+1*s(5580)+1*s(5616)+1 Such that:s(5616) =< 1 s(5580) =< 2 aux(281) =< V1 aux(282) =< 2*V1+1 aux(283) =< V1/2 aux(284) =< 2/3*V1 aux(285) =< 2/3*V1+1/3 aux(286) =< 2/5*V1 aux(287) =< 3/7*V1 aux(288) =< V aux(289) =< 2*V+1 aux(290) =< V/2 aux(291) =< 2/3*V aux(292) =< 2/3*V+1/3 aux(293) =< 2/5*V aux(294) =< 3/7*V s(5197) =< aux(285) s(5232) =< aux(292) s(5235) =< aux(288) s(5236) =< aux(288) s(5237) =< aux(288) s(5238) =< aux(288) s(5239) =< aux(288) s(5240) =< aux(288) s(5232) =< aux(288) s(5232) =< aux(289) s(5238) =< aux(290) s(5237) =< aux(291) s(5238) =< aux(291) s(5236) =< aux(293) s(5241) =< aux(294) s(5242) =< aux(288)+2 s(5243) =< aux(288)+3 s(5244) =< aux(288)+1 s(5245) =< aux(288) s(5238) =< aux(289)*(1/2)+aux(290) s(5239) =< aux(289)*(1/2)+aux(290) s(5237) =< aux(289)*(1/3)+aux(291) s(5238) =< aux(289)*(1/3)+aux(291) s(5239) =< aux(289)*(1/3)+aux(291) s(5236) =< aux(289)*(3/5)+s(5232)*(1/5)+aux(293) s(5237) =< aux(289)*(3/5)+s(5232)*(1/5)+aux(293) s(5238) =< aux(289)*(3/5)+s(5232)*(1/5)+aux(293) s(5239) =< aux(289)*(3/5)+s(5232)*(1/5)+aux(293) s(5241) =< aux(289)*(2/7)+aux(294) s(5235) =< aux(289)*(2/7)+aux(294) s(5246) =< s(5239)*s(5242) s(5247) =< s(5239)*s(5243) s(5248) =< s(5238)*s(5244) s(5249) =< s(5236)*s(5244) s(5250) =< s(5236)*s(5245) s(5251) =< s(5235)*s(5242) s(5252) =< s(5241)*s(5245) s(5253) =< s(5246) s(5254) =< s(5247) s(5255) =< s(5254)*s(5243) s(5256) =< s(5253)*s(5242) s(5257) =< s(5248) s(5258) =< s(5250) s(5259) =< s(5251) s(5260) =< s(5259)*s(5242) s(5261) =< s(5252) s(5262) =< s(5261)*aux(288) s(5200) =< aux(281) s(5201) =< aux(281) s(5202) =< aux(281) s(5203) =< aux(281) s(5204) =< aux(281) s(5205) =< aux(281) s(5197) =< aux(281) s(5197) =< aux(282) s(5203) =< aux(283) s(5202) =< aux(284) s(5203) =< aux(284) s(5201) =< aux(286) s(5206) =< aux(287) s(5207) =< aux(281)+2 s(5208) =< aux(281)+3 s(5209) =< aux(281)+1 s(5210) =< aux(281) s(5203) =< aux(282)*(1/2)+aux(283) s(5204) =< aux(282)*(1/2)+aux(283) s(5202) =< aux(282)*(1/3)+aux(284) s(5203) =< aux(282)*(1/3)+aux(284) s(5204) =< aux(282)*(1/3)+aux(284) s(5201) =< aux(282)*(3/5)+s(5197)*(1/5)+aux(286) s(5202) =< aux(282)*(3/5)+s(5197)*(1/5)+aux(286) s(5203) =< aux(282)*(3/5)+s(5197)*(1/5)+aux(286) s(5204) =< aux(282)*(3/5)+s(5197)*(1/5)+aux(286) s(5206) =< aux(282)*(2/7)+aux(287) s(5200) =< aux(282)*(2/7)+aux(287) s(5211) =< s(5204)*s(5207) s(5212) =< s(5204)*s(5208) s(5213) =< s(5203)*s(5209) s(5214) =< s(5201)*s(5209) s(5215) =< s(5201)*s(5210) s(5216) =< s(5200)*s(5207) s(5217) =< s(5206)*s(5210) s(5218) =< s(5211) s(5219) =< s(5212) s(5220) =< s(5219)*s(5208) s(5221) =< s(5218)*s(5207) s(5222) =< s(5213) s(5223) =< s(5215) s(5224) =< s(5216) s(5225) =< s(5224)*s(5207) s(5226) =< s(5217) s(5227) =< s(5226)*aux(281) with precondition: [Out=2,V1>=1,V>=0] * Chain [86]: 11*s(5624)+2*s(5625)+2*s(5626)+1*s(5627)+10*s(5628)+2*s(5629)+10*s(5630)+1*s(5638)+14*s(5642)+32*s(5643)+2*s(5644)+2*s(5645)+2*s(5646)+2*s(5647)+76*s(5648)+6*s(5649)+44*s(5650)+4*s(5651)+2*s(5652)+0 Such that:s(5617) =< V1 s(5618) =< 2*V1+1 s(5619) =< V1/2 s(5620) =< 2/3*V1 s(5621) =< 2/3*V1+1/3 s(5622) =< 2/5*V1 s(5623) =< 3/7*V1 aux(295) =< 2 s(5652) =< aux(295) s(5624) =< s(5617) s(5625) =< s(5617) s(5626) =< s(5617) s(5627) =< s(5617) s(5628) =< s(5617) s(5629) =< s(5617) s(5621) =< s(5617) s(5621) =< s(5618) s(5627) =< s(5619) s(5626) =< s(5620) s(5627) =< s(5620) s(5625) =< s(5622) s(5630) =< s(5623) s(5631) =< s(5617)+2 s(5632) =< s(5617)+3 s(5633) =< s(5617)+1 s(5634) =< s(5617) s(5627) =< s(5618)*(1/2)+s(5619) s(5628) =< s(5618)*(1/2)+s(5619) s(5626) =< s(5618)*(1/3)+s(5620) s(5627) =< s(5618)*(1/3)+s(5620) s(5628) =< s(5618)*(1/3)+s(5620) s(5625) =< s(5618)*(3/5)+s(5621)*(1/5)+s(5622) s(5626) =< s(5618)*(3/5)+s(5621)*(1/5)+s(5622) s(5627) =< s(5618)*(3/5)+s(5621)*(1/5)+s(5622) s(5628) =< s(5618)*(3/5)+s(5621)*(1/5)+s(5622) s(5630) =< s(5618)*(2/7)+s(5623) s(5624) =< s(5618)*(2/7)+s(5623) s(5635) =< s(5628)*s(5631) s(5636) =< s(5628)*s(5632) s(5637) =< s(5627)*s(5633) s(5638) =< s(5625)*s(5633) s(5639) =< s(5625)*s(5634) s(5640) =< s(5624)*s(5631) s(5641) =< s(5630)*s(5634) s(5642) =< s(5635) s(5643) =< s(5636) s(5644) =< s(5643)*s(5632) s(5645) =< s(5642)*s(5631) s(5646) =< s(5637) s(5647) =< s(5639) s(5648) =< s(5640) s(5649) =< s(5648)*s(5631) s(5650) =< s(5641) s(5651) =< s(5650)*s(5617) with precondition: [V=2,Out=0,V1>=0] * Chain [85]: 11*s(5661)+2*s(5662)+2*s(5663)+1*s(5664)+10*s(5665)+2*s(5666)+10*s(5667)+1*s(5675)+14*s(5679)+32*s(5680)+2*s(5681)+2*s(5682)+2*s(5683)+2*s(5684)+76*s(5685)+6*s(5686)+44*s(5687)+4*s(5688)+1*s(5689)+1 Such that:s(5689) =< 2 s(5654) =< V1 s(5655) =< 2*V1+1 s(5656) =< V1/2 s(5657) =< 2/3*V1 s(5658) =< 2/3*V1+1/3 s(5659) =< 2/5*V1 s(5660) =< 3/7*V1 s(5661) =< s(5654) s(5662) =< s(5654) s(5663) =< s(5654) s(5664) =< s(5654) s(5665) =< s(5654) s(5666) =< s(5654) s(5658) =< s(5654) s(5658) =< s(5655) s(5664) =< s(5656) s(5663) =< s(5657) s(5664) =< s(5657) s(5662) =< s(5659) s(5667) =< s(5660) s(5668) =< s(5654)+2 s(5669) =< s(5654)+3 s(5670) =< s(5654)+1 s(5671) =< s(5654) s(5664) =< s(5655)*(1/2)+s(5656) s(5665) =< s(5655)*(1/2)+s(5656) s(5663) =< s(5655)*(1/3)+s(5657) s(5664) =< s(5655)*(1/3)+s(5657) s(5665) =< s(5655)*(1/3)+s(5657) s(5662) =< s(5655)*(3/5)+s(5658)*(1/5)+s(5659) s(5663) =< s(5655)*(3/5)+s(5658)*(1/5)+s(5659) s(5664) =< s(5655)*(3/5)+s(5658)*(1/5)+s(5659) s(5665) =< s(5655)*(3/5)+s(5658)*(1/5)+s(5659) s(5667) =< s(5655)*(2/7)+s(5660) s(5661) =< s(5655)*(2/7)+s(5660) s(5672) =< s(5665)*s(5668) s(5673) =< s(5665)*s(5669) s(5674) =< s(5664)*s(5670) s(5675) =< s(5662)*s(5670) s(5676) =< s(5662)*s(5671) s(5677) =< s(5661)*s(5668) s(5678) =< s(5667)*s(5671) s(5679) =< s(5672) s(5680) =< s(5673) s(5681) =< s(5680)*s(5669) s(5682) =< s(5679)*s(5668) s(5683) =< s(5674) s(5684) =< s(5676) s(5685) =< s(5677) s(5686) =< s(5685)*s(5668) s(5687) =< s(5678) s(5688) =< s(5687)*s(5654) with precondition: [V=2,Out=1,V1>=2] * Chain [84]: 33*s(5697)+6*s(5698)+6*s(5699)+3*s(5700)+30*s(5701)+6*s(5702)+30*s(5703)+3*s(5711)+42*s(5715)+96*s(5716)+6*s(5717)+6*s(5718)+6*s(5719)+6*s(5720)+228*s(5721)+18*s(5722)+132*s(5723)+12*s(5724)+1*s(5760)+1*s(5796)+11*s(5804)+2*s(5805)+2*s(5806)+1*s(5807)+10*s(5808)+2*s(5809)+10*s(5810)+1*s(5818)+14*s(5822)+32*s(5823)+2*s(5824)+2*s(5825)+2*s(5826)+2*s(5827)+76*s(5828)+6*s(5829)+44*s(5830)+4*s(5831)+1 Such that:s(5760) =< 1 s(5796) =< 2 s(5797) =< V s(5798) =< 2*V+1 s(5799) =< V/2 s(5800) =< 2/3*V s(5801) =< 2/3*V+1/3 s(5802) =< 2/5*V s(5803) =< 3/7*V aux(296) =< V1 aux(297) =< 2*V1+1 aux(298) =< V1/2 aux(299) =< 2/3*V1 aux(300) =< 2/3*V1+1/3 aux(301) =< 2/5*V1 aux(302) =< 3/7*V1 s(5694) =< aux(300) s(5697) =< aux(296) s(5698) =< aux(296) s(5699) =< aux(296) s(5700) =< aux(296) s(5701) =< aux(296) s(5702) =< aux(296) s(5694) =< aux(296) s(5694) =< aux(297) s(5700) =< aux(298) s(5699) =< aux(299) s(5700) =< aux(299) s(5698) =< aux(301) s(5703) =< aux(302) s(5704) =< aux(296)+2 s(5705) =< aux(296)+3 s(5706) =< aux(296)+1 s(5707) =< aux(296) s(5700) =< aux(297)*(1/2)+aux(298) s(5701) =< aux(297)*(1/2)+aux(298) s(5699) =< aux(297)*(1/3)+aux(299) s(5700) =< aux(297)*(1/3)+aux(299) s(5701) =< aux(297)*(1/3)+aux(299) s(5698) =< aux(297)*(3/5)+s(5694)*(1/5)+aux(301) s(5699) =< aux(297)*(3/5)+s(5694)*(1/5)+aux(301) s(5700) =< aux(297)*(3/5)+s(5694)*(1/5)+aux(301) s(5701) =< aux(297)*(3/5)+s(5694)*(1/5)+aux(301) s(5703) =< aux(297)*(2/7)+aux(302) s(5697) =< aux(297)*(2/7)+aux(302) s(5708) =< s(5701)*s(5704) s(5709) =< s(5701)*s(5705) s(5710) =< s(5700)*s(5706) s(5711) =< s(5698)*s(5706) s(5712) =< s(5698)*s(5707) s(5713) =< s(5697)*s(5704) s(5714) =< s(5703)*s(5707) s(5715) =< s(5708) s(5716) =< s(5709) s(5717) =< s(5716)*s(5705) s(5718) =< s(5715)*s(5704) s(5719) =< s(5710) s(5720) =< s(5712) s(5721) =< s(5713) s(5722) =< s(5721)*s(5704) s(5723) =< s(5714) s(5724) =< s(5723)*aux(296) s(5804) =< s(5797) s(5805) =< s(5797) s(5806) =< s(5797) s(5807) =< s(5797) s(5808) =< s(5797) s(5809) =< s(5797) s(5801) =< s(5797) s(5801) =< s(5798) s(5807) =< s(5799) s(5806) =< s(5800) s(5807) =< s(5800) s(5805) =< s(5802) s(5810) =< s(5803) s(5811) =< s(5797)+2 s(5812) =< s(5797)+3 s(5813) =< s(5797)+1 s(5814) =< s(5797) s(5807) =< s(5798)*(1/2)+s(5799) s(5808) =< s(5798)*(1/2)+s(5799) s(5806) =< s(5798)*(1/3)+s(5800) s(5807) =< s(5798)*(1/3)+s(5800) s(5808) =< s(5798)*(1/3)+s(5800) s(5805) =< s(5798)*(3/5)+s(5801)*(1/5)+s(5802) s(5806) =< s(5798)*(3/5)+s(5801)*(1/5)+s(5802) s(5807) =< s(5798)*(3/5)+s(5801)*(1/5)+s(5802) s(5808) =< s(5798)*(3/5)+s(5801)*(1/5)+s(5802) s(5810) =< s(5798)*(2/7)+s(5803) s(5804) =< s(5798)*(2/7)+s(5803) s(5815) =< s(5808)*s(5811) s(5816) =< s(5808)*s(5812) s(5817) =< s(5807)*s(5813) s(5818) =< s(5805)*s(5813) s(5819) =< s(5805)*s(5814) s(5820) =< s(5804)*s(5811) s(5821) =< s(5810)*s(5814) s(5822) =< s(5815) s(5823) =< s(5816) s(5824) =< s(5823)*s(5812) s(5825) =< s(5822)*s(5811) s(5826) =< s(5817) s(5827) =< s(5819) s(5828) =< s(5820) s(5829) =< s(5828)*s(5811) s(5830) =< s(5821) s(5831) =< s(5830)*s(5797) with precondition: [Out=2,V1>=0,V>=1] #### Cost of chains of start(V1,V,V5): * Chain [90]: 572*s(6055)+42*s(6056)+292*s(6060)+16*s(6063)+185*s(6072)+8*s(6075)+737*s(6090)+134*s(6091)+134*s(6092)+67*s(6093)+670*s(6094)+670*s(6096)+67*s(6104)+938*s(6108)+2144*s(6109)+134*s(6110)+134*s(6111)+134*s(6112)+134*s(6113)+5092*s(6114)+402*s(6115)+2948*s(6116)+268*s(6117)+570*s(6135)+46*s(6136)+550*s(6139)+100*s(6140)+100*s(6141)+50*s(6142)+500*s(6143)+500*s(6144)+50*s(6152)+700*s(6156)+1600*s(6157)+100*s(6158)+100*s(6159)+100*s(6160)+100*s(6161)+3800*s(6162)+300*s(6163)+2200*s(6164)+200*s(6165)+39*s(6255)+6*s(6258)+220*s(6259)+40*s(6260)+40*s(6261)+20*s(6262)+200*s(6263)+200*s(6264)+20*s(6272)+280*s(6276)+640*s(6277)+40*s(6278)+40*s(6279)+40*s(6280)+40*s(6281)+1520*s(6282)+120*s(6283)+880*s(6284)+80*s(6285)+11 Such that:s(6247) =< 2*V5+1 s(6248) =< V5/2 s(6249) =< 2/3*V5 s(6250) =< 2/3*V5+1/3 s(6251) =< 2/5*V5 s(6252) =< 3/7*V5 aux(320) =< 1 aux(321) =< 2 aux(322) =< V1 aux(323) =< 2*V1+1 aux(324) =< V1/2 aux(325) =< 2/3*V1 aux(326) =< 2/3*V1+1/3 aux(327) =< 2/5*V1 aux(328) =< 3/7*V1 aux(329) =< V aux(330) =< 2*V+1 aux(331) =< V/2 aux(332) =< 2/3*V aux(333) =< 2/3*V+1/3 aux(334) =< 2/5*V aux(335) =< 3/7*V aux(336) =< V5 s(6255) =< aux(320) s(6135) =< aux(321) s(6072) =< aux(322) s(6087) =< aux(326) s(6060) =< aux(329) s(6134) =< aux(333) s(6254) =< s(6250) s(6055) =< aux(336) s(6056) =< s(6055)*aux(336) s(6258) =< s(6255)*aux(320) s(6259) =< aux(336) s(6260) =< aux(336) s(6261) =< aux(336) s(6262) =< aux(336) s(6263) =< aux(336) s(6254) =< aux(336) s(6254) =< s(6247) s(6262) =< s(6248) s(6261) =< s(6249) s(6262) =< s(6249) s(6260) =< s(6251) s(6264) =< s(6252) s(6265) =< aux(336)+2 s(6266) =< aux(336)+3 s(6267) =< aux(336)+1 s(6268) =< aux(336) s(6262) =< s(6247)*(1/2)+s(6248) s(6263) =< s(6247)*(1/2)+s(6248) s(6261) =< s(6247)*(1/3)+s(6249) s(6262) =< s(6247)*(1/3)+s(6249) s(6263) =< s(6247)*(1/3)+s(6249) s(6260) =< s(6247)*(3/5)+s(6254)*(1/5)+s(6251) s(6261) =< s(6247)*(3/5)+s(6254)*(1/5)+s(6251) s(6262) =< s(6247)*(3/5)+s(6254)*(1/5)+s(6251) s(6263) =< s(6247)*(3/5)+s(6254)*(1/5)+s(6251) s(6264) =< s(6247)*(2/7)+s(6252) s(6259) =< s(6247)*(2/7)+s(6252) s(6269) =< s(6263)*s(6265) s(6270) =< s(6263)*s(6266) s(6271) =< s(6262)*s(6267) s(6272) =< s(6260)*s(6267) s(6273) =< s(6260)*s(6268) s(6274) =< s(6259)*s(6265) s(6275) =< s(6264)*s(6268) s(6276) =< s(6269) s(6277) =< s(6270) s(6278) =< s(6277)*s(6266) s(6279) =< s(6276)*s(6265) s(6280) =< s(6271) s(6281) =< s(6273) s(6282) =< s(6274) s(6283) =< s(6282)*s(6265) s(6284) =< s(6275) s(6285) =< s(6284)*aux(336) s(6090) =< aux(322) s(6091) =< aux(322) s(6092) =< aux(322) s(6093) =< aux(322) s(6094) =< aux(322) s(6087) =< aux(322) s(6087) =< aux(323) s(6093) =< aux(324) s(6092) =< aux(325) s(6093) =< aux(325) s(6091) =< aux(327) s(6096) =< aux(328) s(6097) =< aux(322)+2 s(6098) =< aux(322)+3 s(6099) =< aux(322)+1 s(6100) =< aux(322) s(6093) =< aux(323)*(1/2)+aux(324) s(6094) =< aux(323)*(1/2)+aux(324) s(6092) =< aux(323)*(1/3)+aux(325) s(6093) =< aux(323)*(1/3)+aux(325) s(6094) =< aux(323)*(1/3)+aux(325) s(6091) =< aux(323)*(3/5)+s(6087)*(1/5)+aux(327) s(6092) =< aux(323)*(3/5)+s(6087)*(1/5)+aux(327) s(6093) =< aux(323)*(3/5)+s(6087)*(1/5)+aux(327) s(6094) =< aux(323)*(3/5)+s(6087)*(1/5)+aux(327) s(6096) =< aux(323)*(2/7)+aux(328) s(6090) =< aux(323)*(2/7)+aux(328) s(6101) =< s(6094)*s(6097) s(6102) =< s(6094)*s(6098) s(6103) =< s(6093)*s(6099) s(6104) =< s(6091)*s(6099) s(6105) =< s(6091)*s(6100) s(6106) =< s(6090)*s(6097) s(6107) =< s(6096)*s(6100) s(6108) =< s(6101) s(6109) =< s(6102) s(6110) =< s(6109)*s(6098) s(6111) =< s(6108)*s(6097) s(6112) =< s(6103) s(6113) =< s(6105) s(6114) =< s(6106) s(6115) =< s(6114)*s(6097) s(6116) =< s(6107) s(6117) =< s(6116)*aux(322) s(6136) =< s(6135)*aux(321) s(6139) =< aux(329) s(6140) =< aux(329) s(6141) =< aux(329) s(6142) =< aux(329) s(6143) =< aux(329) s(6134) =< aux(329) s(6134) =< aux(330) s(6142) =< aux(331) s(6141) =< aux(332) s(6142) =< aux(332) s(6140) =< aux(334) s(6144) =< aux(335) s(6145) =< aux(329)+2 s(6146) =< aux(329)+3 s(6147) =< aux(329)+1 s(6148) =< aux(329) s(6142) =< aux(330)*(1/2)+aux(331) s(6143) =< aux(330)*(1/2)+aux(331) s(6141) =< aux(330)*(1/3)+aux(332) s(6142) =< aux(330)*(1/3)+aux(332) s(6143) =< aux(330)*(1/3)+aux(332) s(6140) =< aux(330)*(3/5)+s(6134)*(1/5)+aux(334) s(6141) =< aux(330)*(3/5)+s(6134)*(1/5)+aux(334) s(6142) =< aux(330)*(3/5)+s(6134)*(1/5)+aux(334) s(6143) =< aux(330)*(3/5)+s(6134)*(1/5)+aux(334) s(6144) =< aux(330)*(2/7)+aux(335) s(6139) =< aux(330)*(2/7)+aux(335) s(6149) =< s(6143)*s(6145) s(6150) =< s(6143)*s(6146) s(6151) =< s(6142)*s(6147) s(6152) =< s(6140)*s(6147) s(6153) =< s(6140)*s(6148) s(6154) =< s(6139)*s(6145) s(6155) =< s(6144)*s(6148) s(6156) =< s(6149) s(6157) =< s(6150) s(6158) =< s(6157)*s(6146) s(6159) =< s(6156)*s(6145) s(6160) =< s(6151) s(6161) =< s(6153) s(6162) =< s(6154) s(6163) =< s(6162)*s(6145) s(6164) =< s(6155) s(6165) =< s(6164)*aux(329) s(6063) =< s(6060)*aux(329) s(6075) =< s(6072)*aux(322) with precondition: [] Closed-form bounds of start(V1,V,V5): ------------------------------------- * Chain [90] with precondition: [] - Upper bound: nat(V1)*23970+1380+nat(V1)*11465*nat(V1)+nat(V1)*670*nat(V1)*nat(V1)+nat(V1)*268*nat(V1)*nat(3/7*V1)+nat(V1)*2948*nat(3/7*V1)+nat(V)*18042+nat(V)*8566*nat(V)+nat(V)*500*nat(V)*nat(V)+nat(V)*200*nat(V)*nat(3/7*V)+nat(V)*2200*nat(3/7*V)+nat(V5)*7672+nat(V5)*3462*nat(V5)+nat(V5)*200*nat(V5)*nat(V5)+nat(V5)*80*nat(V5)*nat(3/7*V5)+nat(V5)*880*nat(3/7*V5)+nat(3/7*V1)*670+nat(3/7*V)*500+nat(3/7*V5)*200 - Complexity: n^3 ### Maximum cost of start(V1,V,V5): nat(V1)*23970+1380+nat(V1)*11465*nat(V1)+nat(V1)*670*nat(V1)*nat(V1)+nat(V1)*268*nat(V1)*nat(3/7*V1)+nat(V1)*2948*nat(3/7*V1)+nat(V)*18042+nat(V)*8566*nat(V)+nat(V)*500*nat(V)*nat(V)+nat(V)*200*nat(V)*nat(3/7*V)+nat(V)*2200*nat(3/7*V)+nat(V5)*7672+nat(V5)*3462*nat(V5)+nat(V5)*200*nat(V5)*nat(V5)+nat(V5)*80*nat(V5)*nat(3/7*V5)+nat(V5)*880*nat(3/7*V5)+nat(3/7*V1)*670+nat(3/7*V)*500+nat(3/7*V5)*200 Asymptotic class: n^3 * Total analysis performed in 22766 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Types: cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0' :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p hole_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p1_4 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4 :: Nat -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: cond1, cond2, gr, neq, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg cond2 < encArg gr < encArg neq < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Types: cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0' :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p hole_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p1_4 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4 :: Nat -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p Generator Equations: gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(0) <=> true gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(x, 1)) <=> s(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond1, cond2, neq, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg cond2 < encArg gr < encArg neq < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, 0)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, 0))) Induction Step: gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, +(n4_4, 1))), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4))) ->_IH *3_4 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Types: cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0' :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p hole_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p1_4 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4 :: Nat -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p Generator Equations: gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(0) <=> true gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(x, 1)) <=> s(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond1, cond2, neq, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg cond2 < encArg gr < encArg neq < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Types: cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0' :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p hole_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p1_4 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4 :: Nat -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p Lemmas: gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(0) <=> true gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(x, 1)) <=> s(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(x)) The following defined symbols remain to be analysed: neq, cond1, cond2, encArg They will be analysed ascendingly in the following order: cond1 = cond2 cond1 < encArg cond2 < encArg neq < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: neq(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_4))) -> *3_4, rt in Omega(n1290_4) Induction Base: neq(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, 0)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, 0))) Induction Step: neq(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, +(n1290_4, 1))), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, +(n1290_4, 1)))) ->_R^Omega(1) neq(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_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: cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) cond2(true, x, y) -> cond1(y, y) cond2(false, x, y) -> cond1(p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) neq(0', 0') -> false neq(0', s(x)) -> true neq(s(x), 0') -> true neq(s(x), s(y)) -> neq(x, y) p(0') -> 0' p(s(x)) -> x encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(0') -> 0' encArg(cons_cond1(x_1, x_2)) -> cond1(encArg(x_1), encArg(x_2)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2) -> cond1(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) Types: cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0' :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p hole_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p1_4 :: s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4 :: Nat -> s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p Lemmas: gr(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) neq(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_4)), gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(1, n1290_4))) -> *3_4, rt in Omega(n1290_4) Generator Equations: gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(0) <=> true gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(x, 1)) <=> s(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(x)) The following defined symbols remain to be analysed: cond2, cond1, encArg They will be analysed ascendingly in the following order: cond1 = cond2 cond1 < encArg cond2 < encArg ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(n6421_4)) -> gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(n6421_4), rt in Omega(0) Induction Base: encArg(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(0)) ->_R^Omega(0) true Induction Step: encArg(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(+(n6421_4, 1))) ->_R^Omega(0) s(encArg(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(n6421_4))) ->_IH s(gen_s:true:false:0':cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p2_4(c6422_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)