/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 190 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 27.2 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), 511 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), 63 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) 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(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0 encode_true -> true ---------------------------------------- (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: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0 encode_true -> true 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: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0 encode_true -> true 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: minus(x, y) -> cond(ge(x, s(y)), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] ge(u, 0) -> true [1] ge(0, s(v)) -> false [1] ge(s(u), s(v)) -> ge(u, v) [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [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: minus(x, y) -> cond(ge(x, s(y)), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] ge(u, 0) -> true [1] ge(0, s(v)) -> false [1] ge(s(u), s(v)) -> ge(u, v) [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [0] The TRS has the following type information: minus :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge cond :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge ge :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge s :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge false :: s:false:0:true:cons_minus:cons_cond:cons_ge 0 :: s:false:0:true:cons_minus:cons_cond:cons_ge true :: s:false:0:true:cons_minus:cons_cond:cons_ge encArg :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge cons_minus :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge cons_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge cons_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge encode_minus :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge encode_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge encode_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge encode_s :: s:false:0:true:cons_minus:cons_cond:cons_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge encode_false :: s:false:0:true:cons_minus:cons_cond:cons_ge encode_0 :: s:false:0:true:cons_minus:cons_cond:cons_ge encode_true :: s:false:0:true:cons_minus:cons_cond:cons_ge 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_minus(v0, v1) -> null_encode_minus [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_ge(v0, v1) -> null_encode_ge [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] cond(v0, v1, v2) -> null_cond [0] ge(v0, v1) -> null_ge [0] And the following fresh constants: null_encArg, null_encode_minus, null_encode_cond, null_encode_ge, null_encode_s, null_encode_false, null_encode_0, null_encode_true, null_cond, null_ge ---------------------------------------- (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: minus(x, y) -> cond(ge(x, s(y)), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] ge(u, 0) -> true [1] ge(0, s(v)) -> false [1] ge(s(u), s(v)) -> ge(u, v) [1] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [0] encArg(v0) -> null_encArg [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_ge(v0, v1) -> null_encode_ge [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] cond(v0, v1, v2) -> null_cond [0] ge(v0, v1) -> null_ge [0] The TRS has the following type information: minus :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge cond :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge ge :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge s :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge false :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge 0 :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge true :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encArg :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge cons_minus :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge cons_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge cons_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_minus :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_s :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge -> s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_false :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_0 :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge encode_true :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encArg :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_minus :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_s :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_false :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_0 :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_encode_true :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_cond :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge null_ge :: s:false:0:true:cons_minus:cons_cond:cons_ge:null_encArg:null_encode_minus:null_encode_cond:null_encode_ge:null_encode_s:null_encode_false:null_encode_0:null_encode_true:null_cond:null_ge 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: false => 1 0 => 0 true => 2 null_encArg => 0 null_encode_minus => 0 null_encode_cond => 0 null_encode_ge => 0 null_encode_s => 0 null_encode_false => 0 null_encode_0 => 0 null_encode_true => 0 null_cond => 0 null_ge => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond(z, z', z'') -{ 1 }-> 0 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond(z, z', z'') -{ 1 }-> 1 + minus(x, 1 + y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> ge(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0 -{ 0 }-> 0 :|: encode_cond(z, z', z'') -{ 0 }-> cond(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_ge(z, z') -{ 0 }-> ge(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_ge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_minus(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 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 :|: ge(z, z') -{ 1 }-> ge(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0 ge(z, z') -{ 1 }-> 2 :|: z = u, z' = 0, u >= 0 ge(z, z') -{ 1 }-> 1 :|: v >= 0, z' = 1 + v, z = 0 ge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> cond(ge(x, 1 + y), x, y) :|: x >= 0, y >= 0, z = x, z' = y 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,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[cond(V1, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[ge(V1, V, Out)],[V1 >= 0,V >= 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, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[fun2(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun3(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun4(Out)],[]). eq(start(V1, V, V5),0,[fun5(Out)],[]). eq(start(V1, V, V5),0,[fun6(Out)],[]). eq(minus(V1, V, Out),1,[ge(V3, 1 + V2, Ret0),cond(Ret0, V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = V3,V = V2]). eq(cond(V1, V, V5, Out),1,[],[Out = 0,V = V4,V5 = V6,V1 = 1,V4 >= 0,V6 >= 0]). eq(cond(V1, V, V5, Out),1,[minus(V8, 1 + V7, Ret1)],[Out = 1 + Ret1,V1 = 2,V = V8,V5 = V7,V8 >= 0,V7 >= 0]). eq(ge(V1, V, Out),1,[],[Out = 2,V1 = V9,V = 0,V9 >= 0]). eq(ge(V1, V, Out),1,[],[Out = 1,V10 >= 0,V = 1 + V10,V1 = 0]). eq(ge(V1, V, Out),1,[ge(V11, V12, Ret2)],[Out = Ret2,V12 >= 0,V = 1 + V12,V1 = 1 + V11,V11 >= 0]). eq(encArg(V1, Out),0,[encArg(V13, Ret11)],[Out = 1 + Ret11,V1 = 1 + V13,V13 >= 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V14, Ret01),encArg(V15, Ret12),minus(Ret01, Ret12, Ret3)],[Out = Ret3,V14 >= 0,V1 = 1 + V14 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V17, Ret02),encArg(V18, Ret13),encArg(V16, Ret21),cond(Ret02, Ret13, Ret21, Ret4)],[Out = Ret4,V17 >= 0,V1 = 1 + V16 + V17 + V18,V16 >= 0,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V20, Ret03),encArg(V19, Ret14),ge(Ret03, Ret14, Ret5)],[Out = Ret5,V20 >= 0,V1 = 1 + V19 + V20,V19 >= 0]). eq(fun(V1, V, Out),0,[encArg(V22, Ret04),encArg(V21, Ret15),minus(Ret04, Ret15, Ret6)],[Out = Ret6,V22 >= 0,V21 >= 0,V1 = V22,V = V21]). eq(fun1(V1, V, V5, Out),0,[encArg(V24, Ret05),encArg(V25, Ret16),encArg(V23, Ret22),cond(Ret05, Ret16, Ret22, Ret7)],[Out = Ret7,V24 >= 0,V23 >= 0,V25 >= 0,V1 = V24,V = V25,V5 = V23]). eq(fun2(V1, V, Out),0,[encArg(V26, Ret06),encArg(V27, Ret17),ge(Ret06, Ret17, Ret8)],[Out = Ret8,V26 >= 0,V27 >= 0,V1 = V26,V = V27]). eq(fun3(V1, Out),0,[encArg(V28, Ret18)],[Out = 1 + Ret18,V28 >= 0,V1 = V28]). eq(fun4(Out),0,[],[Out = 1]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 2]). eq(encArg(V1, Out),0,[],[Out = 0,V29 >= 0,V1 = V29]). eq(fun(V1, V, Out),0,[],[Out = 0,V31 >= 0,V30 >= 0,V1 = V31,V = V30]). eq(fun1(V1, V, V5, Out),0,[],[Out = 0,V33 >= 0,V5 = V34,V32 >= 0,V1 = V33,V = V32,V34 >= 0]). eq(fun2(V1, V, Out),0,[],[Out = 0,V35 >= 0,V36 >= 0,V1 = V35,V = V36]). eq(fun3(V1, Out),0,[],[Out = 0,V37 >= 0,V1 = V37]). eq(fun4(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 0]). eq(cond(V1, V, V5, Out),0,[],[Out = 0,V38 >= 0,V5 = V39,V40 >= 0,V1 = V38,V = V40,V39 >= 0]). eq(ge(V1, V, Out),0,[],[Out = 0,V42 >= 0,V41 >= 0,V1 = V42,V = V41]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(cond(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(ge(V1,V,Out),[V1,V],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(fun2(V1,V,Out),[V1,V],[Out]). input_output_vars(fun3(V1,Out),[V1],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(Out),[],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [ge/3] 1. recursive : [cond/4,minus/3] 2. recursive [non_tail,multiple] : [encArg/2] 3. non_recursive : [fun/3] 4. non_recursive : [fun1/4] 5. non_recursive : [fun2/3] 6. non_recursive : [fun3/2] 7. non_recursive : [fun4/1] 8. non_recursive : [fun5/1] 9. non_recursive : [fun6/1] 10. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into ge/3 1. SCC is partially evaluated into minus/3 2. SCC is partially evaluated into encArg/2 3. SCC is partially evaluated into fun/3 4. SCC is partially evaluated into fun1/4 5. SCC is partially evaluated into fun2/3 6. SCC is partially evaluated into fun3/2 7. SCC is partially evaluated into fun4/1 8. SCC is completely evaluated into other SCCs 9. SCC is partially evaluated into fun6/1 10. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations ge/3 * CE 19 is refined into CE [43] * CE 16 is refined into CE [44] * CE 17 is refined into CE [45] * CE 18 is refined into CE [46] ### Cost equations --> "Loop" of ge/3 * CEs [46] --> Loop 23 * CEs [43] --> Loop 24 * CEs [44] --> Loop 25 * CEs [45] --> Loop 26 ### Ranking functions of CR ge(V1,V,Out) * RF of phase [23]: [V,V1] #### Partial ranking functions of CR ge(V1,V,Out) * Partial RF of phase [23]: - RF of loop [23:1]: V V1 ### Specialization of cost equations minus/3 * CE 13 is refined into CE [47,48,49,50] * CE 15 is refined into CE [51,52] * CE 14 is refined into CE [53] ### Cost equations --> "Loop" of minus/3 * CEs [53] --> Loop 27 * CEs [47,48,49,50,51,52] --> Loop 28 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [27]: [V1-V] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [27]: - RF of loop [27:1]: V1-V ### Specialization of cost equations encArg/2 * CE 25 is refined into CE [54] * CE 26 is refined into CE [55] * CE 24 is refined into CE [56] * CE 27 is refined into CE [57,58] * CE 28 is refined into CE [59,60,61,62,63] * CE 23 is refined into CE [64] * CE 21 is refined into CE [65,66] * CE 20 is refined into CE [67] * CE 22 is refined into CE [68] ### Cost equations --> "Loop" of encArg/2 * CEs [66] --> Loop 29 * CEs [65] --> Loop 30 * CEs [67,68] --> Loop 31 * CEs [64] --> Loop 32 * CEs [58] --> Loop 33 * CEs [63] --> Loop 34 * CEs [60] --> Loop 35 * CEs [62] --> Loop 36 * CEs [59] --> Loop 37 * CEs [57,61] --> Loop 38 * CEs [54] --> Loop 39 * CEs [55] --> Loop 40 * CEs [56] --> Loop 41 ### Ranking functions of CR encArg(V1,Out) * RF of phase [29,30,31,32,33,34,35,36,37,38]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [29,30,31,32,33,34,35,36,37,38]: - RF of loop [29:1,29:2,29:3,30:1,30:2,30:3,31:1,31:2,31:3,32:1,33:1,33:2,34:1,34:2,35:1,35:2,36:1,36:2,37:1,37:2,38:1,38:2]: V1 ### Specialization of cost equations fun/3 * CE 29 is refined into CE [69,70,71,72,73,74,75,76,77,78,79,80,81,82] * CE 30 is refined into CE [83] ### Cost equations --> "Loop" of fun/3 * CEs [72] --> Loop 42 * CEs [71,81] --> Loop 43 * CEs [70,74,76,79] --> Loop 44 * CEs [69,73,75,77,78,80,82,83] --> Loop 45 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun1/4 * CE 31 is refined into CE [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110] * CE 32 is refined into CE [111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138] * CE 33 is refined into CE [139,140,141,142,143,144,145,146,147] * CE 34 is refined into CE [148] ### Cost equations --> "Loop" of fun1/4 * CEs [118,121] --> Loop 46 * CEs [117,119,120] --> Loop 47 * CEs [87,88,89,105,106,107,142,143,144] --> Loop 48 * CEs [114,128] --> Loop 49 * CEs [113,123,127,137] --> Loop 50 * CEs [85,91,94,100,103,109,140,146] --> Loop 51 * CEs [112,116,126,130,132,135] --> Loop 52 * CEs [111,115,122,124,125,129,131,133,134,136,138] --> Loop 53 * CEs [84,86,90,92,93,95,96,97,98,99,101,102,104,108,110,139,141,145,147,148] --> Loop 54 ### Ranking functions of CR fun1(V1,V,V5,Out) #### Partial ranking functions of CR fun1(V1,V,V5,Out) ### Specialization of cost equations fun2/3 * CE 35 is refined into CE [149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174] * CE 36 is refined into CE [175] ### Cost equations --> "Loop" of fun2/3 * CEs [157] --> Loop 55 * CEs [154,156,171] --> Loop 56 * CEs [155,172] --> Loop 57 * CEs [149,152,162,168] --> Loop 58 * CEs [150,153,158,160,163,165,166,169,173] --> Loop 59 * CEs [151,159,161,164,167,170,174,175] --> Loop 60 ### Ranking functions of CR fun2(V1,V,Out) #### Partial ranking functions of CR fun2(V1,V,Out) ### Specialization of cost equations fun3/2 * CE 37 is refined into CE [176,177,178] * CE 38 is refined into CE [179] ### Cost equations --> "Loop" of fun3/2 * CEs [178] --> Loop 61 * CEs [179] --> Loop 62 * CEs [176,177] --> Loop 63 ### Ranking functions of CR fun3(V1,Out) #### Partial ranking functions of CR fun3(V1,Out) ### Specialization of cost equations fun4/1 * CE 39 is refined into CE [180] * CE 40 is refined into CE [181] ### Cost equations --> "Loop" of fun4/1 * CEs [180] --> Loop 64 * CEs [181] --> Loop 65 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun6/1 * CE 41 is refined into CE [182] * CE 42 is refined into CE [183] ### Cost equations --> "Loop" of fun6/1 * CEs [182] --> Loop 66 * CEs [183] --> Loop 67 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [184] * CE 2 is refined into CE [185,186] * CE 3 is refined into CE [187] * CE 4 is refined into CE [188,189] * CE 5 is refined into CE [190,191,192,193,194] * CE 6 is refined into CE [195,196,197] * CE 7 is refined into CE [198,199] * CE 8 is refined into CE [200,201,202,203,204,205] * CE 9 is refined into CE [206,207,208] * CE 10 is refined into CE [209,210,211] * CE 11 is refined into CE [212,213] * CE 12 is refined into CE [214,215] ### Cost equations --> "Loop" of start/3 * CEs [184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215] --> Loop 68 ### Ranking functions of CR start(V1,V,V5) #### Partial ranking functions of CR start(V1,V,V5) Computing Bounds ===================================== #### Cost of chains of ge(V1,V,Out): * Chain [[23],26]: 1*it(23)+1 Such that:it(23) =< V1 with precondition: [Out=1,V1>=1,V>=V1+1] * Chain [[23],25]: 1*it(23)+1 Such that:it(23) =< V with precondition: [Out=2,V>=1,V1>=V] * Chain [[23],24]: 1*it(23)+0 Such that:it(23) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [26]: 1 with precondition: [V1=0,Out=1,V>=1] * Chain [25]: 1 with precondition: [V=0,Out=2,V1>=0] * Chain [24]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[27],28]: 3*it(27)+2*s(2)+2*s(3)+1*s(8)+3 Such that:aux(2) =< V+Out+1 it(27) =< Out aux(4) =< V1 s(3) =< aux(4) s(2) =< aux(2) s(8) =< it(27)*aux(4) with precondition: [V>=0,Out>=1,V1>=Out+V] * Chain [28]: 2*s(2)+2*s(3)+3 Such that:aux(1) =< V1 aux(2) =< V+1 s(3) =< aux(1) s(2) =< aux(2) with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of encArg(V1,Out): * Chain [41]: 0 with precondition: [V1=1,Out=1] * Chain [40]: 0 with precondition: [V1=2,Out=2] * Chain [39]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([29,30,31,32,33,34,35,36,37,38],[[41],[40],[39]])]: 4*it(29)+4*it(30)+1*it(31)+3*it(33)+1*it(34)+1*it(35)+1*it(36)+1*it(37)+3*it(38)+7*s(49)+1*s(50)+2*s(52)+2*s(53)+7*s(56)+1*s(57)+1*s(59)+1*s(60)+2*s(61)+2*s(62)+1*s(63)+0 Such that:s(15) =< 2*V1 aux(22) =< V1 aux(23) =< 2*V1+1 aux(24) =< 2/3*V1 aux(25) =< 3/5*V1 aux(26) =< 3/7*V1 aux(27) =< 4/5*V1 aux(28) =< 4/7*V1 it(31) =< aux(22) it(33) =< aux(22) it(34) =< aux(22) it(35) =< aux(22) it(36) =< aux(22) it(37) =< aux(22) it(38) =< aux(22) it([39]) =< aux(23) it(34) =< aux(24) it(36) =< aux(24) it(30) =< aux(25) it(29) =< aux(26) it(33) =< aux(27) it(34) =< aux(27) it(36) =< aux(27) it(37) =< aux(27) it(36) =< aux(28) aux(21) =< s(15)+1 aux(8) =< s(15) aux(13) =< s(15)+2 aux(15) =< s(15)-1 aux(10) =< s(15)-2 it(33) =< it([39])*(1/5)+aux(27) it(34) =< it([39])*(1/5)+aux(27) it(35) =< it([39])*(1/5)+aux(27) it(36) =< it([39])*(1/5)+aux(27) it(37) =< it([39])*(1/5)+aux(27) it(38) =< it([39])*(1/5)+aux(27) it(36) =< it([39])*(3/7)+aux(28) it(37) =< it([39])*(3/7)+aux(28) it(38) =< it([39])*(3/7)+aux(28) it(34) =< it([39])*(1/3)+aux(24) it(35) =< it([39])*(1/3)+aux(24) it(36) =< it([39])*(1/3)+aux(24) it(37) =< it([39])*(1/3)+aux(24) it(38) =< it([39])*(1/3)+aux(24) it(30) =< it([39])*(1/5)+aux(25) it(31) =< it([39])*(1/5)+aux(25) it(29) =< it([39])*(2/7)+aux(26) it(30) =< it([39])*(2/7)+aux(26) it(31) =< it([39])*(2/7)+aux(26) s(64) =< it(38)*aux(21) s(63) =< it(38)*aux(8) s(65) =< it(38)*aux(13) s(60) =< it(36)*aux(15) s(59) =< it(34)*aux(15) s(58) =< it(33)*aux(13) s(54) =< it(30)*aux(8) s(55) =< it(30)*aux(10) s(51) =< it(29)*aux(8) s(61) =< s(65) s(62) =< s(64) s(56) =< s(58) s(57) =< s(56)*aux(13) s(52) =< s(55) s(53) =< s(54) s(49) =< s(51) s(50) =< s(49)*s(15) with precondition: [V1>=1,Out>=0,2*V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [45]: 2*s(114)+6*s(115)+2*s(116)+2*s(117)+2*s(118)+2*s(119)+6*s(120)+8*s(121)+8*s(122)+2*s(129)+2*s(131)+2*s(132)+4*s(137)+4*s(138)+14*s(139)+2*s(140)+4*s(141)+4*s(142)+14*s(143)+2*s(144)+3*s(153)+9*s(154)+3*s(155)+3*s(156)+3*s(157)+3*s(158)+9*s(159)+12*s(160)+12*s(161)+3*s(168)+3*s(170)+3*s(171)+6*s(176)+6*s(177)+21*s(178)+3*s(179)+6*s(180)+6*s(181)+21*s(182)+3*s(183)+4*s(186)+6*s(187)+6*s(230)+6*s(272)+2*s(277)+3 Such that:s(275) =< 3 aux(34) =< 1 aux(35) =< 2 aux(36) =< V1 aux(37) =< 2*V1 aux(38) =< 2*V1+1 aux(39) =< 2/3*V1 aux(40) =< 3/5*V1 aux(41) =< 3/7*V1 aux(42) =< 4/5*V1 aux(43) =< 4/7*V1 aux(44) =< V aux(45) =< 2*V aux(46) =< 2*V+1 aux(47) =< 2/3*V aux(48) =< 3/5*V aux(49) =< 3/7*V aux(50) =< 4/5*V aux(51) =< 4/7*V s(186) =< aux(37) s(230) =< aux(34) s(114) =< aux(36) s(115) =< aux(36) s(116) =< aux(36) s(117) =< aux(36) s(118) =< aux(36) s(119) =< aux(36) s(120) =< aux(36) s(116) =< aux(39) s(118) =< aux(39) s(121) =< aux(40) s(122) =< aux(41) s(115) =< aux(42) s(116) =< aux(42) s(118) =< aux(42) s(119) =< aux(42) s(118) =< aux(43) s(123) =< aux(37)+1 s(124) =< aux(37) s(125) =< aux(37)+2 s(126) =< aux(37)-1 s(127) =< aux(37)-2 s(115) =< aux(38)*(1/5)+aux(42) s(116) =< aux(38)*(1/5)+aux(42) s(117) =< aux(38)*(1/5)+aux(42) s(118) =< aux(38)*(1/5)+aux(42) s(119) =< aux(38)*(1/5)+aux(42) s(120) =< aux(38)*(1/5)+aux(42) s(118) =< aux(38)*(3/7)+aux(43) s(119) =< aux(38)*(3/7)+aux(43) s(120) =< aux(38)*(3/7)+aux(43) s(116) =< aux(38)*(1/3)+aux(39) s(117) =< aux(38)*(1/3)+aux(39) s(118) =< aux(38)*(1/3)+aux(39) s(119) =< aux(38)*(1/3)+aux(39) s(120) =< aux(38)*(1/3)+aux(39) s(121) =< aux(38)*(1/5)+aux(40) s(114) =< aux(38)*(1/5)+aux(40) s(122) =< aux(38)*(2/7)+aux(41) s(121) =< aux(38)*(2/7)+aux(41) s(114) =< aux(38)*(2/7)+aux(41) s(128) =< s(120)*s(123) s(129) =< s(120)*s(124) s(130) =< s(120)*s(125) s(131) =< s(118)*s(126) s(132) =< s(116)*s(126) s(133) =< s(115)*s(125) s(134) =< s(121)*s(124) s(135) =< s(121)*s(127) s(136) =< s(122)*s(124) s(137) =< s(130) s(138) =< s(128) s(139) =< s(133) s(140) =< s(139)*s(125) s(141) =< s(135) s(142) =< s(134) s(143) =< s(136) s(144) =< s(143)*aux(37) s(272) =< aux(35) s(187) =< aux(46) s(153) =< aux(44) s(154) =< aux(44) s(155) =< aux(44) s(156) =< aux(44) s(157) =< aux(44) s(158) =< aux(44) s(159) =< aux(44) s(155) =< aux(47) s(157) =< aux(47) s(160) =< aux(48) s(161) =< aux(49) s(154) =< aux(50) s(155) =< aux(50) s(157) =< aux(50) s(158) =< aux(50) s(157) =< aux(51) s(162) =< aux(45)+1 s(163) =< aux(45) s(164) =< aux(45)+2 s(165) =< aux(45)-1 s(166) =< aux(45)-2 s(154) =< aux(46)*(1/5)+aux(50) s(155) =< aux(46)*(1/5)+aux(50) s(156) =< aux(46)*(1/5)+aux(50) s(157) =< aux(46)*(1/5)+aux(50) s(158) =< aux(46)*(1/5)+aux(50) s(159) =< aux(46)*(1/5)+aux(50) s(157) =< aux(46)*(3/7)+aux(51) s(158) =< aux(46)*(3/7)+aux(51) s(159) =< aux(46)*(3/7)+aux(51) s(155) =< aux(46)*(1/3)+aux(47) s(156) =< aux(46)*(1/3)+aux(47) s(157) =< aux(46)*(1/3)+aux(47) s(158) =< aux(46)*(1/3)+aux(47) s(159) =< aux(46)*(1/3)+aux(47) s(160) =< aux(46)*(1/5)+aux(48) s(153) =< aux(46)*(1/5)+aux(48) s(161) =< aux(46)*(2/7)+aux(49) s(160) =< aux(46)*(2/7)+aux(49) s(153) =< aux(46)*(2/7)+aux(49) s(167) =< s(159)*s(162) s(168) =< s(159)*s(163) s(169) =< s(159)*s(164) s(170) =< s(157)*s(165) s(171) =< s(155)*s(165) s(172) =< s(154)*s(164) s(173) =< s(160)*s(163) s(174) =< s(160)*s(166) s(175) =< s(161)*s(163) s(176) =< s(169) s(177) =< s(167) s(178) =< s(172) s(179) =< s(178)*s(164) s(180) =< s(174) s(181) =< s(173) s(182) =< s(175) s(183) =< s(182)*aux(45) s(277) =< s(275) with precondition: [Out=0,V1>=0,V>=0] * Chain [44]: 2*s(337)+6*s(338)+2*s(339)+2*s(340)+2*s(341)+2*s(342)+6*s(343)+8*s(344)+8*s(345)+2*s(352)+2*s(354)+2*s(355)+4*s(360)+4*s(361)+14*s(362)+2*s(363)+4*s(364)+4*s(365)+14*s(366)+2*s(367)+2*s(376)+6*s(377)+2*s(378)+2*s(379)+2*s(380)+2*s(381)+6*s(382)+8*s(383)+8*s(384)+2*s(391)+2*s(393)+2*s(394)+4*s(399)+4*s(400)+14*s(401)+2*s(402)+4*s(403)+4*s(404)+14*s(405)+2*s(406)+10*s(408)+4*s(411)+2*s(412)+10*s(498)+4*s(501)+2*s(502)+3 Such that:aux(58) =< 2 aux(59) =< 3 aux(60) =< V1 aux(61) =< 2*V1 aux(62) =< 2*V1+1 aux(63) =< 2/3*V1 aux(64) =< 3/5*V1 aux(65) =< 3/7*V1 aux(66) =< 4/5*V1 aux(67) =< 4/7*V1 aux(68) =< V aux(69) =< 2*V aux(70) =< 2*V+1 aux(71) =< 2/3*V aux(72) =< 3/5*V aux(73) =< 3/7*V aux(74) =< 4/5*V aux(75) =< 4/7*V s(498) =< aux(58) s(501) =< aux(59) s(502) =< s(498)*aux(58) s(376) =< aux(68) s(377) =< aux(68) s(378) =< aux(68) s(379) =< aux(68) s(380) =< aux(68) s(381) =< aux(68) s(382) =< aux(68) s(378) =< aux(71) s(380) =< aux(71) s(383) =< aux(72) s(384) =< aux(73) s(377) =< aux(74) s(378) =< aux(74) s(380) =< aux(74) s(381) =< aux(74) s(380) =< aux(75) s(385) =< aux(69)+1 s(386) =< aux(69) s(387) =< aux(69)+2 s(388) =< aux(69)-1 s(389) =< aux(69)-2 s(377) =< aux(70)*(1/5)+aux(74) s(378) =< aux(70)*(1/5)+aux(74) s(379) =< aux(70)*(1/5)+aux(74) s(380) =< aux(70)*(1/5)+aux(74) s(381) =< aux(70)*(1/5)+aux(74) s(382) =< aux(70)*(1/5)+aux(74) s(380) =< aux(70)*(3/7)+aux(75) s(381) =< aux(70)*(3/7)+aux(75) s(382) =< aux(70)*(3/7)+aux(75) s(378) =< aux(70)*(1/3)+aux(71) s(379) =< aux(70)*(1/3)+aux(71) s(380) =< aux(70)*(1/3)+aux(71) s(381) =< aux(70)*(1/3)+aux(71) s(382) =< aux(70)*(1/3)+aux(71) s(383) =< aux(70)*(1/5)+aux(72) s(376) =< aux(70)*(1/5)+aux(72) s(384) =< aux(70)*(2/7)+aux(73) s(383) =< aux(70)*(2/7)+aux(73) s(376) =< aux(70)*(2/7)+aux(73) s(390) =< s(382)*s(385) s(391) =< s(382)*s(386) s(392) =< s(382)*s(387) s(393) =< s(380)*s(388) s(394) =< s(378)*s(388) s(395) =< s(377)*s(387) s(396) =< s(383)*s(386) s(397) =< s(383)*s(389) s(398) =< s(384)*s(386) s(399) =< s(392) s(400) =< s(390) s(401) =< s(395) s(402) =< s(401)*s(387) s(403) =< s(397) s(404) =< s(396) s(405) =< s(398) s(406) =< s(405)*aux(69) s(408) =< aux(61) s(411) =< aux(62) s(412) =< s(408)*aux(61) s(337) =< aux(60) s(338) =< aux(60) s(339) =< aux(60) s(340) =< aux(60) s(341) =< aux(60) s(342) =< aux(60) s(343) =< aux(60) s(339) =< aux(63) s(341) =< aux(63) s(344) =< aux(64) s(345) =< aux(65) s(338) =< aux(66) s(339) =< aux(66) s(341) =< aux(66) s(342) =< aux(66) s(341) =< aux(67) s(346) =< aux(61)+1 s(347) =< aux(61) s(348) =< aux(61)+2 s(349) =< aux(61)-1 s(350) =< aux(61)-2 s(338) =< aux(62)*(1/5)+aux(66) s(339) =< aux(62)*(1/5)+aux(66) s(340) =< aux(62)*(1/5)+aux(66) s(341) =< aux(62)*(1/5)+aux(66) s(342) =< aux(62)*(1/5)+aux(66) s(343) =< aux(62)*(1/5)+aux(66) s(341) =< aux(62)*(3/7)+aux(67) s(342) =< aux(62)*(3/7)+aux(67) s(343) =< aux(62)*(3/7)+aux(67) s(339) =< aux(62)*(1/3)+aux(63) s(340) =< aux(62)*(1/3)+aux(63) s(341) =< aux(62)*(1/3)+aux(63) s(342) =< aux(62)*(1/3)+aux(63) s(343) =< aux(62)*(1/3)+aux(63) s(344) =< aux(62)*(1/5)+aux(64) s(337) =< aux(62)*(1/5)+aux(64) s(345) =< aux(62)*(2/7)+aux(65) s(344) =< aux(62)*(2/7)+aux(65) s(337) =< aux(62)*(2/7)+aux(65) s(351) =< s(343)*s(346) s(352) =< s(343)*s(347) s(353) =< s(343)*s(348) s(354) =< s(341)*s(349) s(355) =< s(339)*s(349) s(356) =< s(338)*s(348) s(357) =< s(344)*s(347) s(358) =< s(344)*s(350) s(359) =< s(345)*s(347) s(360) =< s(353) s(361) =< s(351) s(362) =< s(356) s(363) =< s(362)*s(348) s(364) =< s(358) s(365) =< s(357) s(366) =< s(359) s(367) =< s(366)*aux(61) with precondition: [V1>=1,V>=0,Out>=1,2*V1>=Out] * Chain [43]: 1*s(517)+3*s(518)+1*s(519)+1*s(520)+1*s(521)+1*s(522)+3*s(523)+4*s(524)+4*s(525)+1*s(532)+1*s(534)+1*s(535)+2*s(540)+2*s(541)+7*s(542)+1*s(543)+2*s(544)+2*s(545)+7*s(546)+1*s(547)+2*s(550)+4*s(551)+3 Such that:s(509) =< V1 aux(76) =< 2*V1 s(511) =< 2*V1+1 s(512) =< 2/3*V1 s(513) =< 3/5*V1 s(514) =< 3/7*V1 s(515) =< 4/5*V1 s(516) =< 4/7*V1 aux(77) =< 3 s(550) =< aux(76) s(551) =< aux(77) s(517) =< s(509) s(518) =< s(509) s(519) =< s(509) s(520) =< s(509) s(521) =< s(509) s(522) =< s(509) s(523) =< s(509) s(519) =< s(512) s(521) =< s(512) s(524) =< s(513) s(525) =< s(514) s(518) =< s(515) s(519) =< s(515) s(521) =< s(515) s(522) =< s(515) s(521) =< s(516) s(526) =< aux(76)+1 s(527) =< aux(76) s(528) =< aux(76)+2 s(529) =< aux(76)-1 s(530) =< aux(76)-2 s(518) =< s(511)*(1/5)+s(515) s(519) =< s(511)*(1/5)+s(515) s(520) =< s(511)*(1/5)+s(515) s(521) =< s(511)*(1/5)+s(515) s(522) =< s(511)*(1/5)+s(515) s(523) =< s(511)*(1/5)+s(515) s(521) =< s(511)*(3/7)+s(516) s(522) =< s(511)*(3/7)+s(516) s(523) =< s(511)*(3/7)+s(516) s(519) =< s(511)*(1/3)+s(512) s(520) =< s(511)*(1/3)+s(512) s(521) =< s(511)*(1/3)+s(512) s(522) =< s(511)*(1/3)+s(512) s(523) =< s(511)*(1/3)+s(512) s(524) =< s(511)*(1/5)+s(513) s(517) =< s(511)*(1/5)+s(513) s(525) =< s(511)*(2/7)+s(514) s(524) =< s(511)*(2/7)+s(514) s(517) =< s(511)*(2/7)+s(514) s(531) =< s(523)*s(526) s(532) =< s(523)*s(527) s(533) =< s(523)*s(528) s(534) =< s(521)*s(529) s(535) =< s(519)*s(529) s(536) =< s(518)*s(528) s(537) =< s(524)*s(527) s(538) =< s(524)*s(530) s(539) =< s(525)*s(527) s(540) =< s(533) s(541) =< s(531) s(542) =< s(536) s(543) =< s(542)*s(528) s(544) =< s(538) s(545) =< s(537) s(546) =< s(539) s(547) =< s(546)*aux(76) with precondition: [V=2,Out=0,V1>=0] * Chain [42]: 1*s(564)+3*s(565)+1*s(566)+1*s(567)+1*s(568)+1*s(569)+3*s(570)+4*s(571)+4*s(572)+1*s(579)+1*s(581)+1*s(582)+2*s(587)+2*s(588)+7*s(589)+1*s(590)+2*s(591)+2*s(592)+7*s(593)+1*s(594)+5*s(596)+2*s(599)+1*s(600)+3 Such that:s(556) =< V1 s(559) =< 2/3*V1 s(560) =< 3/5*V1 s(561) =< 3/7*V1 s(562) =< 4/5*V1 s(563) =< 4/7*V1 aux(78) =< 2*V1 aux(79) =< 2*V1+1 s(596) =< aux(78) s(599) =< aux(79) s(600) =< s(596)*aux(78) s(564) =< s(556) s(565) =< s(556) s(566) =< s(556) s(567) =< s(556) s(568) =< s(556) s(569) =< s(556) s(570) =< s(556) s(566) =< s(559) s(568) =< s(559) s(571) =< s(560) s(572) =< s(561) s(565) =< s(562) s(566) =< s(562) s(568) =< s(562) s(569) =< s(562) s(568) =< s(563) s(573) =< aux(78)+1 s(574) =< aux(78) s(575) =< aux(78)+2 s(576) =< aux(78)-1 s(577) =< aux(78)-2 s(565) =< aux(79)*(1/5)+s(562) s(566) =< aux(79)*(1/5)+s(562) s(567) =< aux(79)*(1/5)+s(562) s(568) =< aux(79)*(1/5)+s(562) s(569) =< aux(79)*(1/5)+s(562) s(570) =< aux(79)*(1/5)+s(562) s(568) =< aux(79)*(3/7)+s(563) s(569) =< aux(79)*(3/7)+s(563) s(570) =< aux(79)*(3/7)+s(563) s(566) =< aux(79)*(1/3)+s(559) s(567) =< aux(79)*(1/3)+s(559) s(568) =< aux(79)*(1/3)+s(559) s(569) =< aux(79)*(1/3)+s(559) s(570) =< aux(79)*(1/3)+s(559) s(571) =< aux(79)*(1/5)+s(560) s(564) =< aux(79)*(1/5)+s(560) s(572) =< aux(79)*(2/7)+s(561) s(571) =< aux(79)*(2/7)+s(561) s(564) =< aux(79)*(2/7)+s(561) s(578) =< s(570)*s(573) s(579) =< s(570)*s(574) s(580) =< s(570)*s(575) s(581) =< s(568)*s(576) s(582) =< s(566)*s(576) s(583) =< s(565)*s(575) s(584) =< s(571)*s(574) s(585) =< s(571)*s(577) s(586) =< s(572)*s(574) s(587) =< s(580) s(588) =< s(578) s(589) =< s(583) s(590) =< s(589)*s(575) s(591) =< s(585) s(592) =< s(584) s(593) =< s(586) s(594) =< s(593)*aux(78) with precondition: [V=2,Out>=1,2*V1>=Out+2] #### Cost of chains of fun1(V1,V,V5,Out): * Chain [54]: 8*s(865)+24*s(866)+8*s(867)+8*s(868)+8*s(869)+8*s(870)+24*s(871)+32*s(872)+32*s(873)+8*s(880)+8*s(882)+8*s(883)+16*s(888)+16*s(889)+56*s(890)+8*s(891)+16*s(892)+16*s(893)+56*s(894)+8*s(895)+8*s(904)+24*s(905)+8*s(906)+8*s(907)+8*s(908)+8*s(909)+24*s(910)+32*s(911)+32*s(912)+8*s(919)+8*s(921)+8*s(922)+16*s(927)+16*s(928)+56*s(929)+8*s(930)+16*s(931)+16*s(932)+56*s(933)+8*s(934)+9*s(943)+27*s(944)+9*s(945)+9*s(946)+9*s(947)+9*s(948)+27*s(949)+36*s(950)+36*s(951)+9*s(958)+9*s(960)+9*s(961)+18*s(966)+18*s(967)+63*s(968)+9*s(969)+18*s(970)+18*s(971)+63*s(972)+9*s(973)+1 Such that:aux(97) =< V1 aux(98) =< 2*V1 aux(99) =< 2*V1+1 aux(100) =< 2/3*V1 aux(101) =< 3/5*V1 aux(102) =< 3/7*V1 aux(103) =< 4/5*V1 aux(104) =< 4/7*V1 aux(105) =< V aux(106) =< 2*V aux(107) =< 2*V+1 aux(108) =< 2/3*V aux(109) =< 3/5*V aux(110) =< 3/7*V aux(111) =< 4/5*V aux(112) =< 4/7*V aux(113) =< V5 aux(114) =< 2*V5 aux(115) =< 2*V5+1 aux(116) =< 2/3*V5 aux(117) =< 3/5*V5 aux(118) =< 3/7*V5 aux(119) =< 4/5*V5 aux(120) =< 4/7*V5 s(943) =< aux(113) s(944) =< aux(113) s(945) =< aux(113) s(946) =< aux(113) s(947) =< aux(113) s(948) =< aux(113) s(949) =< aux(113) s(945) =< aux(116) s(947) =< aux(116) s(950) =< aux(117) s(951) =< aux(118) s(944) =< aux(119) s(945) =< aux(119) s(947) =< aux(119) s(948) =< aux(119) s(947) =< aux(120) s(952) =< aux(114)+1 s(953) =< aux(114) s(954) =< aux(114)+2 s(955) =< aux(114)-1 s(956) =< aux(114)-2 s(944) =< aux(115)*(1/5)+aux(119) s(945) =< aux(115)*(1/5)+aux(119) s(946) =< aux(115)*(1/5)+aux(119) s(947) =< aux(115)*(1/5)+aux(119) s(948) =< aux(115)*(1/5)+aux(119) s(949) =< aux(115)*(1/5)+aux(119) s(947) =< aux(115)*(3/7)+aux(120) s(948) =< aux(115)*(3/7)+aux(120) s(949) =< aux(115)*(3/7)+aux(120) s(945) =< aux(115)*(1/3)+aux(116) s(946) =< aux(115)*(1/3)+aux(116) s(947) =< aux(115)*(1/3)+aux(116) s(948) =< aux(115)*(1/3)+aux(116) s(949) =< aux(115)*(1/3)+aux(116) s(950) =< aux(115)*(1/5)+aux(117) s(943) =< aux(115)*(1/5)+aux(117) s(951) =< aux(115)*(2/7)+aux(118) s(950) =< aux(115)*(2/7)+aux(118) s(943) =< aux(115)*(2/7)+aux(118) s(957) =< s(949)*s(952) s(958) =< s(949)*s(953) s(959) =< s(949)*s(954) s(960) =< s(947)*s(955) s(961) =< s(945)*s(955) s(962) =< s(944)*s(954) s(963) =< s(950)*s(953) s(964) =< s(950)*s(956) s(965) =< s(951)*s(953) s(966) =< s(959) s(967) =< s(957) s(968) =< s(962) s(969) =< s(968)*s(954) s(970) =< s(964) s(971) =< s(963) s(972) =< s(965) s(973) =< s(972)*aux(114) s(904) =< aux(105) s(905) =< aux(105) s(906) =< aux(105) s(907) =< aux(105) s(908) =< aux(105) s(909) =< aux(105) s(910) =< aux(105) s(906) =< aux(108) s(908) =< aux(108) s(911) =< aux(109) s(912) =< aux(110) s(905) =< aux(111) s(906) =< aux(111) s(908) =< aux(111) s(909) =< aux(111) s(908) =< aux(112) s(913) =< aux(106)+1 s(914) =< aux(106) s(915) =< aux(106)+2 s(916) =< aux(106)-1 s(917) =< aux(106)-2 s(905) =< aux(107)*(1/5)+aux(111) s(906) =< aux(107)*(1/5)+aux(111) s(907) =< aux(107)*(1/5)+aux(111) s(908) =< aux(107)*(1/5)+aux(111) s(909) =< aux(107)*(1/5)+aux(111) s(910) =< aux(107)*(1/5)+aux(111) s(908) =< aux(107)*(3/7)+aux(112) s(909) =< aux(107)*(3/7)+aux(112) s(910) =< aux(107)*(3/7)+aux(112) s(906) =< aux(107)*(1/3)+aux(108) s(907) =< aux(107)*(1/3)+aux(108) s(908) =< aux(107)*(1/3)+aux(108) s(909) =< aux(107)*(1/3)+aux(108) s(910) =< aux(107)*(1/3)+aux(108) s(911) =< aux(107)*(1/5)+aux(109) s(904) =< aux(107)*(1/5)+aux(109) s(912) =< aux(107)*(2/7)+aux(110) s(911) =< aux(107)*(2/7)+aux(110) s(904) =< aux(107)*(2/7)+aux(110) s(918) =< s(910)*s(913) s(919) =< s(910)*s(914) s(920) =< s(910)*s(915) s(921) =< s(908)*s(916) s(922) =< s(906)*s(916) s(923) =< s(905)*s(915) s(924) =< s(911)*s(914) s(925) =< s(911)*s(917) s(926) =< s(912)*s(914) s(927) =< s(920) s(928) =< s(918) s(929) =< s(923) s(930) =< s(929)*s(915) s(931) =< s(925) s(932) =< s(924) s(933) =< s(926) s(934) =< s(933)*aux(106) s(865) =< aux(97) s(866) =< aux(97) s(867) =< aux(97) s(868) =< aux(97) s(869) =< aux(97) s(870) =< aux(97) s(871) =< aux(97) s(867) =< aux(100) s(869) =< aux(100) s(872) =< aux(101) s(873) =< aux(102) s(866) =< aux(103) s(867) =< aux(103) s(869) =< aux(103) s(870) =< aux(103) s(869) =< aux(104) s(874) =< aux(98)+1 s(875) =< aux(98) s(876) =< aux(98)+2 s(877) =< aux(98)-1 s(878) =< aux(98)-2 s(866) =< aux(99)*(1/5)+aux(103) s(867) =< aux(99)*(1/5)+aux(103) s(868) =< aux(99)*(1/5)+aux(103) s(869) =< aux(99)*(1/5)+aux(103) s(870) =< aux(99)*(1/5)+aux(103) s(871) =< aux(99)*(1/5)+aux(103) s(869) =< aux(99)*(3/7)+aux(104) s(870) =< aux(99)*(3/7)+aux(104) s(871) =< aux(99)*(3/7)+aux(104) s(867) =< aux(99)*(1/3)+aux(100) s(868) =< aux(99)*(1/3)+aux(100) s(869) =< aux(99)*(1/3)+aux(100) s(870) =< aux(99)*(1/3)+aux(100) s(871) =< aux(99)*(1/3)+aux(100) s(872) =< aux(99)*(1/5)+aux(101) s(865) =< aux(99)*(1/5)+aux(101) s(873) =< aux(99)*(2/7)+aux(102) s(872) =< aux(99)*(2/7)+aux(102) s(865) =< aux(99)*(2/7)+aux(102) s(879) =< s(871)*s(874) s(880) =< s(871)*s(875) s(881) =< s(871)*s(876) s(882) =< s(869)*s(877) s(883) =< s(867)*s(877) s(884) =< s(866)*s(876) s(885) =< s(872)*s(875) s(886) =< s(872)*s(878) s(887) =< s(873)*s(875) s(888) =< s(881) s(889) =< s(879) s(890) =< s(884) s(891) =< s(890)*s(876) s(892) =< s(886) s(893) =< s(885) s(894) =< s(887) s(895) =< s(894)*aux(98) with precondition: [Out=0,V1>=0,V>=0,V5>=0] * Chain [53]: 4*s(1840)+12*s(1841)+4*s(1842)+4*s(1843)+4*s(1844)+4*s(1845)+12*s(1846)+16*s(1847)+16*s(1848)+4*s(1855)+4*s(1857)+4*s(1858)+8*s(1863)+8*s(1864)+28*s(1865)+4*s(1866)+8*s(1867)+8*s(1868)+28*s(1869)+4*s(1870)+4*s(1879)+12*s(1880)+4*s(1881)+4*s(1882)+4*s(1883)+4*s(1884)+12*s(1885)+16*s(1886)+16*s(1887)+4*s(1894)+4*s(1896)+4*s(1897)+8*s(1902)+8*s(1903)+28*s(1904)+4*s(1905)+8*s(1906)+8*s(1907)+28*s(1908)+4*s(1909)+5*s(1918)+15*s(1919)+5*s(1920)+5*s(1921)+5*s(1922)+5*s(1923)+15*s(1924)+20*s(1925)+20*s(1926)+5*s(1933)+5*s(1935)+5*s(1936)+10*s(1941)+10*s(1942)+35*s(1943)+5*s(1944)+10*s(1945)+10*s(1946)+35*s(1947)+5*s(1948)+8*s(1951)+10*s(1952)+16*s(2034)+2*s(2331)+4 Such that:s(2329) =< 4 aux(126) =< 2 aux(127) =< V1 aux(128) =< 2*V1 aux(129) =< 2*V1+1 aux(130) =< 2/3*V1 aux(131) =< 3/5*V1 aux(132) =< 3/7*V1 aux(133) =< 4/5*V1 aux(134) =< 4/7*V1 aux(135) =< V aux(136) =< 2*V aux(137) =< 2*V+1 aux(138) =< 2/3*V aux(139) =< 3/5*V aux(140) =< 3/7*V aux(141) =< 4/5*V aux(142) =< 4/7*V aux(143) =< V5 aux(144) =< 2*V5 aux(145) =< 2*V5+1 aux(146) =< 2*V5+2 aux(147) =< 2/3*V5 aux(148) =< 3/5*V5 aux(149) =< 3/7*V5 aux(150) =< 4/5*V5 aux(151) =< 4/7*V5 s(2034) =< aux(126) s(1951) =< aux(136) s(1879) =< aux(135) s(1880) =< aux(135) s(1881) =< aux(135) s(1882) =< aux(135) s(1883) =< aux(135) s(1884) =< aux(135) s(1885) =< aux(135) s(1881) =< aux(138) s(1883) =< aux(138) s(1886) =< aux(139) s(1887) =< aux(140) s(1880) =< aux(141) s(1881) =< aux(141) s(1883) =< aux(141) s(1884) =< aux(141) s(1883) =< aux(142) s(1888) =< aux(136)+1 s(1889) =< aux(136) s(1890) =< aux(136)+2 s(1891) =< aux(136)-1 s(1892) =< aux(136)-2 s(1880) =< aux(137)*(1/5)+aux(141) s(1881) =< aux(137)*(1/5)+aux(141) s(1882) =< aux(137)*(1/5)+aux(141) s(1883) =< aux(137)*(1/5)+aux(141) s(1884) =< aux(137)*(1/5)+aux(141) s(1885) =< aux(137)*(1/5)+aux(141) s(1883) =< aux(137)*(3/7)+aux(142) s(1884) =< aux(137)*(3/7)+aux(142) s(1885) =< aux(137)*(3/7)+aux(142) s(1881) =< aux(137)*(1/3)+aux(138) s(1882) =< aux(137)*(1/3)+aux(138) s(1883) =< aux(137)*(1/3)+aux(138) s(1884) =< aux(137)*(1/3)+aux(138) s(1885) =< aux(137)*(1/3)+aux(138) s(1886) =< aux(137)*(1/5)+aux(139) s(1879) =< aux(137)*(1/5)+aux(139) s(1887) =< aux(137)*(2/7)+aux(140) s(1886) =< aux(137)*(2/7)+aux(140) s(1879) =< aux(137)*(2/7)+aux(140) s(1893) =< s(1885)*s(1888) s(1894) =< s(1885)*s(1889) s(1895) =< s(1885)*s(1890) s(1896) =< s(1883)*s(1891) s(1897) =< s(1881)*s(1891) s(1898) =< s(1880)*s(1890) s(1899) =< s(1886)*s(1889) s(1900) =< s(1886)*s(1892) s(1901) =< s(1887)*s(1889) s(1902) =< s(1895) s(1903) =< s(1893) s(1904) =< s(1898) s(1905) =< s(1904)*s(1890) s(1906) =< s(1900) s(1907) =< s(1899) s(1908) =< s(1901) s(1909) =< s(1908)*aux(136) s(1840) =< aux(127) s(1841) =< aux(127) s(1842) =< aux(127) s(1843) =< aux(127) s(1844) =< aux(127) s(1845) =< aux(127) s(1846) =< aux(127) s(1842) =< aux(130) s(1844) =< aux(130) s(1847) =< aux(131) s(1848) =< aux(132) s(1841) =< aux(133) s(1842) =< aux(133) s(1844) =< aux(133) s(1845) =< aux(133) s(1844) =< aux(134) s(1849) =< aux(128)+1 s(1850) =< aux(128) s(1851) =< aux(128)+2 s(1852) =< aux(128)-1 s(1853) =< aux(128)-2 s(1841) =< aux(129)*(1/5)+aux(133) s(1842) =< aux(129)*(1/5)+aux(133) s(1843) =< aux(129)*(1/5)+aux(133) s(1844) =< aux(129)*(1/5)+aux(133) s(1845) =< aux(129)*(1/5)+aux(133) s(1846) =< aux(129)*(1/5)+aux(133) s(1844) =< aux(129)*(3/7)+aux(134) s(1845) =< aux(129)*(3/7)+aux(134) s(1846) =< aux(129)*(3/7)+aux(134) s(1842) =< aux(129)*(1/3)+aux(130) s(1843) =< aux(129)*(1/3)+aux(130) s(1844) =< aux(129)*(1/3)+aux(130) s(1845) =< aux(129)*(1/3)+aux(130) s(1846) =< aux(129)*(1/3)+aux(130) s(1847) =< aux(129)*(1/5)+aux(131) s(1840) =< aux(129)*(1/5)+aux(131) s(1848) =< aux(129)*(2/7)+aux(132) s(1847) =< aux(129)*(2/7)+aux(132) s(1840) =< aux(129)*(2/7)+aux(132) s(1854) =< s(1846)*s(1849) s(1855) =< s(1846)*s(1850) s(1856) =< s(1846)*s(1851) s(1857) =< s(1844)*s(1852) s(1858) =< s(1842)*s(1852) s(1859) =< s(1841)*s(1851) s(1860) =< s(1847)*s(1850) s(1861) =< s(1847)*s(1853) s(1862) =< s(1848)*s(1850) s(1863) =< s(1856) s(1864) =< s(1854) s(1865) =< s(1859) s(1866) =< s(1865)*s(1851) s(1867) =< s(1861) s(1868) =< s(1860) s(1869) =< s(1862) s(1870) =< s(1869)*aux(128) s(1952) =< aux(146) s(1918) =< aux(143) s(1919) =< aux(143) s(1920) =< aux(143) s(1921) =< aux(143) s(1922) =< aux(143) s(1923) =< aux(143) s(1924) =< aux(143) s(1920) =< aux(147) s(1922) =< aux(147) s(1925) =< aux(148) s(1926) =< aux(149) s(1919) =< aux(150) s(1920) =< aux(150) s(1922) =< aux(150) s(1923) =< aux(150) s(1922) =< aux(151) s(1927) =< aux(144)+1 s(1928) =< aux(144) s(1929) =< aux(144)+2 s(1930) =< aux(144)-1 s(1931) =< aux(144)-2 s(1919) =< aux(145)*(1/5)+aux(150) s(1920) =< aux(145)*(1/5)+aux(150) s(1921) =< aux(145)*(1/5)+aux(150) s(1922) =< aux(145)*(1/5)+aux(150) s(1923) =< aux(145)*(1/5)+aux(150) s(1924) =< aux(145)*(1/5)+aux(150) s(1922) =< aux(145)*(3/7)+aux(151) s(1923) =< aux(145)*(3/7)+aux(151) s(1924) =< aux(145)*(3/7)+aux(151) s(1920) =< aux(145)*(1/3)+aux(147) s(1921) =< aux(145)*(1/3)+aux(147) s(1922) =< aux(145)*(1/3)+aux(147) s(1923) =< aux(145)*(1/3)+aux(147) s(1924) =< aux(145)*(1/3)+aux(147) s(1925) =< aux(145)*(1/5)+aux(148) s(1918) =< aux(145)*(1/5)+aux(148) s(1926) =< aux(145)*(2/7)+aux(149) s(1925) =< aux(145)*(2/7)+aux(149) s(1918) =< aux(145)*(2/7)+aux(149) s(1932) =< s(1924)*s(1927) s(1933) =< s(1924)*s(1928) s(1934) =< s(1924)*s(1929) s(1935) =< s(1922)*s(1930) s(1936) =< s(1920)*s(1930) s(1937) =< s(1919)*s(1929) s(1938) =< s(1925)*s(1928) s(1939) =< s(1925)*s(1931) s(1940) =< s(1926)*s(1928) s(1941) =< s(1934) s(1942) =< s(1932) s(1943) =< s(1937) s(1944) =< s(1943)*s(1929) s(1945) =< s(1939) s(1946) =< s(1938) s(1947) =< s(1940) s(1948) =< s(1947)*aux(144) s(2331) =< s(2329) with precondition: [Out=1,V1>=1,V>=0,V5>=0] * Chain [52]: 2*s(2391)+6*s(2392)+2*s(2393)+2*s(2394)+2*s(2395)+2*s(2396)+6*s(2397)+8*s(2398)+8*s(2399)+2*s(2406)+2*s(2408)+2*s(2409)+4*s(2414)+4*s(2415)+14*s(2416)+2*s(2417)+4*s(2418)+4*s(2419)+14*s(2420)+2*s(2421)+4*s(2430)+12*s(2431)+4*s(2432)+4*s(2433)+4*s(2434)+4*s(2435)+12*s(2436)+16*s(2437)+16*s(2438)+4*s(2445)+4*s(2447)+4*s(2448)+8*s(2453)+8*s(2454)+28*s(2455)+4*s(2456)+8*s(2457)+8*s(2458)+28*s(2459)+4*s(2460)+3*s(2469)+9*s(2470)+3*s(2471)+3*s(2472)+3*s(2473)+3*s(2474)+9*s(2475)+12*s(2476)+12*s(2477)+3*s(2484)+3*s(2486)+3*s(2487)+6*s(2492)+6*s(2493)+21*s(2494)+3*s(2495)+6*s(2496)+6*s(2497)+21*s(2498)+3*s(2499)+20*s(2501)+8*s(2504)+4*s(2505)+6*s(2759)+4*s(2761)+4*s(2762)+2*s(2763)+4 Such that:aux(160) =< 1 aux(161) =< 2 aux(162) =< 3 aux(163) =< V1 aux(164) =< 2*V1 aux(165) =< 2*V1+1 aux(166) =< 2/3*V1 aux(167) =< 3/5*V1 aux(168) =< 3/7*V1 aux(169) =< 4/5*V1 aux(170) =< 4/7*V1 aux(171) =< V aux(172) =< 2*V aux(173) =< 2*V+1 aux(174) =< 2/3*V aux(175) =< 3/5*V aux(176) =< 3/7*V aux(177) =< 4/5*V aux(178) =< 4/7*V aux(179) =< V5 aux(180) =< 2*V5 aux(181) =< 2*V5+1 aux(182) =< 2/3*V5 aux(183) =< 3/5*V5 aux(184) =< 3/7*V5 aux(185) =< 4/5*V5 aux(186) =< 4/7*V5 s(2759) =< aux(160) s(2761) =< aux(161) s(2762) =< aux(162) s(2763) =< s(2759)*aux(161) s(2469) =< aux(179) s(2470) =< aux(179) s(2471) =< aux(179) s(2472) =< aux(179) s(2473) =< aux(179) s(2474) =< aux(179) s(2475) =< aux(179) s(2471) =< aux(182) s(2473) =< aux(182) s(2476) =< aux(183) s(2477) =< aux(184) s(2470) =< aux(185) s(2471) =< aux(185) s(2473) =< aux(185) s(2474) =< aux(185) s(2473) =< aux(186) s(2478) =< aux(180)+1 s(2479) =< aux(180) s(2480) =< aux(180)+2 s(2481) =< aux(180)-1 s(2482) =< aux(180)-2 s(2470) =< aux(181)*(1/5)+aux(185) s(2471) =< aux(181)*(1/5)+aux(185) s(2472) =< aux(181)*(1/5)+aux(185) s(2473) =< aux(181)*(1/5)+aux(185) s(2474) =< aux(181)*(1/5)+aux(185) s(2475) =< aux(181)*(1/5)+aux(185) s(2473) =< aux(181)*(3/7)+aux(186) s(2474) =< aux(181)*(3/7)+aux(186) s(2475) =< aux(181)*(3/7)+aux(186) s(2471) =< aux(181)*(1/3)+aux(182) s(2472) =< aux(181)*(1/3)+aux(182) s(2473) =< aux(181)*(1/3)+aux(182) s(2474) =< aux(181)*(1/3)+aux(182) s(2475) =< aux(181)*(1/3)+aux(182) s(2476) =< aux(181)*(1/5)+aux(183) s(2469) =< aux(181)*(1/5)+aux(183) s(2477) =< aux(181)*(2/7)+aux(184) s(2476) =< aux(181)*(2/7)+aux(184) s(2469) =< aux(181)*(2/7)+aux(184) s(2483) =< s(2475)*s(2478) s(2484) =< s(2475)*s(2479) s(2485) =< s(2475)*s(2480) s(2486) =< s(2473)*s(2481) s(2487) =< s(2471)*s(2481) s(2488) =< s(2470)*s(2480) s(2489) =< s(2476)*s(2479) s(2490) =< s(2476)*s(2482) s(2491) =< s(2477)*s(2479) s(2492) =< s(2485) s(2493) =< s(2483) s(2494) =< s(2488) s(2495) =< s(2494)*s(2480) s(2496) =< s(2490) s(2497) =< s(2489) s(2498) =< s(2491) s(2499) =< s(2498)*aux(180) s(2501) =< aux(172) s(2504) =< aux(173) s(2505) =< s(2501)*aux(172) s(2430) =< aux(171) s(2431) =< aux(171) s(2432) =< aux(171) s(2433) =< aux(171) s(2434) =< aux(171) s(2435) =< aux(171) s(2436) =< aux(171) s(2432) =< aux(174) s(2434) =< aux(174) s(2437) =< aux(175) s(2438) =< aux(176) s(2431) =< aux(177) s(2432) =< aux(177) s(2434) =< aux(177) s(2435) =< aux(177) s(2434) =< aux(178) s(2439) =< aux(172)+1 s(2440) =< aux(172) s(2441) =< aux(172)+2 s(2442) =< aux(172)-1 s(2443) =< aux(172)-2 s(2431) =< aux(173)*(1/5)+aux(177) s(2432) =< aux(173)*(1/5)+aux(177) s(2433) =< aux(173)*(1/5)+aux(177) s(2434) =< aux(173)*(1/5)+aux(177) s(2435) =< aux(173)*(1/5)+aux(177) s(2436) =< aux(173)*(1/5)+aux(177) s(2434) =< aux(173)*(3/7)+aux(178) s(2435) =< aux(173)*(3/7)+aux(178) s(2436) =< aux(173)*(3/7)+aux(178) s(2432) =< aux(173)*(1/3)+aux(174) s(2433) =< aux(173)*(1/3)+aux(174) s(2434) =< aux(173)*(1/3)+aux(174) s(2435) =< aux(173)*(1/3)+aux(174) s(2436) =< aux(173)*(1/3)+aux(174) s(2437) =< aux(173)*(1/5)+aux(175) s(2430) =< aux(173)*(1/5)+aux(175) s(2438) =< aux(173)*(2/7)+aux(176) s(2437) =< aux(173)*(2/7)+aux(176) s(2430) =< aux(173)*(2/7)+aux(176) s(2444) =< s(2436)*s(2439) s(2445) =< s(2436)*s(2440) s(2446) =< s(2436)*s(2441) s(2447) =< s(2434)*s(2442) s(2448) =< s(2432)*s(2442) s(2449) =< s(2431)*s(2441) s(2450) =< s(2437)*s(2440) s(2451) =< s(2437)*s(2443) s(2452) =< s(2438)*s(2440) s(2453) =< s(2446) s(2454) =< s(2444) s(2455) =< s(2449) s(2456) =< s(2455)*s(2441) s(2457) =< s(2451) s(2458) =< s(2450) s(2459) =< s(2452) s(2460) =< s(2459)*aux(172) s(2391) =< aux(163) s(2392) =< aux(163) s(2393) =< aux(163) s(2394) =< aux(163) s(2395) =< aux(163) s(2396) =< aux(163) s(2397) =< aux(163) s(2393) =< aux(166) s(2395) =< aux(166) s(2398) =< aux(167) s(2399) =< aux(168) s(2392) =< aux(169) s(2393) =< aux(169) s(2395) =< aux(169) s(2396) =< aux(169) s(2395) =< aux(170) s(2400) =< aux(164)+1 s(2401) =< aux(164) s(2402) =< aux(164)+2 s(2403) =< aux(164)-1 s(2404) =< aux(164)-2 s(2392) =< aux(165)*(1/5)+aux(169) s(2393) =< aux(165)*(1/5)+aux(169) s(2394) =< aux(165)*(1/5)+aux(169) s(2395) =< aux(165)*(1/5)+aux(169) s(2396) =< aux(165)*(1/5)+aux(169) s(2397) =< aux(165)*(1/5)+aux(169) s(2395) =< aux(165)*(3/7)+aux(170) s(2396) =< aux(165)*(3/7)+aux(170) s(2397) =< aux(165)*(3/7)+aux(170) s(2393) =< aux(165)*(1/3)+aux(166) s(2394) =< aux(165)*(1/3)+aux(166) s(2395) =< aux(165)*(1/3)+aux(166) s(2396) =< aux(165)*(1/3)+aux(166) s(2397) =< aux(165)*(1/3)+aux(166) s(2398) =< aux(165)*(1/5)+aux(167) s(2391) =< aux(165)*(1/5)+aux(167) s(2399) =< aux(165)*(2/7)+aux(168) s(2398) =< aux(165)*(2/7)+aux(168) s(2391) =< aux(165)*(2/7)+aux(168) s(2405) =< s(2397)*s(2400) s(2406) =< s(2397)*s(2401) s(2407) =< s(2397)*s(2402) s(2408) =< s(2395)*s(2403) s(2409) =< s(2393)*s(2403) s(2410) =< s(2392)*s(2402) s(2411) =< s(2398)*s(2401) s(2412) =< s(2398)*s(2404) s(2413) =< s(2399)*s(2401) s(2414) =< s(2407) s(2415) =< s(2405) s(2416) =< s(2410) s(2417) =< s(2416)*s(2402) s(2418) =< s(2412) s(2419) =< s(2411) s(2420) =< s(2413) s(2421) =< s(2420)*aux(164) with precondition: [V1>=1,V5>=0,Out>=2,2*V>=Out] * Chain [51]: 4*s(2778)+12*s(2779)+4*s(2780)+4*s(2781)+4*s(2782)+4*s(2783)+12*s(2784)+16*s(2785)+16*s(2786)+4*s(2793)+4*s(2795)+4*s(2796)+8*s(2801)+8*s(2802)+28*s(2803)+4*s(2804)+8*s(2805)+8*s(2806)+28*s(2807)+4*s(2808)+4*s(2817)+12*s(2818)+4*s(2819)+4*s(2820)+4*s(2821)+4*s(2822)+12*s(2823)+16*s(2824)+16*s(2825)+4*s(2832)+4*s(2834)+4*s(2835)+8*s(2840)+8*s(2841)+28*s(2842)+4*s(2843)+8*s(2844)+8*s(2845)+28*s(2846)+4*s(2847)+1 Such that:aux(187) =< V1 aux(188) =< 2*V1 aux(189) =< 2*V1+1 aux(190) =< 2/3*V1 aux(191) =< 3/5*V1 aux(192) =< 3/7*V1 aux(193) =< 4/5*V1 aux(194) =< 4/7*V1 aux(195) =< V aux(196) =< 2*V aux(197) =< 2*V+1 aux(198) =< 2/3*V aux(199) =< 3/5*V aux(200) =< 3/7*V aux(201) =< 4/5*V aux(202) =< 4/7*V s(2817) =< aux(195) s(2818) =< aux(195) s(2819) =< aux(195) s(2820) =< aux(195) s(2821) =< aux(195) s(2822) =< aux(195) s(2823) =< aux(195) s(2819) =< aux(198) s(2821) =< aux(198) s(2824) =< aux(199) s(2825) =< aux(200) s(2818) =< aux(201) s(2819) =< aux(201) s(2821) =< aux(201) s(2822) =< aux(201) s(2821) =< aux(202) s(2826) =< aux(196)+1 s(2827) =< aux(196) s(2828) =< aux(196)+2 s(2829) =< aux(196)-1 s(2830) =< aux(196)-2 s(2818) =< aux(197)*(1/5)+aux(201) s(2819) =< aux(197)*(1/5)+aux(201) s(2820) =< aux(197)*(1/5)+aux(201) s(2821) =< aux(197)*(1/5)+aux(201) s(2822) =< aux(197)*(1/5)+aux(201) s(2823) =< aux(197)*(1/5)+aux(201) s(2821) =< aux(197)*(3/7)+aux(202) s(2822) =< aux(197)*(3/7)+aux(202) s(2823) =< aux(197)*(3/7)+aux(202) s(2819) =< aux(197)*(1/3)+aux(198) s(2820) =< aux(197)*(1/3)+aux(198) s(2821) =< aux(197)*(1/3)+aux(198) s(2822) =< aux(197)*(1/3)+aux(198) s(2823) =< aux(197)*(1/3)+aux(198) s(2824) =< aux(197)*(1/5)+aux(199) s(2817) =< aux(197)*(1/5)+aux(199) s(2825) =< aux(197)*(2/7)+aux(200) s(2824) =< aux(197)*(2/7)+aux(200) s(2817) =< aux(197)*(2/7)+aux(200) s(2831) =< s(2823)*s(2826) s(2832) =< s(2823)*s(2827) s(2833) =< s(2823)*s(2828) s(2834) =< s(2821)*s(2829) s(2835) =< s(2819)*s(2829) s(2836) =< s(2818)*s(2828) s(2837) =< s(2824)*s(2827) s(2838) =< s(2824)*s(2830) s(2839) =< s(2825)*s(2827) s(2840) =< s(2833) s(2841) =< s(2831) s(2842) =< s(2836) s(2843) =< s(2842)*s(2828) s(2844) =< s(2838) s(2845) =< s(2837) s(2846) =< s(2839) s(2847) =< s(2846)*aux(196) s(2778) =< aux(187) s(2779) =< aux(187) s(2780) =< aux(187) s(2781) =< aux(187) s(2782) =< aux(187) s(2783) =< aux(187) s(2784) =< aux(187) s(2780) =< aux(190) s(2782) =< aux(190) s(2785) =< aux(191) s(2786) =< aux(192) s(2779) =< aux(193) s(2780) =< aux(193) s(2782) =< aux(193) s(2783) =< aux(193) s(2782) =< aux(194) s(2787) =< aux(188)+1 s(2788) =< aux(188) s(2789) =< aux(188)+2 s(2790) =< aux(188)-1 s(2791) =< aux(188)-2 s(2779) =< aux(189)*(1/5)+aux(193) s(2780) =< aux(189)*(1/5)+aux(193) s(2781) =< aux(189)*(1/5)+aux(193) s(2782) =< aux(189)*(1/5)+aux(193) s(2783) =< aux(189)*(1/5)+aux(193) s(2784) =< aux(189)*(1/5)+aux(193) s(2782) =< aux(189)*(3/7)+aux(194) s(2783) =< aux(189)*(3/7)+aux(194) s(2784) =< aux(189)*(3/7)+aux(194) s(2780) =< aux(189)*(1/3)+aux(190) s(2781) =< aux(189)*(1/3)+aux(190) s(2782) =< aux(189)*(1/3)+aux(190) s(2783) =< aux(189)*(1/3)+aux(190) s(2784) =< aux(189)*(1/3)+aux(190) s(2785) =< aux(189)*(1/5)+aux(191) s(2778) =< aux(189)*(1/5)+aux(191) s(2786) =< aux(189)*(2/7)+aux(192) s(2785) =< aux(189)*(2/7)+aux(192) s(2778) =< aux(189)*(2/7)+aux(192) s(2792) =< s(2784)*s(2787) s(2793) =< s(2784)*s(2788) s(2794) =< s(2784)*s(2789) s(2795) =< s(2782)*s(2790) s(2796) =< s(2780)*s(2790) s(2797) =< s(2779)*s(2789) s(2798) =< s(2785)*s(2788) s(2799) =< s(2785)*s(2791) s(2800) =< s(2786)*s(2788) s(2801) =< s(2794) s(2802) =< s(2792) s(2803) =< s(2797) s(2804) =< s(2803)*s(2789) s(2805) =< s(2799) s(2806) =< s(2798) s(2807) =< s(2800) s(2808) =< s(2807)*aux(188) with precondition: [V5=2,Out=0,V1>=0,V>=0] * Chain [50]: 2*s(3090)+6*s(3091)+2*s(3092)+2*s(3093)+2*s(3094)+2*s(3095)+6*s(3096)+8*s(3097)+8*s(3098)+2*s(3105)+2*s(3107)+2*s(3108)+4*s(3113)+4*s(3114)+14*s(3115)+2*s(3116)+4*s(3117)+4*s(3118)+14*s(3119)+2*s(3120)+2*s(3129)+6*s(3130)+2*s(3131)+2*s(3132)+2*s(3133)+2*s(3134)+6*s(3135)+8*s(3136)+8*s(3137)+2*s(3144)+2*s(3146)+2*s(3147)+4*s(3152)+4*s(3153)+14*s(3154)+2*s(3155)+4*s(3156)+4*s(3157)+14*s(3158)+2*s(3159)+4*s(3162)+8*s(3163)+4 Such that:aux(205) =< 4 aux(206) =< V1 aux(207) =< 2*V1 aux(208) =< 2*V1+1 aux(209) =< 2/3*V1 aux(210) =< 3/5*V1 aux(211) =< 3/7*V1 aux(212) =< 4/5*V1 aux(213) =< 4/7*V1 aux(214) =< V aux(215) =< 2*V aux(216) =< 2*V+1 aux(217) =< 2/3*V aux(218) =< 3/5*V aux(219) =< 3/7*V aux(220) =< 4/5*V aux(221) =< 4/7*V s(3162) =< aux(215) s(3163) =< aux(205) s(3129) =< aux(214) s(3130) =< aux(214) s(3131) =< aux(214) s(3132) =< aux(214) s(3133) =< aux(214) s(3134) =< aux(214) s(3135) =< aux(214) s(3131) =< aux(217) s(3133) =< aux(217) s(3136) =< aux(218) s(3137) =< aux(219) s(3130) =< aux(220) s(3131) =< aux(220) s(3133) =< aux(220) s(3134) =< aux(220) s(3133) =< aux(221) s(3138) =< aux(215)+1 s(3139) =< aux(215) s(3140) =< aux(215)+2 s(3141) =< aux(215)-1 s(3142) =< aux(215)-2 s(3130) =< aux(216)*(1/5)+aux(220) s(3131) =< aux(216)*(1/5)+aux(220) s(3132) =< aux(216)*(1/5)+aux(220) s(3133) =< aux(216)*(1/5)+aux(220) s(3134) =< aux(216)*(1/5)+aux(220) s(3135) =< aux(216)*(1/5)+aux(220) s(3133) =< aux(216)*(3/7)+aux(221) s(3134) =< aux(216)*(3/7)+aux(221) s(3135) =< aux(216)*(3/7)+aux(221) s(3131) =< aux(216)*(1/3)+aux(217) s(3132) =< aux(216)*(1/3)+aux(217) s(3133) =< aux(216)*(1/3)+aux(217) s(3134) =< aux(216)*(1/3)+aux(217) s(3135) =< aux(216)*(1/3)+aux(217) s(3136) =< aux(216)*(1/5)+aux(218) s(3129) =< aux(216)*(1/5)+aux(218) s(3137) =< aux(216)*(2/7)+aux(219) s(3136) =< aux(216)*(2/7)+aux(219) s(3129) =< aux(216)*(2/7)+aux(219) s(3143) =< s(3135)*s(3138) s(3144) =< s(3135)*s(3139) s(3145) =< s(3135)*s(3140) s(3146) =< s(3133)*s(3141) s(3147) =< s(3131)*s(3141) s(3148) =< s(3130)*s(3140) s(3149) =< s(3136)*s(3139) s(3150) =< s(3136)*s(3142) s(3151) =< s(3137)*s(3139) s(3152) =< s(3145) s(3153) =< s(3143) s(3154) =< s(3148) s(3155) =< s(3154)*s(3140) s(3156) =< s(3150) s(3157) =< s(3149) s(3158) =< s(3151) s(3159) =< s(3158)*aux(215) s(3090) =< aux(206) s(3091) =< aux(206) s(3092) =< aux(206) s(3093) =< aux(206) s(3094) =< aux(206) s(3095) =< aux(206) s(3096) =< aux(206) s(3092) =< aux(209) s(3094) =< aux(209) s(3097) =< aux(210) s(3098) =< aux(211) s(3091) =< aux(212) s(3092) =< aux(212) s(3094) =< aux(212) s(3095) =< aux(212) s(3094) =< aux(213) s(3099) =< aux(207)+1 s(3100) =< aux(207) s(3101) =< aux(207)+2 s(3102) =< aux(207)-1 s(3103) =< aux(207)-2 s(3091) =< aux(208)*(1/5)+aux(212) s(3092) =< aux(208)*(1/5)+aux(212) s(3093) =< aux(208)*(1/5)+aux(212) s(3094) =< aux(208)*(1/5)+aux(212) s(3095) =< aux(208)*(1/5)+aux(212) s(3096) =< aux(208)*(1/5)+aux(212) s(3094) =< aux(208)*(3/7)+aux(213) s(3095) =< aux(208)*(3/7)+aux(213) s(3096) =< aux(208)*(3/7)+aux(213) s(3092) =< aux(208)*(1/3)+aux(209) s(3093) =< aux(208)*(1/3)+aux(209) s(3094) =< aux(208)*(1/3)+aux(209) s(3095) =< aux(208)*(1/3)+aux(209) s(3096) =< aux(208)*(1/3)+aux(209) s(3097) =< aux(208)*(1/5)+aux(210) s(3090) =< aux(208)*(1/5)+aux(210) s(3098) =< aux(208)*(2/7)+aux(211) s(3097) =< aux(208)*(2/7)+aux(211) s(3090) =< aux(208)*(2/7)+aux(211) s(3104) =< s(3096)*s(3099) s(3105) =< s(3096)*s(3100) s(3106) =< s(3096)*s(3101) s(3107) =< s(3094)*s(3102) s(3108) =< s(3092)*s(3102) s(3109) =< s(3091)*s(3101) s(3110) =< s(3097)*s(3100) s(3111) =< s(3097)*s(3103) s(3112) =< s(3098)*s(3100) s(3113) =< s(3106) s(3114) =< s(3104) s(3115) =< s(3109) s(3116) =< s(3115)*s(3101) s(3117) =< s(3111) s(3118) =< s(3110) s(3119) =< s(3112) s(3120) =< s(3119)*aux(207) with precondition: [V5=2,Out=1,V1>=1,V>=0] * Chain [49]: 1*s(3262)+3*s(3263)+1*s(3264)+1*s(3265)+1*s(3266)+1*s(3267)+3*s(3268)+4*s(3269)+4*s(3270)+1*s(3277)+1*s(3279)+1*s(3280)+2*s(3285)+2*s(3286)+7*s(3287)+1*s(3288)+2*s(3289)+2*s(3290)+7*s(3291)+1*s(3292)+2*s(3301)+6*s(3302)+2*s(3303)+2*s(3304)+2*s(3305)+2*s(3306)+6*s(3307)+8*s(3308)+8*s(3309)+2*s(3316)+2*s(3318)+2*s(3319)+4*s(3324)+4*s(3325)+14*s(3326)+2*s(3327)+4*s(3328)+4*s(3329)+14*s(3330)+2*s(3331)+10*s(3333)+4*s(3336)+2*s(3337)+4 Such that:s(3254) =< V1 s(3255) =< 2*V1 s(3256) =< 2*V1+1 s(3257) =< 2/3*V1 s(3258) =< 3/5*V1 s(3259) =< 3/7*V1 s(3260) =< 4/5*V1 s(3261) =< 4/7*V1 aux(226) =< V aux(227) =< 2*V aux(228) =< 2*V+1 aux(229) =< 2/3*V aux(230) =< 3/5*V aux(231) =< 3/7*V aux(232) =< 4/5*V aux(233) =< 4/7*V s(3333) =< aux(227) s(3336) =< aux(228) s(3337) =< s(3333)*aux(227) s(3301) =< aux(226) s(3302) =< aux(226) s(3303) =< aux(226) s(3304) =< aux(226) s(3305) =< aux(226) s(3306) =< aux(226) s(3307) =< aux(226) s(3303) =< aux(229) s(3305) =< aux(229) s(3308) =< aux(230) s(3309) =< aux(231) s(3302) =< aux(232) s(3303) =< aux(232) s(3305) =< aux(232) s(3306) =< aux(232) s(3305) =< aux(233) s(3310) =< aux(227)+1 s(3311) =< aux(227) s(3312) =< aux(227)+2 s(3313) =< aux(227)-1 s(3314) =< aux(227)-2 s(3302) =< aux(228)*(1/5)+aux(232) s(3303) =< aux(228)*(1/5)+aux(232) s(3304) =< aux(228)*(1/5)+aux(232) s(3305) =< aux(228)*(1/5)+aux(232) s(3306) =< aux(228)*(1/5)+aux(232) s(3307) =< aux(228)*(1/5)+aux(232) s(3305) =< aux(228)*(3/7)+aux(233) s(3306) =< aux(228)*(3/7)+aux(233) s(3307) =< aux(228)*(3/7)+aux(233) s(3303) =< aux(228)*(1/3)+aux(229) s(3304) =< aux(228)*(1/3)+aux(229) s(3305) =< aux(228)*(1/3)+aux(229) s(3306) =< aux(228)*(1/3)+aux(229) s(3307) =< aux(228)*(1/3)+aux(229) s(3308) =< aux(228)*(1/5)+aux(230) s(3301) =< aux(228)*(1/5)+aux(230) s(3309) =< aux(228)*(2/7)+aux(231) s(3308) =< aux(228)*(2/7)+aux(231) s(3301) =< aux(228)*(2/7)+aux(231) s(3315) =< s(3307)*s(3310) s(3316) =< s(3307)*s(3311) s(3317) =< s(3307)*s(3312) s(3318) =< s(3305)*s(3313) s(3319) =< s(3303)*s(3313) s(3320) =< s(3302)*s(3312) s(3321) =< s(3308)*s(3311) s(3322) =< s(3308)*s(3314) s(3323) =< s(3309)*s(3311) s(3324) =< s(3317) s(3325) =< s(3315) s(3326) =< s(3320) s(3327) =< s(3326)*s(3312) s(3328) =< s(3322) s(3329) =< s(3321) s(3330) =< s(3323) s(3331) =< s(3330)*aux(227) s(3262) =< s(3254) s(3263) =< s(3254) s(3264) =< s(3254) s(3265) =< s(3254) s(3266) =< s(3254) s(3267) =< s(3254) s(3268) =< s(3254) s(3264) =< s(3257) s(3266) =< s(3257) s(3269) =< s(3258) s(3270) =< s(3259) s(3263) =< s(3260) s(3264) =< s(3260) s(3266) =< s(3260) s(3267) =< s(3260) s(3266) =< s(3261) s(3271) =< s(3255)+1 s(3272) =< s(3255) s(3273) =< s(3255)+2 s(3274) =< s(3255)-1 s(3275) =< s(3255)-2 s(3263) =< s(3256)*(1/5)+s(3260) s(3264) =< s(3256)*(1/5)+s(3260) s(3265) =< s(3256)*(1/5)+s(3260) s(3266) =< s(3256)*(1/5)+s(3260) s(3267) =< s(3256)*(1/5)+s(3260) s(3268) =< s(3256)*(1/5)+s(3260) s(3266) =< s(3256)*(3/7)+s(3261) s(3267) =< s(3256)*(3/7)+s(3261) s(3268) =< s(3256)*(3/7)+s(3261) s(3264) =< s(3256)*(1/3)+s(3257) s(3265) =< s(3256)*(1/3)+s(3257) s(3266) =< s(3256)*(1/3)+s(3257) s(3267) =< s(3256)*(1/3)+s(3257) s(3268) =< s(3256)*(1/3)+s(3257) s(3269) =< s(3256)*(1/5)+s(3258) s(3262) =< s(3256)*(1/5)+s(3258) s(3270) =< s(3256)*(2/7)+s(3259) s(3269) =< s(3256)*(2/7)+s(3259) s(3262) =< s(3256)*(2/7)+s(3259) s(3276) =< s(3268)*s(3271) s(3277) =< s(3268)*s(3272) s(3278) =< s(3268)*s(3273) s(3279) =< s(3266)*s(3274) s(3280) =< s(3264)*s(3274) s(3281) =< s(3263)*s(3273) s(3282) =< s(3269)*s(3272) s(3283) =< s(3269)*s(3275) s(3284) =< s(3270)*s(3272) s(3285) =< s(3278) s(3286) =< s(3276) s(3287) =< s(3281) s(3288) =< s(3287)*s(3273) s(3289) =< s(3283) s(3290) =< s(3282) s(3291) =< s(3284) s(3292) =< s(3291)*s(3255) with precondition: [V5=2,V1>=1,Out>=2,2*V>=Out+2] * Chain [48]: 6*s(3391)+18*s(3392)+6*s(3393)+6*s(3394)+6*s(3395)+6*s(3396)+18*s(3397)+24*s(3398)+24*s(3399)+6*s(3406)+6*s(3408)+6*s(3409)+12*s(3414)+12*s(3415)+42*s(3416)+6*s(3417)+12*s(3418)+12*s(3419)+42*s(3420)+6*s(3421)+3*s(3430)+9*s(3431)+3*s(3432)+3*s(3433)+3*s(3434)+3*s(3435)+9*s(3436)+12*s(3437)+12*s(3438)+3*s(3445)+3*s(3447)+3*s(3448)+6*s(3453)+6*s(3454)+21*s(3455)+3*s(3456)+6*s(3457)+6*s(3458)+21*s(3459)+3*s(3460)+1 Such that:aux(234) =< V1 aux(235) =< 2*V1 aux(236) =< 2*V1+1 aux(237) =< 2/3*V1 aux(238) =< 3/5*V1 aux(239) =< 3/7*V1 aux(240) =< 4/5*V1 aux(241) =< 4/7*V1 aux(242) =< V5 aux(243) =< 2*V5 aux(244) =< 2*V5+1 aux(245) =< 2/3*V5 aux(246) =< 3/5*V5 aux(247) =< 3/7*V5 aux(248) =< 4/5*V5 aux(249) =< 4/7*V5 s(3430) =< aux(242) s(3431) =< aux(242) s(3432) =< aux(242) s(3433) =< aux(242) s(3434) =< aux(242) s(3435) =< aux(242) s(3436) =< aux(242) s(3432) =< aux(245) s(3434) =< aux(245) s(3437) =< aux(246) s(3438) =< aux(247) s(3431) =< aux(248) s(3432) =< aux(248) s(3434) =< aux(248) s(3435) =< aux(248) s(3434) =< aux(249) s(3439) =< aux(243)+1 s(3440) =< aux(243) s(3441) =< aux(243)+2 s(3442) =< aux(243)-1 s(3443) =< aux(243)-2 s(3431) =< aux(244)*(1/5)+aux(248) s(3432) =< aux(244)*(1/5)+aux(248) s(3433) =< aux(244)*(1/5)+aux(248) s(3434) =< aux(244)*(1/5)+aux(248) s(3435) =< aux(244)*(1/5)+aux(248) s(3436) =< aux(244)*(1/5)+aux(248) s(3434) =< aux(244)*(3/7)+aux(249) s(3435) =< aux(244)*(3/7)+aux(249) s(3436) =< aux(244)*(3/7)+aux(249) s(3432) =< aux(244)*(1/3)+aux(245) s(3433) =< aux(244)*(1/3)+aux(245) s(3434) =< aux(244)*(1/3)+aux(245) s(3435) =< aux(244)*(1/3)+aux(245) s(3436) =< aux(244)*(1/3)+aux(245) s(3437) =< aux(244)*(1/5)+aux(246) s(3430) =< aux(244)*(1/5)+aux(246) s(3438) =< aux(244)*(2/7)+aux(247) s(3437) =< aux(244)*(2/7)+aux(247) s(3430) =< aux(244)*(2/7)+aux(247) s(3444) =< s(3436)*s(3439) s(3445) =< s(3436)*s(3440) s(3446) =< s(3436)*s(3441) s(3447) =< s(3434)*s(3442) s(3448) =< s(3432)*s(3442) s(3449) =< s(3431)*s(3441) s(3450) =< s(3437)*s(3440) s(3451) =< s(3437)*s(3443) s(3452) =< s(3438)*s(3440) s(3453) =< s(3446) s(3454) =< s(3444) s(3455) =< s(3449) s(3456) =< s(3455)*s(3441) s(3457) =< s(3451) s(3458) =< s(3450) s(3459) =< s(3452) s(3460) =< s(3459)*aux(243) s(3391) =< aux(234) s(3392) =< aux(234) s(3393) =< aux(234) s(3394) =< aux(234) s(3395) =< aux(234) s(3396) =< aux(234) s(3397) =< aux(234) s(3393) =< aux(237) s(3395) =< aux(237) s(3398) =< aux(238) s(3399) =< aux(239) s(3392) =< aux(240) s(3393) =< aux(240) s(3395) =< aux(240) s(3396) =< aux(240) s(3395) =< aux(241) s(3400) =< aux(235)+1 s(3401) =< aux(235) s(3402) =< aux(235)+2 s(3403) =< aux(235)-1 s(3404) =< aux(235)-2 s(3392) =< aux(236)*(1/5)+aux(240) s(3393) =< aux(236)*(1/5)+aux(240) s(3394) =< aux(236)*(1/5)+aux(240) s(3395) =< aux(236)*(1/5)+aux(240) s(3396) =< aux(236)*(1/5)+aux(240) s(3397) =< aux(236)*(1/5)+aux(240) s(3395) =< aux(236)*(3/7)+aux(241) s(3396) =< aux(236)*(3/7)+aux(241) s(3397) =< aux(236)*(3/7)+aux(241) s(3393) =< aux(236)*(1/3)+aux(237) s(3394) =< aux(236)*(1/3)+aux(237) s(3395) =< aux(236)*(1/3)+aux(237) s(3396) =< aux(236)*(1/3)+aux(237) s(3397) =< aux(236)*(1/3)+aux(237) s(3398) =< aux(236)*(1/5)+aux(238) s(3391) =< aux(236)*(1/5)+aux(238) s(3399) =< aux(236)*(2/7)+aux(239) s(3398) =< aux(236)*(2/7)+aux(239) s(3391) =< aux(236)*(2/7)+aux(239) s(3405) =< s(3397)*s(3400) s(3406) =< s(3397)*s(3401) s(3407) =< s(3397)*s(3402) s(3408) =< s(3395)*s(3403) s(3409) =< s(3393)*s(3403) s(3410) =< s(3392)*s(3402) s(3411) =< s(3398)*s(3401) s(3412) =< s(3398)*s(3404) s(3413) =< s(3399)*s(3401) s(3414) =< s(3407) s(3415) =< s(3405) s(3416) =< s(3410) s(3417) =< s(3416)*s(3402) s(3418) =< s(3412) s(3419) =< s(3411) s(3420) =< s(3413) s(3421) =< s(3420)*aux(235) with precondition: [V=2,Out=0,V1>=0,V5>=0] * Chain [47]: 3*s(3742)+9*s(3743)+3*s(3744)+3*s(3745)+3*s(3746)+3*s(3747)+9*s(3748)+12*s(3749)+12*s(3750)+3*s(3757)+3*s(3759)+3*s(3760)+6*s(3765)+6*s(3766)+21*s(3767)+3*s(3768)+6*s(3769)+6*s(3770)+21*s(3771)+3*s(3772)+1*s(3781)+3*s(3782)+1*s(3783)+1*s(3784)+1*s(3785)+1*s(3786)+3*s(3787)+4*s(3788)+4*s(3789)+1*s(3796)+1*s(3798)+1*s(3799)+2*s(3804)+2*s(3805)+7*s(3806)+1*s(3807)+2*s(3808)+2*s(3809)+7*s(3810)+1*s(3811)+8*s(3814)+2*s(3815)+2*s(3858)+4 Such that:s(3856) =< 4 s(3773) =< V5 s(3774) =< 2*V5 s(3775) =< 2*V5+1 s(3813) =< 2*V5+2 s(3776) =< 2/3*V5 s(3777) =< 3/5*V5 s(3778) =< 3/7*V5 s(3779) =< 4/5*V5 s(3780) =< 4/7*V5 aux(251) =< 2 aux(252) =< V1 aux(253) =< 2*V1 aux(254) =< 2*V1+1 aux(255) =< 2/3*V1 aux(256) =< 3/5*V1 aux(257) =< 3/7*V1 aux(258) =< 4/5*V1 aux(259) =< 4/7*V1 s(3814) =< aux(251) s(3815) =< s(3813) s(3781) =< s(3773) s(3782) =< s(3773) s(3783) =< s(3773) s(3784) =< s(3773) s(3785) =< s(3773) s(3786) =< s(3773) s(3787) =< s(3773) s(3783) =< s(3776) s(3785) =< s(3776) s(3788) =< s(3777) s(3789) =< s(3778) s(3782) =< s(3779) s(3783) =< s(3779) s(3785) =< s(3779) s(3786) =< s(3779) s(3785) =< s(3780) s(3790) =< s(3774)+1 s(3791) =< s(3774) s(3792) =< s(3774)+2 s(3793) =< s(3774)-1 s(3794) =< s(3774)-2 s(3782) =< s(3775)*(1/5)+s(3779) s(3783) =< s(3775)*(1/5)+s(3779) s(3784) =< s(3775)*(1/5)+s(3779) s(3785) =< s(3775)*(1/5)+s(3779) s(3786) =< s(3775)*(1/5)+s(3779) s(3787) =< s(3775)*(1/5)+s(3779) s(3785) =< s(3775)*(3/7)+s(3780) s(3786) =< s(3775)*(3/7)+s(3780) s(3787) =< s(3775)*(3/7)+s(3780) s(3783) =< s(3775)*(1/3)+s(3776) s(3784) =< s(3775)*(1/3)+s(3776) s(3785) =< s(3775)*(1/3)+s(3776) s(3786) =< s(3775)*(1/3)+s(3776) s(3787) =< s(3775)*(1/3)+s(3776) s(3788) =< s(3775)*(1/5)+s(3777) s(3781) =< s(3775)*(1/5)+s(3777) s(3789) =< s(3775)*(2/7)+s(3778) s(3788) =< s(3775)*(2/7)+s(3778) s(3781) =< s(3775)*(2/7)+s(3778) s(3795) =< s(3787)*s(3790) s(3796) =< s(3787)*s(3791) s(3797) =< s(3787)*s(3792) s(3798) =< s(3785)*s(3793) s(3799) =< s(3783)*s(3793) s(3800) =< s(3782)*s(3792) s(3801) =< s(3788)*s(3791) s(3802) =< s(3788)*s(3794) s(3803) =< s(3789)*s(3791) s(3804) =< s(3797) s(3805) =< s(3795) s(3806) =< s(3800) s(3807) =< s(3806)*s(3792) s(3808) =< s(3802) s(3809) =< s(3801) s(3810) =< s(3803) s(3811) =< s(3810)*s(3774) s(3742) =< aux(252) s(3743) =< aux(252) s(3744) =< aux(252) s(3745) =< aux(252) s(3746) =< aux(252) s(3747) =< aux(252) s(3748) =< aux(252) s(3744) =< aux(255) s(3746) =< aux(255) s(3749) =< aux(256) s(3750) =< aux(257) s(3743) =< aux(258) s(3744) =< aux(258) s(3746) =< aux(258) s(3747) =< aux(258) s(3746) =< aux(259) s(3751) =< aux(253)+1 s(3752) =< aux(253) s(3753) =< aux(253)+2 s(3754) =< aux(253)-1 s(3755) =< aux(253)-2 s(3743) =< aux(254)*(1/5)+aux(258) s(3744) =< aux(254)*(1/5)+aux(258) s(3745) =< aux(254)*(1/5)+aux(258) s(3746) =< aux(254)*(1/5)+aux(258) s(3747) =< aux(254)*(1/5)+aux(258) s(3748) =< aux(254)*(1/5)+aux(258) s(3746) =< aux(254)*(3/7)+aux(259) s(3747) =< aux(254)*(3/7)+aux(259) s(3748) =< aux(254)*(3/7)+aux(259) s(3744) =< aux(254)*(1/3)+aux(255) s(3745) =< aux(254)*(1/3)+aux(255) s(3746) =< aux(254)*(1/3)+aux(255) s(3747) =< aux(254)*(1/3)+aux(255) s(3748) =< aux(254)*(1/3)+aux(255) s(3749) =< aux(254)*(1/5)+aux(256) s(3742) =< aux(254)*(1/5)+aux(256) s(3750) =< aux(254)*(2/7)+aux(257) s(3749) =< aux(254)*(2/7)+aux(257) s(3742) =< aux(254)*(2/7)+aux(257) s(3756) =< s(3748)*s(3751) s(3757) =< s(3748)*s(3752) s(3758) =< s(3748)*s(3753) s(3759) =< s(3746)*s(3754) s(3760) =< s(3744)*s(3754) s(3761) =< s(3743)*s(3753) s(3762) =< s(3749)*s(3752) s(3763) =< s(3749)*s(3755) s(3764) =< s(3750)*s(3752) s(3765) =< s(3758) s(3766) =< s(3756) s(3767) =< s(3761) s(3768) =< s(3767)*s(3753) s(3769) =< s(3763) s(3770) =< s(3762) s(3771) =< s(3764) s(3772) =< s(3771)*aux(253) s(3858) =< s(3856) with precondition: [V=2,Out=1,V1>=1,V5>=0] * Chain [46]: 2*s(3910)+6*s(3911)+2*s(3912)+2*s(3913)+2*s(3914)+2*s(3915)+6*s(3916)+8*s(3917)+8*s(3918)+2*s(3925)+2*s(3927)+2*s(3928)+4*s(3933)+4*s(3934)+14*s(3935)+2*s(3936)+4*s(3937)+4*s(3938)+14*s(3939)+2*s(3940)+1*s(3949)+3*s(3950)+1*s(3951)+1*s(3952)+1*s(3953)+1*s(3954)+3*s(3955)+4*s(3956)+4*s(3957)+1*s(3964)+1*s(3966)+1*s(3967)+2*s(3972)+2*s(3973)+7*s(3974)+1*s(3975)+2*s(3976)+2*s(3977)+7*s(3978)+1*s(3979)+6*s(3981)+4*s(3983)+4*s(3984)+2*s(3985)+4 Such that:s(3941) =< V5 s(3942) =< 2*V5 s(3943) =< 2*V5+1 s(3944) =< 2/3*V5 s(3945) =< 3/5*V5 s(3946) =< 3/7*V5 s(3947) =< 4/5*V5 s(3948) =< 4/7*V5 aux(260) =< 1 aux(261) =< 2 aux(262) =< 3 aux(263) =< V1 aux(264) =< 2*V1 aux(265) =< 2*V1+1 aux(266) =< 2/3*V1 aux(267) =< 3/5*V1 aux(268) =< 3/7*V1 aux(269) =< 4/5*V1 aux(270) =< 4/7*V1 s(3981) =< aux(260) s(3983) =< aux(261) s(3984) =< aux(262) s(3985) =< s(3981)*aux(261) s(3949) =< s(3941) s(3950) =< s(3941) s(3951) =< s(3941) s(3952) =< s(3941) s(3953) =< s(3941) s(3954) =< s(3941) s(3955) =< s(3941) s(3951) =< s(3944) s(3953) =< s(3944) s(3956) =< s(3945) s(3957) =< s(3946) s(3950) =< s(3947) s(3951) =< s(3947) s(3953) =< s(3947) s(3954) =< s(3947) s(3953) =< s(3948) s(3958) =< s(3942)+1 s(3959) =< s(3942) s(3960) =< s(3942)+2 s(3961) =< s(3942)-1 s(3962) =< s(3942)-2 s(3950) =< s(3943)*(1/5)+s(3947) s(3951) =< s(3943)*(1/5)+s(3947) s(3952) =< s(3943)*(1/5)+s(3947) s(3953) =< s(3943)*(1/5)+s(3947) s(3954) =< s(3943)*(1/5)+s(3947) s(3955) =< s(3943)*(1/5)+s(3947) s(3953) =< s(3943)*(3/7)+s(3948) s(3954) =< s(3943)*(3/7)+s(3948) s(3955) =< s(3943)*(3/7)+s(3948) s(3951) =< s(3943)*(1/3)+s(3944) s(3952) =< s(3943)*(1/3)+s(3944) s(3953) =< s(3943)*(1/3)+s(3944) s(3954) =< s(3943)*(1/3)+s(3944) s(3955) =< s(3943)*(1/3)+s(3944) s(3956) =< s(3943)*(1/5)+s(3945) s(3949) =< s(3943)*(1/5)+s(3945) s(3957) =< s(3943)*(2/7)+s(3946) s(3956) =< s(3943)*(2/7)+s(3946) s(3949) =< s(3943)*(2/7)+s(3946) s(3963) =< s(3955)*s(3958) s(3964) =< s(3955)*s(3959) s(3965) =< s(3955)*s(3960) s(3966) =< s(3953)*s(3961) s(3967) =< s(3951)*s(3961) s(3968) =< s(3950)*s(3960) s(3969) =< s(3956)*s(3959) s(3970) =< s(3956)*s(3962) s(3971) =< s(3957)*s(3959) s(3972) =< s(3965) s(3973) =< s(3963) s(3974) =< s(3968) s(3975) =< s(3974)*s(3960) s(3976) =< s(3970) s(3977) =< s(3969) s(3978) =< s(3971) s(3979) =< s(3978)*s(3942) s(3910) =< aux(263) s(3911) =< aux(263) s(3912) =< aux(263) s(3913) =< aux(263) s(3914) =< aux(263) s(3915) =< aux(263) s(3916) =< aux(263) s(3912) =< aux(266) s(3914) =< aux(266) s(3917) =< aux(267) s(3918) =< aux(268) s(3911) =< aux(269) s(3912) =< aux(269) s(3914) =< aux(269) s(3915) =< aux(269) s(3914) =< aux(270) s(3919) =< aux(264)+1 s(3920) =< aux(264) s(3921) =< aux(264)+2 s(3922) =< aux(264)-1 s(3923) =< aux(264)-2 s(3911) =< aux(265)*(1/5)+aux(269) s(3912) =< aux(265)*(1/5)+aux(269) s(3913) =< aux(265)*(1/5)+aux(269) s(3914) =< aux(265)*(1/5)+aux(269) s(3915) =< aux(265)*(1/5)+aux(269) s(3916) =< aux(265)*(1/5)+aux(269) s(3914) =< aux(265)*(3/7)+aux(270) s(3915) =< aux(265)*(3/7)+aux(270) s(3916) =< aux(265)*(3/7)+aux(270) s(3912) =< aux(265)*(1/3)+aux(266) s(3913) =< aux(265)*(1/3)+aux(266) s(3914) =< aux(265)*(1/3)+aux(266) s(3915) =< aux(265)*(1/3)+aux(266) s(3916) =< aux(265)*(1/3)+aux(266) s(3917) =< aux(265)*(1/5)+aux(267) s(3910) =< aux(265)*(1/5)+aux(267) s(3918) =< aux(265)*(2/7)+aux(268) s(3917) =< aux(265)*(2/7)+aux(268) s(3910) =< aux(265)*(2/7)+aux(268) s(3924) =< s(3916)*s(3919) s(3925) =< s(3916)*s(3920) s(3926) =< s(3916)*s(3921) s(3927) =< s(3914)*s(3922) s(3928) =< s(3912)*s(3922) s(3929) =< s(3911)*s(3921) s(3930) =< s(3917)*s(3920) s(3931) =< s(3917)*s(3923) s(3932) =< s(3918)*s(3920) s(3933) =< s(3926) s(3934) =< s(3924) s(3935) =< s(3929) s(3936) =< s(3935)*s(3921) s(3937) =< s(3931) s(3938) =< s(3930) s(3939) =< s(3932) s(3940) =< s(3939)*aux(264) with precondition: [V=2,Out=2,V1>=1,V5>=0] #### Cost of chains of fun2(V1,V,Out): * Chain [60]: 2*s(4654)+6*s(4655)+2*s(4656)+2*s(4657)+2*s(4658)+2*s(4659)+6*s(4660)+8*s(4661)+8*s(4662)+2*s(4669)+2*s(4671)+2*s(4672)+4*s(4677)+4*s(4678)+14*s(4679)+2*s(4680)+4*s(4681)+4*s(4682)+14*s(4683)+2*s(4684)+3*s(4693)+9*s(4694)+3*s(4695)+3*s(4696)+3*s(4697)+3*s(4698)+9*s(4699)+12*s(4700)+12*s(4701)+3*s(4708)+3*s(4710)+3*s(4711)+6*s(4716)+6*s(4717)+21*s(4718)+3*s(4719)+6*s(4720)+6*s(4721)+21*s(4722)+3*s(4723)+3*s(4724)+1*s(4805)+0 Such that:s(4805) =< 2 aux(328) =< V1 aux(329) =< 2*V1 aux(330) =< 2*V1+1 aux(331) =< 2/3*V1 aux(332) =< 3/5*V1 aux(333) =< 3/7*V1 aux(334) =< 4/5*V1 aux(335) =< 4/7*V1 aux(336) =< V aux(337) =< 2*V aux(338) =< 2*V+1 aux(339) =< 2/3*V aux(340) =< 3/5*V aux(341) =< 3/7*V aux(342) =< 4/5*V aux(343) =< 4/7*V s(4724) =< aux(337) s(4693) =< aux(336) s(4694) =< aux(336) s(4695) =< aux(336) s(4696) =< aux(336) s(4697) =< aux(336) s(4698) =< aux(336) s(4699) =< aux(336) s(4695) =< aux(339) s(4697) =< aux(339) s(4700) =< aux(340) s(4701) =< aux(341) s(4694) =< aux(342) s(4695) =< aux(342) s(4697) =< aux(342) s(4698) =< aux(342) s(4697) =< aux(343) s(4702) =< aux(337)+1 s(4703) =< aux(337) s(4704) =< aux(337)+2 s(4705) =< aux(337)-1 s(4706) =< aux(337)-2 s(4694) =< aux(338)*(1/5)+aux(342) s(4695) =< aux(338)*(1/5)+aux(342) s(4696) =< aux(338)*(1/5)+aux(342) s(4697) =< aux(338)*(1/5)+aux(342) s(4698) =< aux(338)*(1/5)+aux(342) s(4699) =< aux(338)*(1/5)+aux(342) s(4697) =< aux(338)*(3/7)+aux(343) s(4698) =< aux(338)*(3/7)+aux(343) s(4699) =< aux(338)*(3/7)+aux(343) s(4695) =< aux(338)*(1/3)+aux(339) s(4696) =< aux(338)*(1/3)+aux(339) s(4697) =< aux(338)*(1/3)+aux(339) s(4698) =< aux(338)*(1/3)+aux(339) s(4699) =< aux(338)*(1/3)+aux(339) s(4700) =< aux(338)*(1/5)+aux(340) s(4693) =< aux(338)*(1/5)+aux(340) s(4701) =< aux(338)*(2/7)+aux(341) s(4700) =< aux(338)*(2/7)+aux(341) s(4693) =< aux(338)*(2/7)+aux(341) s(4707) =< s(4699)*s(4702) s(4708) =< s(4699)*s(4703) s(4709) =< s(4699)*s(4704) s(4710) =< s(4697)*s(4705) s(4711) =< s(4695)*s(4705) s(4712) =< s(4694)*s(4704) s(4713) =< s(4700)*s(4703) s(4714) =< s(4700)*s(4706) s(4715) =< s(4701)*s(4703) s(4716) =< s(4709) s(4717) =< s(4707) s(4718) =< s(4712) s(4719) =< s(4718)*s(4704) s(4720) =< s(4714) s(4721) =< s(4713) s(4722) =< s(4715) s(4723) =< s(4722)*aux(337) s(4654) =< aux(328) s(4655) =< aux(328) s(4656) =< aux(328) s(4657) =< aux(328) s(4658) =< aux(328) s(4659) =< aux(328) s(4660) =< aux(328) s(4656) =< aux(331) s(4658) =< aux(331) s(4661) =< aux(332) s(4662) =< aux(333) s(4655) =< aux(334) s(4656) =< aux(334) s(4658) =< aux(334) s(4659) =< aux(334) s(4658) =< aux(335) s(4663) =< aux(329)+1 s(4664) =< aux(329) s(4665) =< aux(329)+2 s(4666) =< aux(329)-1 s(4667) =< aux(329)-2 s(4655) =< aux(330)*(1/5)+aux(334) s(4656) =< aux(330)*(1/5)+aux(334) s(4657) =< aux(330)*(1/5)+aux(334) s(4658) =< aux(330)*(1/5)+aux(334) s(4659) =< aux(330)*(1/5)+aux(334) s(4660) =< aux(330)*(1/5)+aux(334) s(4658) =< aux(330)*(3/7)+aux(335) s(4659) =< aux(330)*(3/7)+aux(335) s(4660) =< aux(330)*(3/7)+aux(335) s(4656) =< aux(330)*(1/3)+aux(331) s(4657) =< aux(330)*(1/3)+aux(331) s(4658) =< aux(330)*(1/3)+aux(331) s(4659) =< aux(330)*(1/3)+aux(331) s(4660) =< aux(330)*(1/3)+aux(331) s(4661) =< aux(330)*(1/5)+aux(332) s(4654) =< aux(330)*(1/5)+aux(332) s(4662) =< aux(330)*(2/7)+aux(333) s(4661) =< aux(330)*(2/7)+aux(333) s(4654) =< aux(330)*(2/7)+aux(333) s(4668) =< s(4660)*s(4663) s(4669) =< s(4660)*s(4664) s(4670) =< s(4660)*s(4665) s(4671) =< s(4658)*s(4666) s(4672) =< s(4656)*s(4666) s(4673) =< s(4655)*s(4665) s(4674) =< s(4661)*s(4664) s(4675) =< s(4661)*s(4667) s(4676) =< s(4662)*s(4664) s(4677) =< s(4670) s(4678) =< s(4668) s(4679) =< s(4673) s(4680) =< s(4679)*s(4665) s(4681) =< s(4675) s(4682) =< s(4674) s(4683) =< s(4676) s(4684) =< s(4683)*aux(329) with precondition: [Out=0,V1>=0,V>=0] * Chain [59]: 3*s(4856)+9*s(4857)+3*s(4858)+3*s(4859)+3*s(4860)+3*s(4861)+9*s(4862)+12*s(4863)+12*s(4864)+3*s(4871)+3*s(4873)+3*s(4874)+6*s(4879)+6*s(4880)+21*s(4881)+3*s(4882)+6*s(4883)+6*s(4884)+21*s(4885)+3*s(4886)+5*s(4895)+15*s(4896)+5*s(4897)+5*s(4898)+5*s(4899)+5*s(4900)+15*s(4901)+20*s(4902)+20*s(4903)+5*s(4910)+5*s(4912)+5*s(4913)+10*s(4918)+10*s(4919)+35*s(4920)+5*s(4921)+10*s(4922)+10*s(4923)+35*s(4924)+5*s(4925)+1*s(5004)+2*s(5122)+1 Such that:aux(345) =< 2 aux(346) =< V1 aux(347) =< 2*V1 aux(348) =< 2*V1+1 aux(349) =< 2/3*V1 aux(350) =< 3/5*V1 aux(351) =< 3/7*V1 aux(352) =< 4/5*V1 aux(353) =< 4/7*V1 aux(354) =< V aux(355) =< 2*V aux(356) =< 2*V+1 aux(357) =< 2/3*V aux(358) =< 3/5*V aux(359) =< 3/7*V aux(360) =< 4/5*V aux(361) =< 4/7*V s(5122) =< aux(345) s(4895) =< aux(354) s(4896) =< aux(354) s(4897) =< aux(354) s(4898) =< aux(354) s(4899) =< aux(354) s(4900) =< aux(354) s(4901) =< aux(354) s(4897) =< aux(357) s(4899) =< aux(357) s(4902) =< aux(358) s(4903) =< aux(359) s(4896) =< aux(360) s(4897) =< aux(360) s(4899) =< aux(360) s(4900) =< aux(360) s(4899) =< aux(361) s(4904) =< aux(355)+1 s(4905) =< aux(355) s(4906) =< aux(355)+2 s(4907) =< aux(355)-1 s(4908) =< aux(355)-2 s(4896) =< aux(356)*(1/5)+aux(360) s(4897) =< aux(356)*(1/5)+aux(360) s(4898) =< aux(356)*(1/5)+aux(360) s(4899) =< aux(356)*(1/5)+aux(360) s(4900) =< aux(356)*(1/5)+aux(360) s(4901) =< aux(356)*(1/5)+aux(360) s(4899) =< aux(356)*(3/7)+aux(361) s(4900) =< aux(356)*(3/7)+aux(361) s(4901) =< aux(356)*(3/7)+aux(361) s(4897) =< aux(356)*(1/3)+aux(357) s(4898) =< aux(356)*(1/3)+aux(357) s(4899) =< aux(356)*(1/3)+aux(357) s(4900) =< aux(356)*(1/3)+aux(357) s(4901) =< aux(356)*(1/3)+aux(357) s(4902) =< aux(356)*(1/5)+aux(358) s(4895) =< aux(356)*(1/5)+aux(358) s(4903) =< aux(356)*(2/7)+aux(359) s(4902) =< aux(356)*(2/7)+aux(359) s(4895) =< aux(356)*(2/7)+aux(359) s(4909) =< s(4901)*s(4904) s(4910) =< s(4901)*s(4905) s(4911) =< s(4901)*s(4906) s(4912) =< s(4899)*s(4907) s(4913) =< s(4897)*s(4907) s(4914) =< s(4896)*s(4906) s(4915) =< s(4902)*s(4905) s(4916) =< s(4902)*s(4908) s(4917) =< s(4903)*s(4905) s(4918) =< s(4911) s(4919) =< s(4909) s(4920) =< s(4914) s(4921) =< s(4920)*s(4906) s(4922) =< s(4916) s(4923) =< s(4915) s(4924) =< s(4917) s(4925) =< s(4924)*aux(355) s(4856) =< aux(346) s(4857) =< aux(346) s(4858) =< aux(346) s(4859) =< aux(346) s(4860) =< aux(346) s(4861) =< aux(346) s(4862) =< aux(346) s(4858) =< aux(349) s(4860) =< aux(349) s(4863) =< aux(350) s(4864) =< aux(351) s(4857) =< aux(352) s(4858) =< aux(352) s(4860) =< aux(352) s(4861) =< aux(352) s(4860) =< aux(353) s(4865) =< aux(347)+1 s(4866) =< aux(347) s(4867) =< aux(347)+2 s(4868) =< aux(347)-1 s(4869) =< aux(347)-2 s(4857) =< aux(348)*(1/5)+aux(352) s(4858) =< aux(348)*(1/5)+aux(352) s(4859) =< aux(348)*(1/5)+aux(352) s(4860) =< aux(348)*(1/5)+aux(352) s(4861) =< aux(348)*(1/5)+aux(352) s(4862) =< aux(348)*(1/5)+aux(352) s(4860) =< aux(348)*(3/7)+aux(353) s(4861) =< aux(348)*(3/7)+aux(353) s(4862) =< aux(348)*(3/7)+aux(353) s(4858) =< aux(348)*(1/3)+aux(349) s(4859) =< aux(348)*(1/3)+aux(349) s(4860) =< aux(348)*(1/3)+aux(349) s(4861) =< aux(348)*(1/3)+aux(349) s(4862) =< aux(348)*(1/3)+aux(349) s(4863) =< aux(348)*(1/5)+aux(350) s(4856) =< aux(348)*(1/5)+aux(350) s(4864) =< aux(348)*(2/7)+aux(351) s(4863) =< aux(348)*(2/7)+aux(351) s(4856) =< aux(348)*(2/7)+aux(351) s(4870) =< s(4862)*s(4865) s(4871) =< s(4862)*s(4866) s(4872) =< s(4862)*s(4867) s(4873) =< s(4860)*s(4868) s(4874) =< s(4858)*s(4868) s(4875) =< s(4857)*s(4867) s(4876) =< s(4863)*s(4866) s(4877) =< s(4863)*s(4869) s(4878) =< s(4864)*s(4866) s(4879) =< s(4872) s(4880) =< s(4870) s(4881) =< s(4875) s(4882) =< s(4881)*s(4867) s(4883) =< s(4877) s(4884) =< s(4876) s(4885) =< s(4878) s(4886) =< s(4885)*aux(347) s(5004) =< aux(355) with precondition: [Out=2,V1>=0,V>=0] * Chain [58]: 2*s(5171)+6*s(5172)+2*s(5173)+2*s(5174)+2*s(5175)+2*s(5176)+6*s(5177)+8*s(5178)+8*s(5179)+2*s(5186)+2*s(5188)+2*s(5189)+4*s(5194)+4*s(5195)+14*s(5196)+2*s(5197)+4*s(5198)+4*s(5199)+14*s(5200)+2*s(5201)+4*s(5210)+12*s(5211)+4*s(5212)+4*s(5213)+4*s(5214)+4*s(5215)+12*s(5216)+16*s(5217)+16*s(5218)+4*s(5225)+4*s(5227)+4*s(5228)+8*s(5233)+8*s(5234)+28*s(5235)+4*s(5236)+8*s(5237)+8*s(5238)+28*s(5239)+4*s(5240)+1*s(5319)+1*s(5359)+1 Such that:s(5359) =< 2 aux(363) =< V1 aux(364) =< 2*V1 aux(365) =< 2*V1+1 aux(366) =< 2/3*V1 aux(367) =< 3/5*V1 aux(368) =< 3/7*V1 aux(369) =< 4/5*V1 aux(370) =< 4/7*V1 aux(371) =< V aux(372) =< 2*V aux(373) =< 2*V+1 aux(374) =< 2/3*V aux(375) =< 3/5*V aux(376) =< 3/7*V aux(377) =< 4/5*V aux(378) =< 4/7*V s(5210) =< aux(371) s(5211) =< aux(371) s(5212) =< aux(371) s(5213) =< aux(371) s(5214) =< aux(371) s(5215) =< aux(371) s(5216) =< aux(371) s(5212) =< aux(374) s(5214) =< aux(374) s(5217) =< aux(375) s(5218) =< aux(376) s(5211) =< aux(377) s(5212) =< aux(377) s(5214) =< aux(377) s(5215) =< aux(377) s(5214) =< aux(378) s(5219) =< aux(372)+1 s(5220) =< aux(372) s(5221) =< aux(372)+2 s(5222) =< aux(372)-1 s(5223) =< aux(372)-2 s(5211) =< aux(373)*(1/5)+aux(377) s(5212) =< aux(373)*(1/5)+aux(377) s(5213) =< aux(373)*(1/5)+aux(377) s(5214) =< aux(373)*(1/5)+aux(377) s(5215) =< aux(373)*(1/5)+aux(377) s(5216) =< aux(373)*(1/5)+aux(377) s(5214) =< aux(373)*(3/7)+aux(378) s(5215) =< aux(373)*(3/7)+aux(378) s(5216) =< aux(373)*(3/7)+aux(378) s(5212) =< aux(373)*(1/3)+aux(374) s(5213) =< aux(373)*(1/3)+aux(374) s(5214) =< aux(373)*(1/3)+aux(374) s(5215) =< aux(373)*(1/3)+aux(374) s(5216) =< aux(373)*(1/3)+aux(374) s(5217) =< aux(373)*(1/5)+aux(375) s(5210) =< aux(373)*(1/5)+aux(375) s(5218) =< aux(373)*(2/7)+aux(376) s(5217) =< aux(373)*(2/7)+aux(376) s(5210) =< aux(373)*(2/7)+aux(376) s(5224) =< s(5216)*s(5219) s(5225) =< s(5216)*s(5220) s(5226) =< s(5216)*s(5221) s(5227) =< s(5214)*s(5222) s(5228) =< s(5212)*s(5222) s(5229) =< s(5211)*s(5221) s(5230) =< s(5217)*s(5220) s(5231) =< s(5217)*s(5223) s(5232) =< s(5218)*s(5220) s(5233) =< s(5226) s(5234) =< s(5224) s(5235) =< s(5229) s(5236) =< s(5235)*s(5221) s(5237) =< s(5231) s(5238) =< s(5230) s(5239) =< s(5232) s(5240) =< s(5239)*aux(372) s(5171) =< aux(363) s(5172) =< aux(363) s(5173) =< aux(363) s(5174) =< aux(363) s(5175) =< aux(363) s(5176) =< aux(363) s(5177) =< aux(363) s(5173) =< aux(366) s(5175) =< aux(366) s(5178) =< aux(367) s(5179) =< aux(368) s(5172) =< aux(369) s(5173) =< aux(369) s(5175) =< aux(369) s(5176) =< aux(369) s(5175) =< aux(370) s(5180) =< aux(364)+1 s(5181) =< aux(364) s(5182) =< aux(364)+2 s(5183) =< aux(364)-1 s(5184) =< aux(364)-2 s(5172) =< aux(365)*(1/5)+aux(369) s(5173) =< aux(365)*(1/5)+aux(369) s(5174) =< aux(365)*(1/5)+aux(369) s(5175) =< aux(365)*(1/5)+aux(369) s(5176) =< aux(365)*(1/5)+aux(369) s(5177) =< aux(365)*(1/5)+aux(369) s(5175) =< aux(365)*(3/7)+aux(370) s(5176) =< aux(365)*(3/7)+aux(370) s(5177) =< aux(365)*(3/7)+aux(370) s(5173) =< aux(365)*(1/3)+aux(366) s(5174) =< aux(365)*(1/3)+aux(366) s(5175) =< aux(365)*(1/3)+aux(366) s(5176) =< aux(365)*(1/3)+aux(366) s(5177) =< aux(365)*(1/3)+aux(366) s(5178) =< aux(365)*(1/5)+aux(367) s(5171) =< aux(365)*(1/5)+aux(367) s(5179) =< aux(365)*(2/7)+aux(368) s(5178) =< aux(365)*(2/7)+aux(368) s(5171) =< aux(365)*(2/7)+aux(368) s(5185) =< s(5177)*s(5180) s(5186) =< s(5177)*s(5181) s(5187) =< s(5177)*s(5182) s(5188) =< s(5175)*s(5183) s(5189) =< s(5173)*s(5183) s(5190) =< s(5172)*s(5182) s(5191) =< s(5178)*s(5181) s(5192) =< s(5178)*s(5184) s(5193) =< s(5179)*s(5181) s(5194) =< s(5187) s(5195) =< s(5185) s(5196) =< s(5190) s(5197) =< s(5196)*s(5182) s(5198) =< s(5192) s(5199) =< s(5191) s(5200) =< s(5193) s(5201) =< s(5200)*aux(364) s(5319) =< aux(372) with precondition: [Out=1,V1>=0,V>=1] * Chain [57]: 1*s(5407)+3*s(5408)+1*s(5409)+1*s(5410)+1*s(5411)+1*s(5412)+3*s(5413)+4*s(5414)+4*s(5415)+1*s(5422)+1*s(5424)+1*s(5425)+2*s(5430)+2*s(5431)+7*s(5432)+1*s(5433)+2*s(5434)+2*s(5435)+7*s(5436)+1*s(5437)+2*s(5438)+0 Such that:s(5399) =< V1 s(5400) =< 2*V1 s(5401) =< 2*V1+1 s(5402) =< 2/3*V1 s(5403) =< 3/5*V1 s(5404) =< 3/7*V1 s(5405) =< 4/5*V1 s(5406) =< 4/7*V1 aux(379) =< 2 s(5438) =< aux(379) s(5407) =< s(5399) s(5408) =< s(5399) s(5409) =< s(5399) s(5410) =< s(5399) s(5411) =< s(5399) s(5412) =< s(5399) s(5413) =< s(5399) s(5409) =< s(5402) s(5411) =< s(5402) s(5414) =< s(5403) s(5415) =< s(5404) s(5408) =< s(5405) s(5409) =< s(5405) s(5411) =< s(5405) s(5412) =< s(5405) s(5411) =< s(5406) s(5416) =< s(5400)+1 s(5417) =< s(5400) s(5418) =< s(5400)+2 s(5419) =< s(5400)-1 s(5420) =< s(5400)-2 s(5408) =< s(5401)*(1/5)+s(5405) s(5409) =< s(5401)*(1/5)+s(5405) s(5410) =< s(5401)*(1/5)+s(5405) s(5411) =< s(5401)*(1/5)+s(5405) s(5412) =< s(5401)*(1/5)+s(5405) s(5413) =< s(5401)*(1/5)+s(5405) s(5411) =< s(5401)*(3/7)+s(5406) s(5412) =< s(5401)*(3/7)+s(5406) s(5413) =< s(5401)*(3/7)+s(5406) s(5409) =< s(5401)*(1/3)+s(5402) s(5410) =< s(5401)*(1/3)+s(5402) s(5411) =< s(5401)*(1/3)+s(5402) s(5412) =< s(5401)*(1/3)+s(5402) s(5413) =< s(5401)*(1/3)+s(5402) s(5414) =< s(5401)*(1/5)+s(5403) s(5407) =< s(5401)*(1/5)+s(5403) s(5415) =< s(5401)*(2/7)+s(5404) s(5414) =< s(5401)*(2/7)+s(5404) s(5407) =< s(5401)*(2/7)+s(5404) s(5421) =< s(5413)*s(5416) s(5422) =< s(5413)*s(5417) s(5423) =< s(5413)*s(5418) s(5424) =< s(5411)*s(5419) s(5425) =< s(5409)*s(5419) s(5426) =< s(5408)*s(5418) s(5427) =< s(5414)*s(5417) s(5428) =< s(5414)*s(5420) s(5429) =< s(5415)*s(5417) s(5430) =< s(5423) s(5431) =< s(5421) s(5432) =< s(5426) s(5433) =< s(5432)*s(5418) s(5434) =< s(5428) s(5435) =< s(5427) s(5436) =< s(5429) s(5437) =< s(5436)*s(5400) with precondition: [V=2,Out=0,V1>=0] * Chain [56]: 2*s(5448)+6*s(5449)+2*s(5450)+2*s(5451)+2*s(5452)+2*s(5453)+6*s(5454)+8*s(5455)+8*s(5456)+2*s(5463)+2*s(5465)+2*s(5466)+4*s(5471)+4*s(5472)+14*s(5473)+2*s(5474)+4*s(5475)+4*s(5476)+14*s(5477)+2*s(5478)+1*s(5518)+1 Such that:s(5518) =< 1 aux(380) =< V1 aux(381) =< 2*V1 aux(382) =< 2*V1+1 aux(383) =< 2/3*V1 aux(384) =< 3/5*V1 aux(385) =< 3/7*V1 aux(386) =< 4/5*V1 aux(387) =< 4/7*V1 s(5448) =< aux(380) s(5449) =< aux(380) s(5450) =< aux(380) s(5451) =< aux(380) s(5452) =< aux(380) s(5453) =< aux(380) s(5454) =< aux(380) s(5450) =< aux(383) s(5452) =< aux(383) s(5455) =< aux(384) s(5456) =< aux(385) s(5449) =< aux(386) s(5450) =< aux(386) s(5452) =< aux(386) s(5453) =< aux(386) s(5452) =< aux(387) s(5457) =< aux(381)+1 s(5458) =< aux(381) s(5459) =< aux(381)+2 s(5460) =< aux(381)-1 s(5461) =< aux(381)-2 s(5449) =< aux(382)*(1/5)+aux(386) s(5450) =< aux(382)*(1/5)+aux(386) s(5451) =< aux(382)*(1/5)+aux(386) s(5452) =< aux(382)*(1/5)+aux(386) s(5453) =< aux(382)*(1/5)+aux(386) s(5454) =< aux(382)*(1/5)+aux(386) s(5452) =< aux(382)*(3/7)+aux(387) s(5453) =< aux(382)*(3/7)+aux(387) s(5454) =< aux(382)*(3/7)+aux(387) s(5450) =< aux(382)*(1/3)+aux(383) s(5451) =< aux(382)*(1/3)+aux(383) s(5452) =< aux(382)*(1/3)+aux(383) s(5453) =< aux(382)*(1/3)+aux(383) s(5454) =< aux(382)*(1/3)+aux(383) s(5455) =< aux(382)*(1/5)+aux(384) s(5448) =< aux(382)*(1/5)+aux(384) s(5456) =< aux(382)*(2/7)+aux(385) s(5455) =< aux(382)*(2/7)+aux(385) s(5448) =< aux(382)*(2/7)+aux(385) s(5462) =< s(5454)*s(5457) s(5463) =< s(5454)*s(5458) s(5464) =< s(5454)*s(5459) s(5465) =< s(5452)*s(5460) s(5466) =< s(5450)*s(5460) s(5467) =< s(5449)*s(5459) s(5468) =< s(5455)*s(5458) s(5469) =< s(5455)*s(5461) s(5470) =< s(5456)*s(5458) s(5471) =< s(5464) s(5472) =< s(5462) s(5473) =< s(5467) s(5474) =< s(5473)*s(5459) s(5475) =< s(5469) s(5476) =< s(5468) s(5477) =< s(5470) s(5478) =< s(5477)*aux(381) with precondition: [V=2,Out=1,V1>=0] * Chain [55]: 1*s(5527)+3*s(5528)+1*s(5529)+1*s(5530)+1*s(5531)+1*s(5532)+3*s(5533)+4*s(5534)+4*s(5535)+1*s(5542)+1*s(5544)+1*s(5545)+2*s(5550)+2*s(5551)+7*s(5552)+1*s(5553)+2*s(5554)+2*s(5555)+7*s(5556)+1*s(5557)+1*s(5558)+1 Such that:s(5558) =< 2 s(5519) =< V1 s(5520) =< 2*V1 s(5521) =< 2*V1+1 s(5522) =< 2/3*V1 s(5523) =< 3/5*V1 s(5524) =< 3/7*V1 s(5525) =< 4/5*V1 s(5526) =< 4/7*V1 s(5527) =< s(5519) s(5528) =< s(5519) s(5529) =< s(5519) s(5530) =< s(5519) s(5531) =< s(5519) s(5532) =< s(5519) s(5533) =< s(5519) s(5529) =< s(5522) s(5531) =< s(5522) s(5534) =< s(5523) s(5535) =< s(5524) s(5528) =< s(5525) s(5529) =< s(5525) s(5531) =< s(5525) s(5532) =< s(5525) s(5531) =< s(5526) s(5536) =< s(5520)+1 s(5537) =< s(5520) s(5538) =< s(5520)+2 s(5539) =< s(5520)-1 s(5540) =< s(5520)-2 s(5528) =< s(5521)*(1/5)+s(5525) s(5529) =< s(5521)*(1/5)+s(5525) s(5530) =< s(5521)*(1/5)+s(5525) s(5531) =< s(5521)*(1/5)+s(5525) s(5532) =< s(5521)*(1/5)+s(5525) s(5533) =< s(5521)*(1/5)+s(5525) s(5531) =< s(5521)*(3/7)+s(5526) s(5532) =< s(5521)*(3/7)+s(5526) s(5533) =< s(5521)*(3/7)+s(5526) s(5529) =< s(5521)*(1/3)+s(5522) s(5530) =< s(5521)*(1/3)+s(5522) s(5531) =< s(5521)*(1/3)+s(5522) s(5532) =< s(5521)*(1/3)+s(5522) s(5533) =< s(5521)*(1/3)+s(5522) s(5534) =< s(5521)*(1/5)+s(5523) s(5527) =< s(5521)*(1/5)+s(5523) s(5535) =< s(5521)*(2/7)+s(5524) s(5534) =< s(5521)*(2/7)+s(5524) s(5527) =< s(5521)*(2/7)+s(5524) s(5541) =< s(5533)*s(5536) s(5542) =< s(5533)*s(5537) s(5543) =< s(5533)*s(5538) s(5544) =< s(5531)*s(5539) s(5545) =< s(5529)*s(5539) s(5546) =< s(5528)*s(5538) s(5547) =< s(5534)*s(5537) s(5548) =< s(5534)*s(5540) s(5549) =< s(5535)*s(5537) s(5550) =< s(5543) s(5551) =< s(5541) s(5552) =< s(5546) s(5553) =< s(5552)*s(5538) s(5554) =< s(5548) s(5555) =< s(5547) s(5556) =< s(5549) s(5557) =< s(5556)*s(5520) with precondition: [V=2,Out=2,V1>=1] #### Cost of chains of fun3(V1,Out): * Chain [63]: 1*s(5929)+3*s(5930)+1*s(5931)+1*s(5932)+1*s(5933)+1*s(5934)+3*s(5935)+4*s(5936)+4*s(5937)+1*s(5944)+1*s(5946)+1*s(5947)+2*s(5952)+2*s(5953)+7*s(5954)+1*s(5955)+2*s(5956)+2*s(5957)+7*s(5958)+1*s(5959)+0 Such that:s(5921) =< V1 s(5922) =< 2*V1 s(5923) =< 2*V1+1 s(5924) =< 2/3*V1 s(5925) =< 3/5*V1 s(5926) =< 3/7*V1 s(5927) =< 4/5*V1 s(5928) =< 4/7*V1 s(5929) =< s(5921) s(5930) =< s(5921) s(5931) =< s(5921) s(5932) =< s(5921) s(5933) =< s(5921) s(5934) =< s(5921) s(5935) =< s(5921) s(5931) =< s(5924) s(5933) =< s(5924) s(5936) =< s(5925) s(5937) =< s(5926) s(5930) =< s(5927) s(5931) =< s(5927) s(5933) =< s(5927) s(5934) =< s(5927) s(5933) =< s(5928) s(5938) =< s(5922)+1 s(5939) =< s(5922) s(5940) =< s(5922)+2 s(5941) =< s(5922)-1 s(5942) =< s(5922)-2 s(5930) =< s(5923)*(1/5)+s(5927) s(5931) =< s(5923)*(1/5)+s(5927) s(5932) =< s(5923)*(1/5)+s(5927) s(5933) =< s(5923)*(1/5)+s(5927) s(5934) =< s(5923)*(1/5)+s(5927) s(5935) =< s(5923)*(1/5)+s(5927) s(5933) =< s(5923)*(3/7)+s(5928) s(5934) =< s(5923)*(3/7)+s(5928) s(5935) =< s(5923)*(3/7)+s(5928) s(5931) =< s(5923)*(1/3)+s(5924) s(5932) =< s(5923)*(1/3)+s(5924) s(5933) =< s(5923)*(1/3)+s(5924) s(5934) =< s(5923)*(1/3)+s(5924) s(5935) =< s(5923)*(1/3)+s(5924) s(5936) =< s(5923)*(1/5)+s(5925) s(5929) =< s(5923)*(1/5)+s(5925) s(5937) =< s(5923)*(2/7)+s(5926) s(5936) =< s(5923)*(2/7)+s(5926) s(5929) =< s(5923)*(2/7)+s(5926) s(5943) =< s(5935)*s(5938) s(5944) =< s(5935)*s(5939) s(5945) =< s(5935)*s(5940) s(5946) =< s(5933)*s(5941) s(5947) =< s(5931)*s(5941) s(5948) =< s(5930)*s(5940) s(5949) =< s(5936)*s(5939) s(5950) =< s(5936)*s(5942) s(5951) =< s(5937)*s(5939) s(5952) =< s(5945) s(5953) =< s(5943) s(5954) =< s(5948) s(5955) =< s(5954)*s(5940) s(5956) =< s(5950) s(5957) =< s(5949) s(5958) =< s(5951) s(5959) =< s(5958)*s(5922) with precondition: [V1>=1,Out>=1,2*V1+1>=Out] * Chain [62]: 0 with precondition: [Out=0,V1>=0] * Chain [61]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun4(Out): * Chain [65]: 0 with precondition: [Out=0] * Chain [64]: 0 with precondition: [Out=1] #### Cost of chains of fun6(Out): * Chain [67]: 0 with precondition: [Out=0] * Chain [66]: 0 with precondition: [Out=2] #### Cost of chains of start(V1,V,V5): * Chain [68]: 6*s(5962)+2*s(5963)+3*s(5965)+4*s(5968)+1*s(5969)+5*s(5972)+3*s(5975)+2*s(5978)+1*s(5979)+51*s(5991)+153*s(5992)+51*s(5993)+51*s(5994)+51*s(5995)+51*s(5996)+153*s(5997)+204*s(5998)+204*s(5999)+51*s(6006)+51*s(6008)+51*s(6009)+102*s(6014)+102*s(6015)+357*s(6016)+51*s(6017)+102*s(6018)+102*s(6019)+357*s(6020)+51*s(6021)+21*s(6041)+19*s(6042)+55*s(6074)+18*s(6075)+41*s(6076)+123*s(6077)+41*s(6078)+41*s(6079)+41*s(6080)+41*s(6081)+123*s(6082)+164*s(6083)+164*s(6084)+41*s(6091)+41*s(6093)+41*s(6094)+82*s(6099)+82*s(6100)+287*s(6101)+41*s(6102)+82*s(6103)+82*s(6104)+287*s(6105)+41*s(6106)+18*s(6107)+2*s(6128)+6*s(6161)+3*s(6162)+22*s(6218)+66*s(6219)+22*s(6220)+22*s(6221)+22*s(6222)+22*s(6223)+66*s(6224)+88*s(6225)+88*s(6226)+22*s(6233)+22*s(6235)+22*s(6236)+44*s(6241)+44*s(6242)+154*s(6243)+22*s(6244)+44*s(6245)+44*s(6246)+154*s(6247)+22*s(6248)+12*s(6339)+12*s(6402)+47*s(6403)+4*s(6465)+6*s(6499)+4 Such that:s(5974) =< V1+1 s(5975) =< V1-V s(5965) =< V-V5 s(5961) =< V5+2 s(6332) =< 2*V5+2 aux(414) =< 1 aux(415) =< 2 aux(416) =< 3 aux(417) =< 4 aux(418) =< V1 aux(419) =< 2*V1 aux(420) =< 2*V1+1 aux(421) =< 2/3*V1 aux(422) =< 3/5*V1 aux(423) =< 3/7*V1 aux(424) =< 4/5*V1 aux(425) =< 4/7*V1 aux(426) =< V aux(427) =< V+1 aux(428) =< 2*V aux(429) =< 2*V+1 aux(430) =< 2/3*V aux(431) =< 3/5*V aux(432) =< 3/7*V aux(433) =< 4/5*V aux(434) =< 4/7*V aux(435) =< V5 aux(436) =< 2*V5 aux(437) =< 2*V5+1 aux(438) =< 2/3*V5 aux(439) =< 3/5*V5 aux(440) =< 3/7*V5 aux(441) =< 4/5*V5 aux(442) =< 4/7*V5 s(6042) =< aux(414) s(6074) =< aux(415) s(5972) =< aux(418) s(5962) =< aux(426) s(6041) =< aux(419) s(5991) =< aux(418) s(5992) =< aux(418) s(5993) =< aux(418) s(5994) =< aux(418) s(5995) =< aux(418) s(5996) =< aux(418) s(5997) =< aux(418) s(5993) =< aux(421) s(5995) =< aux(421) s(5998) =< aux(422) s(5999) =< aux(423) s(5992) =< aux(424) s(5993) =< aux(424) s(5995) =< aux(424) s(5996) =< aux(424) s(5995) =< aux(425) s(6000) =< aux(419)+1 s(6001) =< aux(419) s(6002) =< aux(419)+2 s(6003) =< aux(419)-1 s(6004) =< aux(419)-2 s(5992) =< aux(420)*(1/5)+aux(424) s(5993) =< aux(420)*(1/5)+aux(424) s(5994) =< aux(420)*(1/5)+aux(424) s(5995) =< aux(420)*(1/5)+aux(424) s(5996) =< aux(420)*(1/5)+aux(424) s(5997) =< aux(420)*(1/5)+aux(424) s(5995) =< aux(420)*(3/7)+aux(425) s(5996) =< aux(420)*(3/7)+aux(425) s(5997) =< aux(420)*(3/7)+aux(425) s(5993) =< aux(420)*(1/3)+aux(421) s(5994) =< aux(420)*(1/3)+aux(421) s(5995) =< aux(420)*(1/3)+aux(421) s(5996) =< aux(420)*(1/3)+aux(421) s(5997) =< aux(420)*(1/3)+aux(421) s(5998) =< aux(420)*(1/5)+aux(422) s(5991) =< aux(420)*(1/5)+aux(422) s(5999) =< aux(420)*(2/7)+aux(423) s(5998) =< aux(420)*(2/7)+aux(423) s(5991) =< aux(420)*(2/7)+aux(423) s(6005) =< s(5997)*s(6000) s(6006) =< s(5997)*s(6001) s(6007) =< s(5997)*s(6002) s(6008) =< s(5995)*s(6003) s(6009) =< s(5993)*s(6003) s(6010) =< s(5992)*s(6002) s(6011) =< s(5998)*s(6001) s(6012) =< s(5998)*s(6004) s(6013) =< s(5999)*s(6001) s(6014) =< s(6007) s(6015) =< s(6005) s(6016) =< s(6010) s(6017) =< s(6016)*s(6002) s(6018) =< s(6012) s(6019) =< s(6011) s(6020) =< s(6013) s(6021) =< s(6020)*aux(419) s(6075) =< aux(429) s(6076) =< aux(426) s(6077) =< aux(426) s(6078) =< aux(426) s(6079) =< aux(426) s(6080) =< aux(426) s(6081) =< aux(426) s(6082) =< aux(426) s(6078) =< aux(430) s(6080) =< aux(430) s(6083) =< aux(431) s(6084) =< aux(432) s(6077) =< aux(433) s(6078) =< aux(433) s(6080) =< aux(433) s(6081) =< aux(433) s(6080) =< aux(434) s(6085) =< aux(428)+1 s(6086) =< aux(428) s(6087) =< aux(428)+2 s(6088) =< aux(428)-1 s(6089) =< aux(428)-2 s(6077) =< aux(429)*(1/5)+aux(433) s(6078) =< aux(429)*(1/5)+aux(433) s(6079) =< aux(429)*(1/5)+aux(433) s(6080) =< aux(429)*(1/5)+aux(433) s(6081) =< aux(429)*(1/5)+aux(433) s(6082) =< aux(429)*(1/5)+aux(433) s(6080) =< aux(429)*(3/7)+aux(434) s(6081) =< aux(429)*(3/7)+aux(434) s(6082) =< aux(429)*(3/7)+aux(434) s(6078) =< aux(429)*(1/3)+aux(430) s(6079) =< aux(429)*(1/3)+aux(430) s(6080) =< aux(429)*(1/3)+aux(430) s(6081) =< aux(429)*(1/3)+aux(430) s(6082) =< aux(429)*(1/3)+aux(430) s(6083) =< aux(429)*(1/5)+aux(431) s(6076) =< aux(429)*(1/5)+aux(431) s(6084) =< aux(429)*(2/7)+aux(432) s(6083) =< aux(429)*(2/7)+aux(432) s(6076) =< aux(429)*(2/7)+aux(432) s(6090) =< s(6082)*s(6085) s(6091) =< s(6082)*s(6086) s(6092) =< s(6082)*s(6087) s(6093) =< s(6080)*s(6088) s(6094) =< s(6078)*s(6088) s(6095) =< s(6077)*s(6087) s(6096) =< s(6083)*s(6086) s(6097) =< s(6083)*s(6089) s(6098) =< s(6084)*s(6086) s(6099) =< s(6092) s(6100) =< s(6090) s(6101) =< s(6095) s(6102) =< s(6101)*s(6087) s(6103) =< s(6097) s(6104) =< s(6096) s(6105) =< s(6098) s(6106) =< s(6105)*aux(428) s(6107) =< aux(416) s(6465) =< s(6042)*aux(415) s(6218) =< aux(435) s(6219) =< aux(435) s(6220) =< aux(435) s(6221) =< aux(435) s(6222) =< aux(435) s(6223) =< aux(435) s(6224) =< aux(435) s(6220) =< aux(438) s(6222) =< aux(438) s(6225) =< aux(439) s(6226) =< aux(440) s(6219) =< aux(441) s(6220) =< aux(441) s(6222) =< aux(441) s(6223) =< aux(441) s(6222) =< aux(442) s(6227) =< aux(436)+1 s(6228) =< aux(436) s(6229) =< aux(436)+2 s(6230) =< aux(436)-1 s(6231) =< aux(436)-2 s(6219) =< aux(437)*(1/5)+aux(441) s(6220) =< aux(437)*(1/5)+aux(441) s(6221) =< aux(437)*(1/5)+aux(441) s(6222) =< aux(437)*(1/5)+aux(441) s(6223) =< aux(437)*(1/5)+aux(441) s(6224) =< aux(437)*(1/5)+aux(441) s(6222) =< aux(437)*(3/7)+aux(442) s(6223) =< aux(437)*(3/7)+aux(442) s(6224) =< aux(437)*(3/7)+aux(442) s(6220) =< aux(437)*(1/3)+aux(438) s(6221) =< aux(437)*(1/3)+aux(438) s(6222) =< aux(437)*(1/3)+aux(438) s(6223) =< aux(437)*(1/3)+aux(438) s(6224) =< aux(437)*(1/3)+aux(438) s(6225) =< aux(437)*(1/5)+aux(439) s(6218) =< aux(437)*(1/5)+aux(439) s(6226) =< aux(437)*(2/7)+aux(440) s(6225) =< aux(437)*(2/7)+aux(440) s(6218) =< aux(437)*(2/7)+aux(440) s(6232) =< s(6224)*s(6227) s(6233) =< s(6224)*s(6228) s(6234) =< s(6224)*s(6229) s(6235) =< s(6222)*s(6230) s(6236) =< s(6220)*s(6230) s(6237) =< s(6219)*s(6229) s(6238) =< s(6225)*s(6228) s(6239) =< s(6225)*s(6231) s(6240) =< s(6226)*s(6228) s(6241) =< s(6234) s(6242) =< s(6232) s(6243) =< s(6237) s(6244) =< s(6243)*s(6229) s(6245) =< s(6239) s(6246) =< s(6238) s(6247) =< s(6240) s(6248) =< s(6247)*aux(436) s(6403) =< aux(428) s(6499) =< s(6403)*aux(428) s(6128) =< s(6074)*aux(415) s(6161) =< aux(420) s(6162) =< s(6041)*aux(419) s(6339) =< s(6332) s(6402) =< aux(417) s(5968) =< aux(427) s(5978) =< s(5974) s(5979) =< s(5975)*aux(418) s(5963) =< s(5961) s(5969) =< s(5965)*aux(426) with precondition: [] Closed-form bounds of start(V1,V,V5): ------------------------------------- * Chain [68] with precondition: [] - Upper bound: nat(V1)*1790+251+nat(V1)*102*nat(nat(2*V1)+ -1)+nat(V1)*816*nat(2*V1)+nat(V1)*51*nat(2*V1)*nat(2*V1)+nat(V1-V)*nat(V1)+nat(V)*1441+nat(V)*82*nat(nat(2*V)+ -1)+nat(V)*656*nat(2*V)+nat(V)*41*nat(2*V)*nat(2*V)+nat(V-V5)*nat(V)+nat(V5)*770+nat(V5)*44*nat(nat(2*V5)+ -1)+nat(V5)*352*nat(2*V5)+nat(V5)*22*nat(2*V5)*nat(2*V5)+nat(nat(2*V1)+ -2)*102*nat(3/5*V1)+nat(nat(2*V)+ -2)*82*nat(3/5*V)+nat(nat(2*V5)+ -2)*44*nat(3/5*V5)+nat(2*V1)*21+nat(2*V1)*3*nat(2*V1)+nat(2*V1)*51*nat(2*V1)*nat(3/7*V1)+nat(2*V1)*102*nat(3/5*V1)+nat(2*V1)*357*nat(3/7*V1)+nat(2*V)*47+nat(2*V)*6*nat(2*V)+nat(2*V)*41*nat(2*V)*nat(3/7*V)+nat(2*V)*82*nat(3/5*V)+nat(2*V)*287*nat(3/7*V)+nat(2*V5)*22*nat(2*V5)*nat(3/7*V5)+nat(2*V5)*44*nat(3/5*V5)+nat(2*V5)*154*nat(3/7*V5)+nat(3/5*V1)*204+nat(3/5*V)*164+nat(3/5*V5)*88+nat(3/7*V1)*204+nat(3/7*V)*164+nat(3/7*V5)*88+nat(V1+1)*2+nat(V+1)*4+nat(V5+2)*2+nat(2*V1+1)*6+nat(2*V+1)*18+nat(2*V5+2)*12+nat(V1-V)*3+nat(V-V5)*3 - Complexity: n^3 ### Maximum cost of start(V1,V,V5): nat(V1)*1790+251+nat(V1)*102*nat(nat(2*V1)+ -1)+nat(V1)*816*nat(2*V1)+nat(V1)*51*nat(2*V1)*nat(2*V1)+nat(V1-V)*nat(V1)+nat(V)*1441+nat(V)*82*nat(nat(2*V)+ -1)+nat(V)*656*nat(2*V)+nat(V)*41*nat(2*V)*nat(2*V)+nat(V-V5)*nat(V)+nat(V5)*770+nat(V5)*44*nat(nat(2*V5)+ -1)+nat(V5)*352*nat(2*V5)+nat(V5)*22*nat(2*V5)*nat(2*V5)+nat(nat(2*V1)+ -2)*102*nat(3/5*V1)+nat(nat(2*V)+ -2)*82*nat(3/5*V)+nat(nat(2*V5)+ -2)*44*nat(3/5*V5)+nat(2*V1)*21+nat(2*V1)*3*nat(2*V1)+nat(2*V1)*51*nat(2*V1)*nat(3/7*V1)+nat(2*V1)*102*nat(3/5*V1)+nat(2*V1)*357*nat(3/7*V1)+nat(2*V)*47+nat(2*V)*6*nat(2*V)+nat(2*V)*41*nat(2*V)*nat(3/7*V)+nat(2*V)*82*nat(3/5*V)+nat(2*V)*287*nat(3/7*V)+nat(2*V5)*22*nat(2*V5)*nat(3/7*V5)+nat(2*V5)*44*nat(3/5*V5)+nat(2*V5)*154*nat(3/7*V5)+nat(3/5*V1)*204+nat(3/5*V)*164+nat(3/5*V5)*88+nat(3/7*V1)*204+nat(3/7*V)*164+nat(3/7*V5)*88+nat(V1+1)*2+nat(V+1)*4+nat(V5+2)*2+nat(2*V1+1)*6+nat(2*V+1)*18+nat(2*V5+2)*12+nat(V1-V)*3+nat(V-V5)*3 Asymptotic class: n^3 * Total analysis performed in 24599 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: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The (relative) TRS S consists of the following rules: encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0' encode_true -> true Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0' encode_true -> true Types: minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge false :: s:false:0':true:cons_minus:cons_cond:cons_ge 0' :: s:false:0':true:cons_minus:cons_cond:cons_ge true :: s:false:0':true:cons_minus:cons_cond:cons_ge encArg :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_false :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_0 :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_true :: s:false:0':true:cons_minus:cons_cond:cons_ge hole_s:false:0':true:cons_minus:cons_cond:cons_ge1_4 :: s:false:0':true:cons_minus:cons_cond:cons_ge gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4 :: Nat -> s:false:0':true:cons_minus:cons_cond:cons_ge ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: minus, cond, ge, encArg They will be analysed ascendingly in the following order: minus = cond ge < minus minus < encArg cond < encArg ge < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0' encode_true -> true Types: minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge false :: s:false:0':true:cons_minus:cons_cond:cons_ge 0' :: s:false:0':true:cons_minus:cons_cond:cons_ge true :: s:false:0':true:cons_minus:cons_cond:cons_ge encArg :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_false :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_0 :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_true :: s:false:0':true:cons_minus:cons_cond:cons_ge hole_s:false:0':true:cons_minus:cons_cond:cons_ge1_4 :: s:false:0':true:cons_minus:cons_cond:cons_ge gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4 :: Nat -> s:false:0':true:cons_minus:cons_cond:cons_ge Generator Equations: gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(0) <=> false gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(x, 1)) <=> s(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(x)) The following defined symbols remain to be analysed: ge, minus, cond, encArg They will be analysed ascendingly in the following order: minus = cond ge < minus minus < encArg cond < encArg ge < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: ge(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, n4_4)), gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: ge(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, 0)), gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, 0))) Induction Step: ge(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, +(n4_4, 1))), gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) ge(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, n4_4)), gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_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: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0' encode_true -> true Types: minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge false :: s:false:0':true:cons_minus:cons_cond:cons_ge 0' :: s:false:0':true:cons_minus:cons_cond:cons_ge true :: s:false:0':true:cons_minus:cons_cond:cons_ge encArg :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_false :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_0 :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_true :: s:false:0':true:cons_minus:cons_cond:cons_ge hole_s:false:0':true:cons_minus:cons_cond:cons_ge1_4 :: s:false:0':true:cons_minus:cons_cond:cons_ge gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4 :: Nat -> s:false:0':true:cons_minus:cons_cond:cons_ge Generator Equations: gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(0) <=> false gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(x, 1)) <=> s(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(x)) The following defined symbols remain to be analysed: ge, minus, cond, encArg They will be analysed ascendingly in the following order: minus = cond ge < minus minus < encArg cond < encArg ge < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(ge(x, s(y)), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_0 -> 0' encode_true -> true Types: minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge false :: s:false:0':true:cons_minus:cons_cond:cons_ge 0' :: s:false:0':true:cons_minus:cons_cond:cons_ge true :: s:false:0':true:cons_minus:cons_cond:cons_ge encArg :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge cons_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_minus :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_cond :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_ge :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_s :: s:false:0':true:cons_minus:cons_cond:cons_ge -> s:false:0':true:cons_minus:cons_cond:cons_ge encode_false :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_0 :: s:false:0':true:cons_minus:cons_cond:cons_ge encode_true :: s:false:0':true:cons_minus:cons_cond:cons_ge hole_s:false:0':true:cons_minus:cons_cond:cons_ge1_4 :: s:false:0':true:cons_minus:cons_cond:cons_ge gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4 :: Nat -> s:false:0':true:cons_minus:cons_cond:cons_ge Lemmas: ge(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, n4_4)), gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(0) <=> false gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(x, 1)) <=> s(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(x)) The following defined symbols remain to be analysed: cond, minus, encArg They will be analysed ascendingly in the following order: minus = cond minus < encArg cond < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(n2205_4)) -> gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(n2205_4), rt in Omega(0) Induction Base: encArg(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(0)) ->_R^Omega(0) false Induction Step: encArg(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(+(n2205_4, 1))) ->_R^Omega(0) s(encArg(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(n2205_4))) ->_IH s(gen_s:false:0':true:cons_minus:cons_cond:cons_ge2_4(c2206_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)