/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 299 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, 23.8 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), 516 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), 190 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 229 ms] (30) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0, v) -> 0 min(u, 0) -> 0 min(s(u), s(v)) -> s(min(u, v)) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0, v) -> 0 min(u, 0) -> 0 min(s(u), s(v)) -> s(min(u, v)) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0, v) -> 0 min(u, 0) -> 0 min(s(u), s(v)) -> s(min(u, v)) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(cons_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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) [1] cond(true, x, y) -> s(minus(x, s(y))) [1] min(0, v) -> 0 [1] min(u, 0) -> 0 [1] min(s(u), s(v)) -> s(min(u, v)) [1] equal(0, 0) -> true [1] equal(s(x), 0) -> false [1] equal(0, s(y)) -> false [1] equal(s(x), s(y)) -> equal(x, y) [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) [1] cond(true, x, y) -> s(minus(x, s(y))) [1] min(0, v) -> 0 [1] min(u, 0) -> 0 [1] min(s(u), s(v)) -> s(min(u, v)) [1] equal(0, 0) -> true [1] equal(s(x), 0) -> false [1] equal(0, s(y)) -> false [1] equal(s(x), s(y)) -> equal(x, y) [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [0] The TRS has the following type information: minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal 0 :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal 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_equal(v0, v1) -> null_encode_equal [0] encode_min(v0, v1) -> null_encode_min [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] cond(v0, v1, v2) -> null_cond [0] min(v0, v1) -> null_min [0] equal(v0, v1) -> null_equal [0] And the following fresh constants: null_encArg, null_encode_minus, null_encode_cond, null_encode_equal, null_encode_min, null_encode_true, null_encode_s, null_encode_0, null_encode_false, null_cond, null_min, null_equal ---------------------------------------- (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(equal(min(x, y), y), x, y) [1] cond(true, x, y) -> s(minus(x, s(y))) [1] min(0, v) -> 0 [1] min(u, 0) -> 0 [1] min(s(u), s(v)) -> s(min(u, v)) [1] equal(0, 0) -> true [1] equal(s(x), 0) -> false [1] equal(0, s(y)) -> false [1] equal(s(x), s(y)) -> equal(x, y) [1] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(0) -> 0 [0] encArg(false) -> false [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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_0 -> 0 [0] encode_false -> false [0] encArg(v0) -> null_encArg [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_equal(v0, v1) -> null_encode_equal [0] encode_min(v0, v1) -> null_encode_min [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] cond(v0, v1, v2) -> null_cond [0] min(v0, v1) -> null_min [0] equal(v0, v1) -> null_equal [0] The TRS has the following type information: minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal true :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal s :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal 0 :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal false :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encArg :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal cons_minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal cons_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal cons_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal cons_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_true :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_s :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal -> true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_0 :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal encode_false :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encArg :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_minus :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_true :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_s :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_0 :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_encode_false :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_cond :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_min :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal null_equal :: true:s:0:false:cons_minus:cons_cond:cons_min:cons_equal:null_encArg:null_encode_minus:null_encode_cond:null_encode_equal:null_encode_min:null_encode_true:null_encode_s:null_encode_0:null_encode_false:null_cond:null_min:null_equal Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: true => 2 0 => 0 false => 1 null_encArg => 0 null_encode_minus => 0 null_encode_cond => 0 null_encode_equal => 0 null_encode_min => 0 null_encode_true => 0 null_encode_s => 0 null_encode_0 => 0 null_encode_false => 0 null_cond => 0 null_min => 0 null_equal => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: 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 }-> min(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> equal(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_equal(z, z') -{ 0 }-> equal(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_equal(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_min(z, z') -{ 0 }-> min(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_min(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 :|: equal(z, z') -{ 1 }-> equal(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x equal(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 equal(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 equal(z, z') -{ 1 }-> 1 :|: z' = 1 + y, y >= 0, z = 0 equal(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 min(z, z') -{ 1 }-> 0 :|: v >= 0, z' = v, z = 0 min(z, z') -{ 1 }-> 0 :|: z = u, z' = 0, u >= 0 min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 min(z, z') -{ 1 }-> 1 + min(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0 minus(z, z') -{ 1 }-> cond(equal(min(x, y), 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,[min(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[equal(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, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun4(Out)],[]). eq(start(V1, V, V5),0,[fun5(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun6(Out)],[]). eq(start(V1, V, V5),0,[fun7(Out)],[]). eq(minus(V1, V, Out),1,[min(V3, V2, Ret00),equal(Ret00, V2, Ret0),cond(Ret0, V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = V3,V = V2]). eq(cond(V1, V, V5, Out),1,[minus(V4, 1 + V6, Ret1)],[Out = 1 + Ret1,V1 = 2,V = V4,V5 = V6,V4 >= 0,V6 >= 0]). eq(min(V1, V, Out),1,[],[Out = 0,V7 >= 0,V = V7,V1 = 0]). eq(min(V1, V, Out),1,[],[Out = 0,V1 = V8,V = 0,V8 >= 0]). eq(min(V1, V, Out),1,[min(V9, V10, Ret11)],[Out = 1 + Ret11,V10 >= 0,V = 1 + V10,V1 = 1 + V9,V9 >= 0]). eq(equal(V1, V, Out),1,[],[Out = 2,V1 = 0,V = 0]). eq(equal(V1, V, Out),1,[],[Out = 1,V11 >= 0,V1 = 1 + V11,V = 0]). eq(equal(V1, V, Out),1,[],[Out = 1,V = 1 + V12,V12 >= 0,V1 = 0]). eq(equal(V1, V, Out),1,[equal(V13, V14, Ret2)],[Out = Ret2,V = 1 + V14,V13 >= 0,V14 >= 0,V1 = 1 + V13]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V15, Ret12)],[Out = 1 + Ret12,V1 = 1 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V16, Ret01),encArg(V17, Ret13),minus(Ret01, Ret13, Ret3)],[Out = Ret3,V16 >= 0,V1 = 1 + V16 + V17,V17 >= 0]). eq(encArg(V1, Out),0,[encArg(V19, Ret02),encArg(V20, Ret14),encArg(V18, Ret21),cond(Ret02, Ret14, Ret21, Ret4)],[Out = Ret4,V19 >= 0,V1 = 1 + V18 + V19 + V20,V18 >= 0,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret03),encArg(V21, Ret15),min(Ret03, Ret15, Ret5)],[Out = Ret5,V22 >= 0,V1 = 1 + V21 + V22,V21 >= 0]). eq(encArg(V1, Out),0,[encArg(V24, Ret04),encArg(V23, Ret16),equal(Ret04, Ret16, Ret6)],[Out = Ret6,V24 >= 0,V1 = 1 + V23 + V24,V23 >= 0]). eq(fun(V1, V, Out),0,[encArg(V25, Ret05),encArg(V26, Ret17),minus(Ret05, Ret17, Ret7)],[Out = Ret7,V25 >= 0,V26 >= 0,V1 = V25,V = V26]). eq(fun1(V1, V, V5, Out),0,[encArg(V28, Ret06),encArg(V29, Ret18),encArg(V27, Ret22),cond(Ret06, Ret18, Ret22, Ret8)],[Out = Ret8,V28 >= 0,V27 >= 0,V29 >= 0,V1 = V28,V = V29,V5 = V27]). eq(fun2(V1, V, Out),0,[encArg(V31, Ret07),encArg(V30, Ret19),equal(Ret07, Ret19, Ret9)],[Out = Ret9,V31 >= 0,V30 >= 0,V1 = V31,V = V30]). eq(fun3(V1, V, Out),0,[encArg(V33, Ret08),encArg(V32, Ret110),min(Ret08, Ret110, Ret10)],[Out = Ret10,V33 >= 0,V32 >= 0,V1 = V33,V = V32]). eq(fun4(Out),0,[],[Out = 2]). eq(fun5(V1, Out),0,[encArg(V34, Ret111)],[Out = 1 + Ret111,V34 >= 0,V1 = V34]). eq(fun6(Out),0,[],[Out = 0]). eq(fun7(Out),0,[],[Out = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V35 >= 0,V1 = V35]). eq(fun(V1, V, Out),0,[],[Out = 0,V37 >= 0,V36 >= 0,V1 = V37,V = V36]). eq(fun1(V1, V, V5, Out),0,[],[Out = 0,V39 >= 0,V5 = V40,V38 >= 0,V1 = V39,V = V38,V40 >= 0]). eq(fun2(V1, V, Out),0,[],[Out = 0,V41 >= 0,V42 >= 0,V1 = V41,V = V42]). eq(fun3(V1, V, Out),0,[],[Out = 0,V43 >= 0,V44 >= 0,V1 = V43,V = V44]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(V1, Out),0,[],[Out = 0,V45 >= 0,V1 = V45]). eq(fun7(Out),0,[],[Out = 0]). eq(cond(V1, V, V5, Out),0,[],[Out = 0,V47 >= 0,V5 = V48,V46 >= 0,V1 = V47,V = V46,V48 >= 0]). eq(min(V1, V, Out),0,[],[Out = 0,V49 >= 0,V50 >= 0,V1 = V49,V = V50]). eq(equal(V1, V, Out),0,[],[Out = 0,V51 >= 0,V52 >= 0,V1 = V51,V = V52]). 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(min(V1,V,Out),[V1,V],[Out]). input_output_vars(equal(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,V,Out),[V1,V],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(V1,Out),[V1],[Out]). input_output_vars(fun6(Out),[],[Out]). input_output_vars(fun7(Out),[],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [equal/3] 1. recursive : [min/3] 2. recursive : [cond/4,minus/3] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun/3] 5. non_recursive : [fun1/4] 6. non_recursive : [fun2/3] 7. non_recursive : [fun3/3] 8. non_recursive : [fun4/1] 9. non_recursive : [fun5/2] 10. non_recursive : [fun6/1] 11. non_recursive : [fun7/1] 12. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into equal/3 1. SCC is partially evaluated into min/3 2. SCC is partially evaluated into minus/3 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun/3 5. SCC is partially evaluated into fun1/4 6. SCC is partially evaluated into fun2/3 7. SCC is partially evaluated into fun3/3 8. SCC is partially evaluated into fun4/1 9. SCC is partially evaluated into fun5/2 10. SCC is completely evaluated into other SCCs 11. SCC is partially evaluated into fun7/1 12. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations equal/3 * CE 24 is refined into CE [49] * CE 21 is refined into CE [50] * CE 22 is refined into CE [51] * CE 20 is refined into CE [52] * CE 23 is refined into CE [53] ### Cost equations --> "Loop" of equal/3 * CEs [53] --> Loop 28 * CEs [49] --> Loop 29 * CEs [50] --> Loop 30 * CEs [51] --> Loop 31 * CEs [52] --> Loop 32 ### Ranking functions of CR equal(V1,V,Out) * RF of phase [28]: [V,V1] #### Partial ranking functions of CR equal(V1,V,Out) * Partial RF of phase [28]: - RF of loop [28:1]: V V1 ### Specialization of cost equations min/3 * CE 17 is refined into CE [54] * CE 16 is refined into CE [55] * CE 19 is refined into CE [56] * CE 18 is refined into CE [57] ### Cost equations --> "Loop" of min/3 * CEs [57] --> Loop 33 * CEs [54] --> Loop 34 * CEs [55,56] --> Loop 35 ### Ranking functions of CR min(V1,V,Out) * RF of phase [33]: [V,V1] #### Partial ranking functions of CR min(V1,V,Out) * Partial RF of phase [33]: - RF of loop [33:1]: V V1 ### Specialization of cost equations minus/3 * CE 15 is refined into CE [58,59] * CE 14 is refined into CE [60,61,62,63,64,65] ### Cost equations --> "Loop" of minus/3 * CEs [60,61,62,63,64,65] --> Loop 36 * CEs [59] --> Loop 37 * CEs [58] --> Loop 38 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [37]: [V1-V+1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [37]: - RF of loop [37:1]: V1-V+1 ### Specialization of cost equations encArg/2 * CE 29 is refined into CE [66] * CE 27 is refined into CE [67] * CE 30 is refined into CE [68] * CE 31 is refined into CE [69,70,71,72] * CE 32 is refined into CE [73,74] * CE 33 is refined into CE [75,76,77,78,79,80,81] * CE 28 is refined into CE [82] * CE 26 is refined into CE [83,84] * CE 25 is refined into CE [85] ### Cost equations --> "Loop" of encArg/2 * CEs [84] --> Loop 39 * CEs [83] --> Loop 40 * CEs [85] --> Loop 41 * CEs [82] --> Loop 42 * CEs [70] --> Loop 43 * CEs [81] --> Loop 44 * CEs [75] --> Loop 45 * CEs [72,80] --> Loop 46 * CEs [74,79] --> Loop 47 * CEs [69,77] --> Loop 48 * CEs [76] --> Loop 49 * CEs [71,73,78] --> Loop 50 * CEs [66] --> Loop 51 * CEs [67] --> Loop 52 * CEs [68] --> Loop 53 ### Ranking functions of CR encArg(V1,Out) * RF of phase [39,40,41,42,43,44,45,46,47,48,49,50]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [39,40,41,42,43,44,45,46,47,48,49,50]: - RF of loop [39:1,39:2,39:3,40:1,40:2,40:3,41:1,41:2,41:3,42:1,43:1,43:2,44:1,44:2,45:1,45:2,46:1,46:2,47:1,47:2,48:1,48:2,49:1,49:2,50:1,50:2]: V1 ### Specialization of cost equations fun/3 * CE 34 is refined into CE [86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108] * CE 35 is refined into CE [109] ### Cost equations --> "Loop" of fun/3 * CEs [91] --> Loop 54 * CEs [90,106] --> Loop 55 * CEs [89,98] --> Loop 56 * CEs [87,93,96,102] --> Loop 57 * CEs [86,92,95,100,101,104,107] --> Loop 58 * CEs [88,94,97,99,103,105,108,109] --> Loop 59 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun1/4 * CE 36 is refined into CE [110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136] * CE 37 is refined into CE [137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164] * CE 38 is refined into CE [165] ### Cost equations --> "Loop" of fun1/4 * CEs [144,147] --> Loop 60 * CEs [143,145,146] --> Loop 61 * CEs [113,114,115,131,132,133] --> Loop 62 * CEs [140,154] --> Loop 63 * CEs [139,149,153,163] --> Loop 64 * CEs [111,117,120,126,129,135] --> Loop 65 * CEs [138,142,152,156,158,161] --> Loop 66 * CEs [137,141,148,150,151,155,157,159,160,162,164] --> Loop 67 * CEs [110,112,116,118,119,121,122,123,124,125,127,128,130,134,136,165] --> Loop 68 ### 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 39 is refined into CE [166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196] * CE 40 is refined into CE [197] ### Cost equations --> "Loop" of fun2/3 * CEs [177] --> Loop 69 * CEs [173,175,176,191,193] --> Loop 70 * CEs [174,194] --> Loop 71 * CEs [167,168,170,171,179,181,183,184,188] --> Loop 72 * CEs [166,172,178,185,187,190,195] --> Loop 73 * CEs [169,180,182,186,189,192,196,197] --> Loop 74 ### Ranking functions of CR fun2(V1,V,Out) #### Partial ranking functions of CR fun2(V1,V,Out) ### Specialization of cost equations fun3/3 * CE 41 is refined into CE [198,199,200,201,202,203,204,205,206,207,208,209,210] * CE 42 is refined into CE [211] ### Cost equations --> "Loop" of fun3/3 * CEs [201] --> Loop 75 * CEs [200,209] --> Loop 76 * CEs [199,204,206] --> Loop 77 * CEs [198,202,203,205,207,208,210,211] --> Loop 78 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun4/1 * CE 43 is refined into CE [212] * CE 44 is refined into CE [213] ### Cost equations --> "Loop" of fun4/1 * CEs [212] --> Loop 79 * CEs [213] --> Loop 80 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/2 * CE 45 is refined into CE [214,215,216] * CE 46 is refined into CE [217] ### Cost equations --> "Loop" of fun5/2 * CEs [216] --> Loop 81 * CEs [217] --> Loop 82 * CEs [214,215] --> Loop 83 ### Ranking functions of CR fun5(V1,Out) #### Partial ranking functions of CR fun5(V1,Out) ### Specialization of cost equations fun7/1 * CE 47 is refined into CE [218] * CE 48 is refined into CE [219] ### Cost equations --> "Loop" of fun7/1 * CEs [218] --> Loop 84 * CEs [219] --> Loop 85 ### Ranking functions of CR fun7(Out) #### Partial ranking functions of CR fun7(Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [220] * CE 2 is refined into CE [221,222] * CE 3 is refined into CE [223,224,225,226] * CE 4 is refined into CE [227,228] * CE 5 is refined into CE [229,230,231,232,233,234,235] * CE 6 is refined into CE [236,237,238] * CE 7 is refined into CE [239,240,241,242] * CE 8 is refined into CE [243,244,245,246,247,248] * CE 9 is refined into CE [249,250,251,252] * CE 10 is refined into CE [253,254] * CE 11 is refined into CE [255,256] * CE 12 is refined into CE [257,258,259] * CE 13 is refined into CE [260,261] ### Cost equations --> "Loop" of start/3 * CEs [220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261] --> Loop 86 ### Ranking functions of CR start(V1,V,V5) #### Partial ranking functions of CR start(V1,V,V5) Computing Bounds ===================================== #### Cost of chains of equal(V1,V,Out): * Chain [[28],32]: 1*it(28)+1 Such that:it(28) =< V1 with precondition: [Out=2,V1=V,V1>=1] * Chain [[28],31]: 1*it(28)+1 Such that:it(28) =< V1 with precondition: [Out=1,V1>=1,V>=V1+1] * Chain [[28],30]: 1*it(28)+1 Such that:it(28) =< V with precondition: [Out=1,V>=1,V1>=V+1] * Chain [[28],29]: 1*it(28)+0 Such that:it(28) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [32]: 1 with precondition: [V1=0,V=0,Out=2] * Chain [31]: 1 with precondition: [V1=0,Out=1,V>=1] * Chain [30]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [29]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of min(V1,V,Out): * Chain [[33],35]: 1*it(33)+1 Such that:it(33) =< Out with precondition: [Out>=1,V1>=Out,V>=Out] * Chain [[33],34]: 1*it(33)+1 Such that:it(33) =< Out with precondition: [V=Out,V>=1,V1>=V] * Chain [35]: 1 with precondition: [Out=0,V1>=0,V>=0] * Chain [34]: 1 with precondition: [V=0,Out=0,V1>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[37],36]: 4*it(37)+10*s(4)+3*s(19)+3 Such that:aux(7) =< V1+1 aux(5) =< V+Out it(37) =< Out s(4) =< aux(5) s(20) =< it(37)*aux(7) s(19) =< s(20) with precondition: [V>=1,Out>=1,V1+1>=Out+V] * Chain [38,[37],36]: 14*it(37)+3*s(19)+7 Such that:aux(7) =< V1+1 aux(8) =< Out it(37) =< aux(8) s(20) =< it(37)*aux(7) s(19) =< s(20) with precondition: [V=0,Out>=2,V1+1>=Out] * Chain [38,36]: 10*s(4)+7 Such that:aux(5) =< 1 s(4) =< aux(5) with precondition: [V=0,Out=1,V1>=0] * Chain [36]: 10*s(4)+3 Such that:aux(5) =< V s(4) =< aux(5) with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of encArg(V1,Out): * Chain [53]: 0 with precondition: [V1=1,Out=1] * Chain [52]: 0 with precondition: [V1=2,Out=2] * Chain [51]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([39,40,41,42,43,44,45,46,47,48,49,50],[[53],[52],[51]])]: 4*it(39)+4*it(40)+7*it(43)+5*it(44)+21*it(45)+1*it(49)+14*s(70)+3*s(71)+10*s(74)+14*s(76)+3*s(77)+2*s(80)+14*s(81)+3*s(82)+3*s(86)+11*s(88)+0 Such that:s(27) =< 2*V1 aux(29) =< V1 aux(30) =< 2*V1+1 aux(31) =< V1/2 aux(32) =< 2/3*V1 aux(33) =< 3/5*V1 aux(34) =< 4/5*V1 it(43) =< aux(29) it(44) =< aux(29) it(45) =< aux(29) it(49) =< aux(29) it([51]) =< aux(30) it(39) =< aux(31) it(44) =< aux(32) it(40) =< aux(33) it(43) =< aux(34) it(44) =< aux(34) it(49) =< aux(34) aux(15) =< s(27) aux(17) =< s(27)-1 aux(23) =< s(27)+1 aux(19) =< s(27)+2 it(43) =< it([51])*(1/5)+aux(34) it(44) =< it([51])*(1/5)+aux(34) it(45) =< it([51])*(1/5)+aux(34) it(49) =< it([51])*(1/5)+aux(34) it(44) =< it([51])*(1/3)+aux(32) it(45) =< it([51])*(1/3)+aux(32) it(49) =< it([51])*(1/3)+aux(32) it(40) =< it([51])*(1/5)+aux(33) it(39) =< it([51])*(1/4)+aux(31) it(40) =< it([51])*(1/4)+aux(31) s(89) =< it(45)*aux(15) s(87) =< it(44)*aux(17) s(80) =< it(44)*aux(17) s(85) =< it(44)*aux(23) s(79) =< it(43)*aux(19) s(75) =< it(40)*aux(17) s(73) =< it(39)*aux(15) s(88) =< s(89) s(86) =< s(87) s(81) =< s(85) s(84) =< s(81)*aux(23) s(82) =< s(84) s(76) =< s(79) s(78) =< s(76)*aux(19) s(77) =< s(78) s(74) =< s(75) s(70) =< s(73) s(72) =< s(70)*s(27) s(71) =< s(72) with precondition: [V1>=1,Out>=0,2*V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [59]: 14*s(134)+10*s(135)+42*s(136)+2*s(137)+8*s(138)+8*s(139)+4*s(146)+22*s(151)+6*s(152)+28*s(153)+6*s(155)+28*s(156)+6*s(158)+20*s(159)+28*s(160)+6*s(162)+21*s(170)+15*s(171)+63*s(172)+3*s(173)+12*s(174)+12*s(175)+6*s(182)+33*s(187)+9*s(188)+42*s(189)+9*s(191)+42*s(192)+9*s(194)+30*s(195)+42*s(196)+9*s(198)+30*s(200)+10*s(278)+3 Such that:s(277) =< 2 aux(38) =< V1 aux(39) =< 2*V1 aux(40) =< 2*V1+1 aux(41) =< V1/2 aux(42) =< 2/3*V1 aux(43) =< 3/5*V1 aux(44) =< 4/5*V1 aux(45) =< V aux(46) =< 2*V aux(47) =< 2*V+1 aux(48) =< V/2 aux(49) =< 2/3*V aux(50) =< 3/5*V aux(51) =< 4/5*V s(278) =< s(277) s(200) =< aux(46) s(170) =< aux(45) s(171) =< aux(45) s(172) =< aux(45) s(173) =< aux(45) s(174) =< aux(48) s(171) =< aux(49) s(175) =< aux(50) s(170) =< aux(51) s(171) =< aux(51) s(173) =< aux(51) s(176) =< aux(46) s(177) =< aux(46)-1 s(178) =< aux(46)+1 s(179) =< aux(46)+2 s(170) =< aux(47)*(1/5)+aux(51) s(171) =< aux(47)*(1/5)+aux(51) s(172) =< aux(47)*(1/5)+aux(51) s(173) =< aux(47)*(1/5)+aux(51) s(171) =< aux(47)*(1/3)+aux(49) s(172) =< aux(47)*(1/3)+aux(49) s(173) =< aux(47)*(1/3)+aux(49) s(175) =< aux(47)*(1/5)+aux(50) s(174) =< aux(47)*(1/4)+aux(48) s(175) =< aux(47)*(1/4)+aux(48) s(180) =< s(172)*s(176) s(181) =< s(171)*s(177) s(182) =< s(171)*s(177) s(183) =< s(171)*s(178) s(184) =< s(170)*s(179) s(185) =< s(175)*s(177) s(186) =< s(174)*s(176) s(187) =< s(180) s(188) =< s(181) s(189) =< s(183) s(190) =< s(189)*s(178) s(191) =< s(190) s(192) =< s(184) s(193) =< s(192)*s(179) s(194) =< s(193) s(195) =< s(185) s(196) =< s(186) s(197) =< s(196)*aux(46) s(198) =< s(197) s(134) =< aux(38) s(135) =< aux(38) s(136) =< aux(38) s(137) =< aux(38) s(138) =< aux(41) s(135) =< aux(42) s(139) =< aux(43) s(134) =< aux(44) s(135) =< aux(44) s(137) =< aux(44) s(140) =< aux(39) s(141) =< aux(39)-1 s(142) =< aux(39)+1 s(143) =< aux(39)+2 s(134) =< aux(40)*(1/5)+aux(44) s(135) =< aux(40)*(1/5)+aux(44) s(136) =< aux(40)*(1/5)+aux(44) s(137) =< aux(40)*(1/5)+aux(44) s(135) =< aux(40)*(1/3)+aux(42) s(136) =< aux(40)*(1/3)+aux(42) s(137) =< aux(40)*(1/3)+aux(42) s(139) =< aux(40)*(1/5)+aux(43) s(138) =< aux(40)*(1/4)+aux(41) s(139) =< aux(40)*(1/4)+aux(41) s(144) =< s(136)*s(140) s(145) =< s(135)*s(141) s(146) =< s(135)*s(141) s(147) =< s(135)*s(142) s(148) =< s(134)*s(143) s(149) =< s(139)*s(141) s(150) =< s(138)*s(140) s(151) =< s(144) s(152) =< s(145) s(153) =< s(147) s(154) =< s(153)*s(142) s(155) =< s(154) s(156) =< s(148) s(157) =< s(156)*s(143) s(158) =< s(157) s(159) =< s(149) s(160) =< s(150) s(161) =< s(160)*aux(39) s(162) =< s(161) with precondition: [Out=0,V1>=0,V>=0] * Chain [58]: 14*s(328)+10*s(329)+42*s(330)+2*s(331)+8*s(332)+8*s(333)+4*s(340)+22*s(345)+6*s(346)+28*s(347)+6*s(349)+28*s(350)+6*s(352)+20*s(353)+28*s(354)+6*s(356)+21*s(364)+15*s(365)+63*s(366)+3*s(367)+12*s(368)+12*s(369)+6*s(376)+33*s(381)+9*s(382)+42*s(383)+9*s(385)+42*s(386)+9*s(388)+30*s(389)+42*s(390)+9*s(392)+64*s(394)+10*s(474)+3*s(476)+7 Such that:aux(52) =< 3 aux(53) =< 1 aux(54) =< V1 aux(55) =< 2*V1 aux(56) =< 2*V1+1 aux(57) =< V1/2 aux(58) =< 2/3*V1 aux(59) =< 3/5*V1 aux(60) =< 4/5*V1 aux(61) =< V aux(62) =< 2*V aux(63) =< 2*V+1 aux(64) =< V/2 aux(65) =< 2/3*V aux(66) =< 3/5*V aux(67) =< 4/5*V s(394) =< aux(53) s(364) =< aux(61) s(365) =< aux(61) s(366) =< aux(61) s(367) =< aux(61) s(368) =< aux(64) s(365) =< aux(65) s(369) =< aux(66) s(364) =< aux(67) s(365) =< aux(67) s(367) =< aux(67) s(370) =< aux(62) s(371) =< aux(62)-1 s(372) =< aux(62)+1 s(373) =< aux(62)+2 s(364) =< aux(63)*(1/5)+aux(67) s(365) =< aux(63)*(1/5)+aux(67) s(366) =< aux(63)*(1/5)+aux(67) s(367) =< aux(63)*(1/5)+aux(67) s(365) =< aux(63)*(1/3)+aux(65) s(366) =< aux(63)*(1/3)+aux(65) s(367) =< aux(63)*(1/3)+aux(65) s(369) =< aux(63)*(1/5)+aux(66) s(368) =< aux(63)*(1/4)+aux(64) s(369) =< aux(63)*(1/4)+aux(64) s(374) =< s(366)*s(370) s(375) =< s(365)*s(371) s(376) =< s(365)*s(371) s(377) =< s(365)*s(372) s(378) =< s(364)*s(373) s(379) =< s(369)*s(371) s(380) =< s(368)*s(370) s(381) =< s(374) s(382) =< s(375) s(383) =< s(377) s(384) =< s(383)*s(372) s(385) =< s(384) s(386) =< s(378) s(387) =< s(386)*s(373) s(388) =< s(387) s(389) =< s(379) s(390) =< s(380) s(391) =< s(390)*aux(62) s(392) =< s(391) s(328) =< aux(54) s(329) =< aux(54) s(330) =< aux(54) s(331) =< aux(54) s(332) =< aux(57) s(329) =< aux(58) s(333) =< aux(59) s(328) =< aux(60) s(329) =< aux(60) s(331) =< aux(60) s(334) =< aux(55) s(335) =< aux(55)-1 s(336) =< aux(55)+1 s(337) =< aux(55)+2 s(328) =< aux(56)*(1/5)+aux(60) s(329) =< aux(56)*(1/5)+aux(60) s(330) =< aux(56)*(1/5)+aux(60) s(331) =< aux(56)*(1/5)+aux(60) s(329) =< aux(56)*(1/3)+aux(58) s(330) =< aux(56)*(1/3)+aux(58) s(331) =< aux(56)*(1/3)+aux(58) s(333) =< aux(56)*(1/5)+aux(59) s(332) =< aux(56)*(1/4)+aux(57) s(333) =< aux(56)*(1/4)+aux(57) s(338) =< s(330)*s(334) s(339) =< s(329)*s(335) s(340) =< s(329)*s(335) s(341) =< s(329)*s(336) s(342) =< s(328)*s(337) s(343) =< s(333)*s(335) s(344) =< s(332)*s(334) s(345) =< s(338) s(346) =< s(339) s(347) =< s(341) s(348) =< s(347)*s(336) s(349) =< s(348) s(350) =< s(342) s(351) =< s(350)*s(337) s(352) =< s(351) s(353) =< s(343) s(354) =< s(344) s(355) =< s(354)*aux(55) s(356) =< s(355) s(474) =< aux(52) s(475) =< s(394)*aux(52) s(476) =< s(475) with precondition: [Out=1,V1>=0,V>=0] * Chain [57]: 14*s(526)+10*s(527)+42*s(528)+2*s(529)+8*s(530)+8*s(531)+4*s(538)+22*s(543)+6*s(544)+28*s(545)+6*s(547)+28*s(548)+6*s(550)+20*s(551)+28*s(552)+6*s(554)+14*s(562)+10*s(563)+42*s(564)+2*s(565)+8*s(566)+8*s(567)+4*s(574)+22*s(579)+6*s(580)+28*s(581)+6*s(583)+28*s(584)+6*s(586)+20*s(587)+28*s(588)+6*s(590)+28*s(593)+6*s(595)+28*s(675)+6*s(677)+7 Such that:aux(72) =< 3 aux(73) =< V1 aux(74) =< 2*V1 aux(75) =< 2*V1+1 aux(76) =< V1/2 aux(77) =< 2/3*V1 aux(78) =< 3/5*V1 aux(79) =< 4/5*V1 aux(80) =< V aux(81) =< 2*V aux(82) =< 2*V+1 aux(83) =< V/2 aux(84) =< 2/3*V aux(85) =< 3/5*V aux(86) =< 4/5*V s(675) =< aux(72) s(676) =< s(675)*aux(72) s(677) =< s(676) s(593) =< aux(75) s(594) =< s(593)*aux(75) s(595) =< s(594) s(562) =< aux(80) s(563) =< aux(80) s(564) =< aux(80) s(565) =< aux(80) s(566) =< aux(83) s(563) =< aux(84) s(567) =< aux(85) s(562) =< aux(86) s(563) =< aux(86) s(565) =< aux(86) s(568) =< aux(81) s(569) =< aux(81)-1 s(570) =< aux(81)+1 s(571) =< aux(81)+2 s(562) =< aux(82)*(1/5)+aux(86) s(563) =< aux(82)*(1/5)+aux(86) s(564) =< aux(82)*(1/5)+aux(86) s(565) =< aux(82)*(1/5)+aux(86) s(563) =< aux(82)*(1/3)+aux(84) s(564) =< aux(82)*(1/3)+aux(84) s(565) =< aux(82)*(1/3)+aux(84) s(567) =< aux(82)*(1/5)+aux(85) s(566) =< aux(82)*(1/4)+aux(83) s(567) =< aux(82)*(1/4)+aux(83) s(572) =< s(564)*s(568) s(573) =< s(563)*s(569) s(574) =< s(563)*s(569) s(575) =< s(563)*s(570) s(576) =< s(562)*s(571) s(577) =< s(567)*s(569) s(578) =< s(566)*s(568) s(579) =< s(572) s(580) =< s(573) s(581) =< s(575) s(582) =< s(581)*s(570) s(583) =< s(582) s(584) =< s(576) s(585) =< s(584)*s(571) s(586) =< s(585) s(587) =< s(577) s(588) =< s(578) s(589) =< s(588)*aux(81) s(590) =< s(589) s(526) =< aux(73) s(527) =< aux(73) s(528) =< aux(73) s(529) =< aux(73) s(530) =< aux(76) s(527) =< aux(77) s(531) =< aux(78) s(526) =< aux(79) s(527) =< aux(79) s(529) =< aux(79) s(532) =< aux(74) s(533) =< aux(74)-1 s(534) =< aux(74)+1 s(535) =< aux(74)+2 s(526) =< aux(75)*(1/5)+aux(79) s(527) =< aux(75)*(1/5)+aux(79) s(528) =< aux(75)*(1/5)+aux(79) s(529) =< aux(75)*(1/5)+aux(79) s(527) =< aux(75)*(1/3)+aux(77) s(528) =< aux(75)*(1/3)+aux(77) s(529) =< aux(75)*(1/3)+aux(77) s(531) =< aux(75)*(1/5)+aux(78) s(530) =< aux(75)*(1/4)+aux(76) s(531) =< aux(75)*(1/4)+aux(76) s(536) =< s(528)*s(532) s(537) =< s(527)*s(533) s(538) =< s(527)*s(533) s(539) =< s(527)*s(534) s(540) =< s(526)*s(535) s(541) =< s(531)*s(533) s(542) =< s(530)*s(532) s(543) =< s(536) s(544) =< s(537) s(545) =< s(539) s(546) =< s(545)*s(534) s(547) =< s(546) s(548) =< s(540) s(549) =< s(548)*s(535) s(550) =< s(549) s(551) =< s(541) s(552) =< s(542) s(553) =< s(552)*aux(74) s(554) =< s(553) with precondition: [V1>=1,V>=0,Out>=2,2*V1+1>=Out] * Chain [56]: 7*s(690)+5*s(691)+21*s(692)+1*s(693)+4*s(694)+4*s(695)+2*s(702)+11*s(707)+3*s(708)+14*s(709)+3*s(711)+14*s(712)+3*s(714)+10*s(715)+14*s(716)+3*s(718)+14*s(726)+10*s(727)+42*s(728)+2*s(729)+8*s(730)+8*s(731)+4*s(738)+22*s(743)+6*s(744)+28*s(745)+6*s(747)+28*s(748)+6*s(750)+20*s(751)+28*s(752)+6*s(754)+4*s(757)+10*s(758)+3*s(760)+4*s(799)+10*s(800)+3*s(802)+3 Such that:s(799) =< 2 aux(89) =< 3 s(683) =< V1 aux(87) =< 2*V1 aux(88) =< 2*V1+1 s(686) =< V1/2 s(687) =< 2/3*V1 s(688) =< 3/5*V1 s(689) =< 4/5*V1 aux(90) =< V aux(91) =< 2*V aux(92) =< 2*V+1 aux(93) =< V/2 aux(94) =< 2/3*V aux(95) =< 3/5*V aux(96) =< 4/5*V s(800) =< aux(89) s(801) =< s(799)*aux(89) s(802) =< s(801) s(726) =< aux(90) s(727) =< aux(90) s(728) =< aux(90) s(729) =< aux(90) s(730) =< aux(93) s(727) =< aux(94) s(731) =< aux(95) s(726) =< aux(96) s(727) =< aux(96) s(729) =< aux(96) s(732) =< aux(91) s(733) =< aux(91)-1 s(734) =< aux(91)+1 s(735) =< aux(91)+2 s(726) =< aux(92)*(1/5)+aux(96) s(727) =< aux(92)*(1/5)+aux(96) s(728) =< aux(92)*(1/5)+aux(96) s(729) =< aux(92)*(1/5)+aux(96) s(727) =< aux(92)*(1/3)+aux(94) s(728) =< aux(92)*(1/3)+aux(94) s(729) =< aux(92)*(1/3)+aux(94) s(731) =< aux(92)*(1/5)+aux(95) s(730) =< aux(92)*(1/4)+aux(93) s(731) =< aux(92)*(1/4)+aux(93) s(736) =< s(728)*s(732) s(737) =< s(727)*s(733) s(738) =< s(727)*s(733) s(739) =< s(727)*s(734) s(740) =< s(726)*s(735) s(741) =< s(731)*s(733) s(742) =< s(730)*s(732) s(743) =< s(736) s(744) =< s(737) s(745) =< s(739) s(746) =< s(745)*s(734) s(747) =< s(746) s(748) =< s(740) s(749) =< s(748)*s(735) s(750) =< s(749) s(751) =< s(741) s(752) =< s(742) s(753) =< s(752)*aux(91) s(754) =< s(753) s(757) =< aux(87) s(758) =< aux(88) s(759) =< s(757)*aux(88) s(760) =< s(759) s(690) =< s(683) s(691) =< s(683) s(692) =< s(683) s(693) =< s(683) s(694) =< s(686) s(691) =< s(687) s(695) =< s(688) s(690) =< s(689) s(691) =< s(689) s(693) =< s(689) s(696) =< aux(87) s(697) =< aux(87)-1 s(698) =< aux(87)+1 s(699) =< aux(87)+2 s(690) =< aux(88)*(1/5)+s(689) s(691) =< aux(88)*(1/5)+s(689) s(692) =< aux(88)*(1/5)+s(689) s(693) =< aux(88)*(1/5)+s(689) s(691) =< aux(88)*(1/3)+s(687) s(692) =< aux(88)*(1/3)+s(687) s(693) =< aux(88)*(1/3)+s(687) s(695) =< aux(88)*(1/5)+s(688) s(694) =< aux(88)*(1/4)+s(686) s(695) =< aux(88)*(1/4)+s(686) s(700) =< s(692)*s(696) s(701) =< s(691)*s(697) s(702) =< s(691)*s(697) s(703) =< s(691)*s(698) s(704) =< s(690)*s(699) s(705) =< s(695)*s(697) s(706) =< s(694)*s(696) s(707) =< s(700) s(708) =< s(701) s(709) =< s(703) s(710) =< s(709)*s(698) s(711) =< s(710) s(712) =< s(704) s(713) =< s(712)*s(699) s(714) =< s(713) s(715) =< s(705) s(716) =< s(706) s(717) =< s(716)*aux(87) s(718) =< s(717) with precondition: [V1>=1,V>=1,Out>=1,2*V1>=Out] * Chain [55]: 7*s(810)+5*s(811)+21*s(812)+1*s(813)+4*s(814)+4*s(815)+2*s(822)+11*s(827)+3*s(828)+14*s(829)+3*s(831)+14*s(832)+3*s(834)+10*s(835)+14*s(836)+3*s(838)+20*s(840)+3 Such that:s(803) =< V1 s(804) =< 2*V1 s(805) =< 2*V1+1 s(806) =< V1/2 s(807) =< 2/3*V1 s(808) =< 3/5*V1 s(809) =< 4/5*V1 aux(97) =< 2 s(840) =< aux(97) s(810) =< s(803) s(811) =< s(803) s(812) =< s(803) s(813) =< s(803) s(814) =< s(806) s(811) =< s(807) s(815) =< s(808) s(810) =< s(809) s(811) =< s(809) s(813) =< s(809) s(816) =< s(804) s(817) =< s(804)-1 s(818) =< s(804)+1 s(819) =< s(804)+2 s(810) =< s(805)*(1/5)+s(809) s(811) =< s(805)*(1/5)+s(809) s(812) =< s(805)*(1/5)+s(809) s(813) =< s(805)*(1/5)+s(809) s(811) =< s(805)*(1/3)+s(807) s(812) =< s(805)*(1/3)+s(807) s(813) =< s(805)*(1/3)+s(807) s(815) =< s(805)*(1/5)+s(808) s(814) =< s(805)*(1/4)+s(806) s(815) =< s(805)*(1/4)+s(806) s(820) =< s(812)*s(816) s(821) =< s(811)*s(817) s(822) =< s(811)*s(817) s(823) =< s(811)*s(818) s(824) =< s(810)*s(819) s(825) =< s(815)*s(817) s(826) =< s(814)*s(816) s(827) =< s(820) s(828) =< s(821) s(829) =< s(823) s(830) =< s(829)*s(818) s(831) =< s(830) s(832) =< s(824) s(833) =< s(832)*s(819) s(834) =< s(833) s(835) =< s(825) s(836) =< s(826) s(837) =< s(836)*s(804) s(838) =< s(837) with precondition: [V=2,Out=0,V1>=0] * Chain [54]: 7*s(850)+5*s(851)+21*s(852)+1*s(853)+4*s(854)+4*s(855)+2*s(862)+11*s(867)+3*s(868)+14*s(869)+3*s(871)+14*s(872)+3*s(874)+10*s(875)+14*s(876)+3*s(878)+4*s(881)+10*s(882)+3*s(884)+3 Such that:s(843) =< V1 s(846) =< V1/2 s(847) =< 2/3*V1 s(848) =< 3/5*V1 s(849) =< 4/5*V1 aux(98) =< 2*V1 aux(99) =< 2*V1+1 s(881) =< aux(98) s(882) =< aux(99) s(883) =< s(881)*aux(99) s(884) =< s(883) s(850) =< s(843) s(851) =< s(843) s(852) =< s(843) s(853) =< s(843) s(854) =< s(846) s(851) =< s(847) s(855) =< s(848) s(850) =< s(849) s(851) =< s(849) s(853) =< s(849) s(856) =< aux(98) s(857) =< aux(98)-1 s(858) =< aux(98)+1 s(859) =< aux(98)+2 s(850) =< aux(99)*(1/5)+s(849) s(851) =< aux(99)*(1/5)+s(849) s(852) =< aux(99)*(1/5)+s(849) s(853) =< aux(99)*(1/5)+s(849) s(851) =< aux(99)*(1/3)+s(847) s(852) =< aux(99)*(1/3)+s(847) s(853) =< aux(99)*(1/3)+s(847) s(855) =< aux(99)*(1/5)+s(848) s(854) =< aux(99)*(1/4)+s(846) s(855) =< aux(99)*(1/4)+s(846) s(860) =< s(852)*s(856) s(861) =< s(851)*s(857) s(862) =< s(851)*s(857) s(863) =< s(851)*s(858) s(864) =< s(850)*s(859) s(865) =< s(855)*s(857) s(866) =< s(854)*s(856) s(867) =< s(860) s(868) =< s(861) s(869) =< s(863) s(870) =< s(869)*s(858) s(871) =< s(870) s(872) =< s(864) s(873) =< s(872)*s(859) s(874) =< s(873) s(875) =< s(865) s(876) =< s(866) s(877) =< s(876)*aux(98) s(878) =< s(877) with precondition: [V=2,Out>=1,2*V1>=Out+1] #### Cost of chains of fun1(V1,V,V5,Out): * Chain [68]: 28*s(1126)+20*s(1127)+84*s(1128)+4*s(1129)+16*s(1130)+16*s(1131)+8*s(1138)+44*s(1143)+12*s(1144)+56*s(1145)+12*s(1147)+56*s(1148)+12*s(1150)+40*s(1151)+56*s(1152)+12*s(1154)+42*s(1162)+30*s(1163)+126*s(1164)+6*s(1165)+24*s(1166)+24*s(1167)+12*s(1174)+66*s(1179)+18*s(1180)+84*s(1181)+18*s(1183)+84*s(1184)+18*s(1186)+60*s(1187)+84*s(1188)+18*s(1190)+49*s(1198)+35*s(1199)+147*s(1200)+7*s(1201)+28*s(1202)+28*s(1203)+14*s(1210)+77*s(1215)+21*s(1216)+98*s(1217)+21*s(1219)+98*s(1220)+21*s(1222)+70*s(1223)+98*s(1224)+21*s(1226)+0 Such that:aux(115) =< V1 aux(116) =< 2*V1 aux(117) =< 2*V1+1 aux(118) =< V1/2 aux(119) =< 2/3*V1 aux(120) =< 3/5*V1 aux(121) =< 4/5*V1 aux(122) =< V aux(123) =< 2*V aux(124) =< 2*V+1 aux(125) =< V/2 aux(126) =< 2/3*V aux(127) =< 3/5*V aux(128) =< 4/5*V aux(129) =< V5 aux(130) =< 2*V5 aux(131) =< 2*V5+1 aux(132) =< V5/2 aux(133) =< 2/3*V5 aux(134) =< 3/5*V5 aux(135) =< 4/5*V5 s(1198) =< aux(129) s(1199) =< aux(129) s(1200) =< aux(129) s(1201) =< aux(129) s(1202) =< aux(132) s(1199) =< aux(133) s(1203) =< aux(134) s(1198) =< aux(135) s(1199) =< aux(135) s(1201) =< aux(135) s(1204) =< aux(130) s(1205) =< aux(130)-1 s(1206) =< aux(130)+1 s(1207) =< aux(130)+2 s(1198) =< aux(131)*(1/5)+aux(135) s(1199) =< aux(131)*(1/5)+aux(135) s(1200) =< aux(131)*(1/5)+aux(135) s(1201) =< aux(131)*(1/5)+aux(135) s(1199) =< aux(131)*(1/3)+aux(133) s(1200) =< aux(131)*(1/3)+aux(133) s(1201) =< aux(131)*(1/3)+aux(133) s(1203) =< aux(131)*(1/5)+aux(134) s(1202) =< aux(131)*(1/4)+aux(132) s(1203) =< aux(131)*(1/4)+aux(132) s(1208) =< s(1200)*s(1204) s(1209) =< s(1199)*s(1205) s(1210) =< s(1199)*s(1205) s(1211) =< s(1199)*s(1206) s(1212) =< s(1198)*s(1207) s(1213) =< s(1203)*s(1205) s(1214) =< s(1202)*s(1204) s(1215) =< s(1208) s(1216) =< s(1209) s(1217) =< s(1211) s(1218) =< s(1217)*s(1206) s(1219) =< s(1218) s(1220) =< s(1212) s(1221) =< s(1220)*s(1207) s(1222) =< s(1221) s(1223) =< s(1213) s(1224) =< s(1214) s(1225) =< s(1224)*aux(130) s(1226) =< s(1225) s(1162) =< aux(122) s(1163) =< aux(122) s(1164) =< aux(122) s(1165) =< aux(122) s(1166) =< aux(125) s(1163) =< aux(126) s(1167) =< aux(127) s(1162) =< aux(128) s(1163) =< aux(128) s(1165) =< aux(128) s(1168) =< aux(123) s(1169) =< aux(123)-1 s(1170) =< aux(123)+1 s(1171) =< aux(123)+2 s(1162) =< aux(124)*(1/5)+aux(128) s(1163) =< aux(124)*(1/5)+aux(128) s(1164) =< aux(124)*(1/5)+aux(128) s(1165) =< aux(124)*(1/5)+aux(128) s(1163) =< aux(124)*(1/3)+aux(126) s(1164) =< aux(124)*(1/3)+aux(126) s(1165) =< aux(124)*(1/3)+aux(126) s(1167) =< aux(124)*(1/5)+aux(127) s(1166) =< aux(124)*(1/4)+aux(125) s(1167) =< aux(124)*(1/4)+aux(125) s(1172) =< s(1164)*s(1168) s(1173) =< s(1163)*s(1169) s(1174) =< s(1163)*s(1169) s(1175) =< s(1163)*s(1170) s(1176) =< s(1162)*s(1171) s(1177) =< s(1167)*s(1169) s(1178) =< s(1166)*s(1168) s(1179) =< s(1172) s(1180) =< s(1173) s(1181) =< s(1175) s(1182) =< s(1181)*s(1170) s(1183) =< s(1182) s(1184) =< s(1176) s(1185) =< s(1184)*s(1171) s(1186) =< s(1185) s(1187) =< s(1177) s(1188) =< s(1178) s(1189) =< s(1188)*aux(123) s(1190) =< s(1189) s(1126) =< aux(115) s(1127) =< aux(115) s(1128) =< aux(115) s(1129) =< aux(115) s(1130) =< aux(118) s(1127) =< aux(119) s(1131) =< aux(120) s(1126) =< aux(121) s(1127) =< aux(121) s(1129) =< aux(121) s(1132) =< aux(116) s(1133) =< aux(116)-1 s(1134) =< aux(116)+1 s(1135) =< aux(116)+2 s(1126) =< aux(117)*(1/5)+aux(121) s(1127) =< aux(117)*(1/5)+aux(121) s(1128) =< aux(117)*(1/5)+aux(121) s(1129) =< aux(117)*(1/5)+aux(121) s(1127) =< aux(117)*(1/3)+aux(119) s(1128) =< aux(117)*(1/3)+aux(119) s(1129) =< aux(117)*(1/3)+aux(119) s(1131) =< aux(117)*(1/5)+aux(120) s(1130) =< aux(117)*(1/4)+aux(118) s(1131) =< aux(117)*(1/4)+aux(118) s(1136) =< s(1128)*s(1132) s(1137) =< s(1127)*s(1133) s(1138) =< s(1127)*s(1133) s(1139) =< s(1127)*s(1134) s(1140) =< s(1126)*s(1135) s(1141) =< s(1131)*s(1133) s(1142) =< s(1130)*s(1132) s(1143) =< s(1136) s(1144) =< s(1137) s(1145) =< s(1139) s(1146) =< s(1145)*s(1134) s(1147) =< s(1146) s(1148) =< s(1140) s(1149) =< s(1148)*s(1135) s(1150) =< s(1149) s(1151) =< s(1141) s(1152) =< s(1142) s(1153) =< s(1152)*aux(116) s(1154) =< s(1153) with precondition: [Out=0,V1>=0,V>=0,V5>=0] * Chain [67]: 28*s(1738)+20*s(1739)+84*s(1740)+4*s(1741)+16*s(1742)+16*s(1743)+8*s(1750)+44*s(1755)+12*s(1756)+56*s(1757)+12*s(1759)+56*s(1760)+12*s(1762)+40*s(1763)+56*s(1764)+12*s(1766)+28*s(1774)+20*s(1775)+84*s(1776)+4*s(1777)+16*s(1778)+16*s(1779)+8*s(1786)+44*s(1791)+12*s(1792)+56*s(1793)+12*s(1795)+56*s(1796)+12*s(1798)+40*s(1799)+56*s(1800)+12*s(1802)+35*s(1810)+25*s(1811)+105*s(1812)+5*s(1813)+20*s(1814)+20*s(1815)+10*s(1822)+55*s(1827)+15*s(1828)+70*s(1829)+15*s(1831)+70*s(1832)+15*s(1834)+50*s(1835)+70*s(1836)+15*s(1838)+50*s(1840)+50*s(1914)+10*s(2178)+4 Such that:s(2177) =< 3 aux(141) =< 1 aux(142) =< V1 aux(143) =< 2*V1 aux(144) =< 2*V1+1 aux(145) =< V1/2 aux(146) =< 2/3*V1 aux(147) =< 3/5*V1 aux(148) =< 4/5*V1 aux(149) =< V aux(150) =< 2*V aux(151) =< 2*V+1 aux(152) =< V/2 aux(153) =< 2/3*V aux(154) =< 3/5*V aux(155) =< 4/5*V aux(156) =< V5 aux(157) =< 2*V5 aux(158) =< 2*V5+1 aux(159) =< V5/2 aux(160) =< 2/3*V5 aux(161) =< 3/5*V5 aux(162) =< 4/5*V5 s(1914) =< aux(141) s(1774) =< aux(149) s(1775) =< aux(149) s(1776) =< aux(149) s(1777) =< aux(149) s(1778) =< aux(152) s(1775) =< aux(153) s(1779) =< aux(154) s(1774) =< aux(155) s(1775) =< aux(155) s(1777) =< aux(155) s(1780) =< aux(150) s(1781) =< aux(150)-1 s(1782) =< aux(150)+1 s(1783) =< aux(150)+2 s(1774) =< aux(151)*(1/5)+aux(155) s(1775) =< aux(151)*(1/5)+aux(155) s(1776) =< aux(151)*(1/5)+aux(155) s(1777) =< aux(151)*(1/5)+aux(155) s(1775) =< aux(151)*(1/3)+aux(153) s(1776) =< aux(151)*(1/3)+aux(153) s(1777) =< aux(151)*(1/3)+aux(153) s(1779) =< aux(151)*(1/5)+aux(154) s(1778) =< aux(151)*(1/4)+aux(152) s(1779) =< aux(151)*(1/4)+aux(152) s(1784) =< s(1776)*s(1780) s(1785) =< s(1775)*s(1781) s(1786) =< s(1775)*s(1781) s(1787) =< s(1775)*s(1782) s(1788) =< s(1774)*s(1783) s(1789) =< s(1779)*s(1781) s(1790) =< s(1778)*s(1780) s(1791) =< s(1784) s(1792) =< s(1785) s(1793) =< s(1787) s(1794) =< s(1793)*s(1782) s(1795) =< s(1794) s(1796) =< s(1788) s(1797) =< s(1796)*s(1783) s(1798) =< s(1797) s(1799) =< s(1789) s(1800) =< s(1790) s(1801) =< s(1800)*aux(150) s(1802) =< s(1801) s(1738) =< aux(142) s(1739) =< aux(142) s(1740) =< aux(142) s(1741) =< aux(142) s(1742) =< aux(145) s(1739) =< aux(146) s(1743) =< aux(147) s(1738) =< aux(148) s(1739) =< aux(148) s(1741) =< aux(148) s(1744) =< aux(143) s(1745) =< aux(143)-1 s(1746) =< aux(143)+1 s(1747) =< aux(143)+2 s(1738) =< aux(144)*(1/5)+aux(148) s(1739) =< aux(144)*(1/5)+aux(148) s(1740) =< aux(144)*(1/5)+aux(148) s(1741) =< aux(144)*(1/5)+aux(148) s(1739) =< aux(144)*(1/3)+aux(146) s(1740) =< aux(144)*(1/3)+aux(146) s(1741) =< aux(144)*(1/3)+aux(146) s(1743) =< aux(144)*(1/5)+aux(147) s(1742) =< aux(144)*(1/4)+aux(145) s(1743) =< aux(144)*(1/4)+aux(145) s(1748) =< s(1740)*s(1744) s(1749) =< s(1739)*s(1745) s(1750) =< s(1739)*s(1745) s(1751) =< s(1739)*s(1746) s(1752) =< s(1738)*s(1747) s(1753) =< s(1743)*s(1745) s(1754) =< s(1742)*s(1744) s(1755) =< s(1748) s(1756) =< s(1749) s(1757) =< s(1751) s(1758) =< s(1757)*s(1746) s(1759) =< s(1758) s(1760) =< s(1752) s(1761) =< s(1760)*s(1747) s(1762) =< s(1761) s(1763) =< s(1753) s(1764) =< s(1754) s(1765) =< s(1764)*aux(143) s(1766) =< s(1765) s(2178) =< s(2177) s(1840) =< aux(158) s(1810) =< aux(156) s(1811) =< aux(156) s(1812) =< aux(156) s(1813) =< aux(156) s(1814) =< aux(159) s(1811) =< aux(160) s(1815) =< aux(161) s(1810) =< aux(162) s(1811) =< aux(162) s(1813) =< aux(162) s(1816) =< aux(157) s(1817) =< aux(157)-1 s(1818) =< aux(157)+1 s(1819) =< aux(157)+2 s(1810) =< aux(158)*(1/5)+aux(162) s(1811) =< aux(158)*(1/5)+aux(162) s(1812) =< aux(158)*(1/5)+aux(162) s(1813) =< aux(158)*(1/5)+aux(162) s(1811) =< aux(158)*(1/3)+aux(160) s(1812) =< aux(158)*(1/3)+aux(160) s(1813) =< aux(158)*(1/3)+aux(160) s(1815) =< aux(158)*(1/5)+aux(161) s(1814) =< aux(158)*(1/4)+aux(159) s(1815) =< aux(158)*(1/4)+aux(159) s(1820) =< s(1812)*s(1816) s(1821) =< s(1811)*s(1817) s(1822) =< s(1811)*s(1817) s(1823) =< s(1811)*s(1818) s(1824) =< s(1810)*s(1819) s(1825) =< s(1815)*s(1817) s(1826) =< s(1814)*s(1816) s(1827) =< s(1820) s(1828) =< s(1821) s(1829) =< s(1823) s(1830) =< s(1829)*s(1818) s(1831) =< s(1830) s(1832) =< s(1824) s(1833) =< s(1832)*s(1819) s(1834) =< s(1833) s(1835) =< s(1825) s(1836) =< s(1826) s(1837) =< s(1836)*aux(157) s(1838) =< s(1837) with precondition: [Out=1,V1>=1,V>=0,V5>=0] * Chain [66]: 14*s(2228)+10*s(2229)+42*s(2230)+2*s(2231)+8*s(2232)+8*s(2233)+4*s(2240)+22*s(2245)+6*s(2246)+28*s(2247)+6*s(2249)+28*s(2250)+6*s(2252)+20*s(2253)+28*s(2254)+6*s(2256)+28*s(2264)+20*s(2265)+84*s(2266)+4*s(2267)+16*s(2268)+16*s(2269)+8*s(2276)+44*s(2281)+12*s(2282)+56*s(2283)+12*s(2285)+56*s(2286)+12*s(2288)+40*s(2289)+56*s(2290)+12*s(2292)+21*s(2300)+15*s(2301)+63*s(2302)+3*s(2303)+12*s(2304)+12*s(2305)+6*s(2312)+33*s(2317)+9*s(2318)+42*s(2319)+9*s(2321)+42*s(2322)+9*s(2324)+30*s(2325)+42*s(2326)+9*s(2328)+16*s(2331)+40*s(2332)+12*s(2334)+8*s(2571)+20*s(2572)+6*s(2574)+4 Such that:aux(173) =< 2 aux(174) =< 3 aux(175) =< V1 aux(176) =< 2*V1 aux(177) =< 2*V1+1 aux(178) =< V1/2 aux(179) =< 2/3*V1 aux(180) =< 3/5*V1 aux(181) =< 4/5*V1 aux(182) =< V aux(183) =< 2*V aux(184) =< 2*V+1 aux(185) =< V/2 aux(186) =< 2/3*V aux(187) =< 3/5*V aux(188) =< 4/5*V aux(189) =< V5 aux(190) =< 2*V5 aux(191) =< 2*V5+1 aux(192) =< V5/2 aux(193) =< 2/3*V5 aux(194) =< 3/5*V5 aux(195) =< 4/5*V5 s(2571) =< aux(173) s(2572) =< aux(174) s(2573) =< s(2571)*aux(174) s(2574) =< s(2573) s(2300) =< aux(189) s(2301) =< aux(189) s(2302) =< aux(189) s(2303) =< aux(189) s(2304) =< aux(192) s(2301) =< aux(193) s(2305) =< aux(194) s(2300) =< aux(195) s(2301) =< aux(195) s(2303) =< aux(195) s(2306) =< aux(190) s(2307) =< aux(190)-1 s(2308) =< aux(190)+1 s(2309) =< aux(190)+2 s(2300) =< aux(191)*(1/5)+aux(195) s(2301) =< aux(191)*(1/5)+aux(195) s(2302) =< aux(191)*(1/5)+aux(195) s(2303) =< aux(191)*(1/5)+aux(195) s(2301) =< aux(191)*(1/3)+aux(193) s(2302) =< aux(191)*(1/3)+aux(193) s(2303) =< aux(191)*(1/3)+aux(193) s(2305) =< aux(191)*(1/5)+aux(194) s(2304) =< aux(191)*(1/4)+aux(192) s(2305) =< aux(191)*(1/4)+aux(192) s(2310) =< s(2302)*s(2306) s(2311) =< s(2301)*s(2307) s(2312) =< s(2301)*s(2307) s(2313) =< s(2301)*s(2308) s(2314) =< s(2300)*s(2309) s(2315) =< s(2305)*s(2307) s(2316) =< s(2304)*s(2306) s(2317) =< s(2310) s(2318) =< s(2311) s(2319) =< s(2313) s(2320) =< s(2319)*s(2308) s(2321) =< s(2320) s(2322) =< s(2314) s(2323) =< s(2322)*s(2309) s(2324) =< s(2323) s(2325) =< s(2315) s(2326) =< s(2316) s(2327) =< s(2326)*aux(190) s(2328) =< s(2327) s(2331) =< aux(183) s(2332) =< aux(184) s(2333) =< s(2331)*aux(184) s(2334) =< s(2333) s(2264) =< aux(182) s(2265) =< aux(182) s(2266) =< aux(182) s(2267) =< aux(182) s(2268) =< aux(185) s(2265) =< aux(186) s(2269) =< aux(187) s(2264) =< aux(188) s(2265) =< aux(188) s(2267) =< aux(188) s(2270) =< aux(183) s(2271) =< aux(183)-1 s(2272) =< aux(183)+1 s(2273) =< aux(183)+2 s(2264) =< aux(184)*(1/5)+aux(188) s(2265) =< aux(184)*(1/5)+aux(188) s(2266) =< aux(184)*(1/5)+aux(188) s(2267) =< aux(184)*(1/5)+aux(188) s(2265) =< aux(184)*(1/3)+aux(186) s(2266) =< aux(184)*(1/3)+aux(186) s(2267) =< aux(184)*(1/3)+aux(186) s(2269) =< aux(184)*(1/5)+aux(187) s(2268) =< aux(184)*(1/4)+aux(185) s(2269) =< aux(184)*(1/4)+aux(185) s(2274) =< s(2266)*s(2270) s(2275) =< s(2265)*s(2271) s(2276) =< s(2265)*s(2271) s(2277) =< s(2265)*s(2272) s(2278) =< s(2264)*s(2273) s(2279) =< s(2269)*s(2271) s(2280) =< s(2268)*s(2270) s(2281) =< s(2274) s(2282) =< s(2275) s(2283) =< s(2277) s(2284) =< s(2283)*s(2272) s(2285) =< s(2284) s(2286) =< s(2278) s(2287) =< s(2286)*s(2273) s(2288) =< s(2287) s(2289) =< s(2279) s(2290) =< s(2280) s(2291) =< s(2290)*aux(183) s(2292) =< s(2291) s(2228) =< aux(175) s(2229) =< aux(175) s(2230) =< aux(175) s(2231) =< aux(175) s(2232) =< aux(178) s(2229) =< aux(179) s(2233) =< aux(180) s(2228) =< aux(181) s(2229) =< aux(181) s(2231) =< aux(181) s(2234) =< aux(176) s(2235) =< aux(176)-1 s(2236) =< aux(176)+1 s(2237) =< aux(176)+2 s(2228) =< aux(177)*(1/5)+aux(181) s(2229) =< aux(177)*(1/5)+aux(181) s(2230) =< aux(177)*(1/5)+aux(181) s(2231) =< aux(177)*(1/5)+aux(181) s(2229) =< aux(177)*(1/3)+aux(179) s(2230) =< aux(177)*(1/3)+aux(179) s(2231) =< aux(177)*(1/3)+aux(179) s(2233) =< aux(177)*(1/5)+aux(180) s(2232) =< aux(177)*(1/4)+aux(178) s(2233) =< aux(177)*(1/4)+aux(178) s(2238) =< s(2230)*s(2234) s(2239) =< s(2229)*s(2235) s(2240) =< s(2229)*s(2235) s(2241) =< s(2229)*s(2236) s(2242) =< s(2228)*s(2237) s(2243) =< s(2233)*s(2235) s(2244) =< s(2232)*s(2234) s(2245) =< s(2238) s(2246) =< s(2239) s(2247) =< s(2241) s(2248) =< s(2247)*s(2236) s(2249) =< s(2248) s(2250) =< s(2242) s(2251) =< s(2250)*s(2237) s(2252) =< s(2251) s(2253) =< s(2243) s(2254) =< s(2244) s(2255) =< s(2254)*aux(176) s(2256) =< s(2255) with precondition: [V1>=1,V>=1,V5>=0,Out>=2,2*V+1>=Out] * Chain [65]: 14*s(2588)+10*s(2589)+42*s(2590)+2*s(2591)+8*s(2592)+8*s(2593)+4*s(2600)+22*s(2605)+6*s(2606)+28*s(2607)+6*s(2609)+28*s(2610)+6*s(2612)+20*s(2613)+28*s(2614)+6*s(2616)+21*s(2624)+15*s(2625)+63*s(2626)+3*s(2627)+12*s(2628)+12*s(2629)+6*s(2636)+33*s(2641)+9*s(2642)+42*s(2643)+9*s(2645)+42*s(2646)+9*s(2648)+30*s(2649)+42*s(2650)+9*s(2652)+0 Such that:aux(196) =< V1 aux(197) =< 2*V1 aux(198) =< 2*V1+1 aux(199) =< V1/2 aux(200) =< 2/3*V1 aux(201) =< 3/5*V1 aux(202) =< 4/5*V1 aux(203) =< V aux(204) =< 2*V aux(205) =< 2*V+1 aux(206) =< V/2 aux(207) =< 2/3*V aux(208) =< 3/5*V aux(209) =< 4/5*V s(2624) =< aux(203) s(2625) =< aux(203) s(2626) =< aux(203) s(2627) =< aux(203) s(2628) =< aux(206) s(2625) =< aux(207) s(2629) =< aux(208) s(2624) =< aux(209) s(2625) =< aux(209) s(2627) =< aux(209) s(2630) =< aux(204) s(2631) =< aux(204)-1 s(2632) =< aux(204)+1 s(2633) =< aux(204)+2 s(2624) =< aux(205)*(1/5)+aux(209) s(2625) =< aux(205)*(1/5)+aux(209) s(2626) =< aux(205)*(1/5)+aux(209) s(2627) =< aux(205)*(1/5)+aux(209) s(2625) =< aux(205)*(1/3)+aux(207) s(2626) =< aux(205)*(1/3)+aux(207) s(2627) =< aux(205)*(1/3)+aux(207) s(2629) =< aux(205)*(1/5)+aux(208) s(2628) =< aux(205)*(1/4)+aux(206) s(2629) =< aux(205)*(1/4)+aux(206) s(2634) =< s(2626)*s(2630) s(2635) =< s(2625)*s(2631) s(2636) =< s(2625)*s(2631) s(2637) =< s(2625)*s(2632) s(2638) =< s(2624)*s(2633) s(2639) =< s(2629)*s(2631) s(2640) =< s(2628)*s(2630) s(2641) =< s(2634) s(2642) =< s(2635) s(2643) =< s(2637) s(2644) =< s(2643)*s(2632) s(2645) =< s(2644) s(2646) =< s(2638) s(2647) =< s(2646)*s(2633) s(2648) =< s(2647) s(2649) =< s(2639) s(2650) =< s(2640) s(2651) =< s(2650)*aux(204) s(2652) =< s(2651) s(2588) =< aux(196) s(2589) =< aux(196) s(2590) =< aux(196) s(2591) =< aux(196) s(2592) =< aux(199) s(2589) =< aux(200) s(2593) =< aux(201) s(2588) =< aux(202) s(2589) =< aux(202) s(2591) =< aux(202) s(2594) =< aux(197) s(2595) =< aux(197)-1 s(2596) =< aux(197)+1 s(2597) =< aux(197)+2 s(2588) =< aux(198)*(1/5)+aux(202) s(2589) =< aux(198)*(1/5)+aux(202) s(2590) =< aux(198)*(1/5)+aux(202) s(2591) =< aux(198)*(1/5)+aux(202) s(2589) =< aux(198)*(1/3)+aux(200) s(2590) =< aux(198)*(1/3)+aux(200) s(2591) =< aux(198)*(1/3)+aux(200) s(2593) =< aux(198)*(1/5)+aux(201) s(2592) =< aux(198)*(1/4)+aux(199) s(2593) =< aux(198)*(1/4)+aux(199) s(2598) =< s(2590)*s(2594) s(2599) =< s(2589)*s(2595) s(2600) =< s(2589)*s(2595) s(2601) =< s(2589)*s(2596) s(2602) =< s(2588)*s(2597) s(2603) =< s(2593)*s(2595) s(2604) =< s(2592)*s(2594) s(2605) =< s(2598) s(2606) =< s(2599) s(2607) =< s(2601) s(2608) =< s(2607)*s(2596) s(2609) =< s(2608) s(2610) =< s(2602) s(2611) =< s(2610)*s(2597) s(2612) =< s(2611) s(2613) =< s(2603) s(2614) =< s(2604) s(2615) =< s(2614)*aux(197) s(2616) =< s(2615) with precondition: [V5=2,Out=0,V1>=0,V>=0] * Chain [64]: 14*s(2768)+10*s(2769)+42*s(2770)+2*s(2771)+8*s(2772)+8*s(2773)+4*s(2780)+22*s(2785)+6*s(2786)+28*s(2787)+6*s(2789)+28*s(2790)+6*s(2792)+20*s(2793)+28*s(2794)+6*s(2796)+14*s(2804)+10*s(2805)+42*s(2806)+2*s(2807)+8*s(2808)+8*s(2809)+4*s(2816)+22*s(2821)+6*s(2822)+28*s(2823)+6*s(2825)+28*s(2826)+6*s(2828)+20*s(2829)+28*s(2830)+6*s(2832)+40*s(2834)+4 Such that:aux(210) =< 3 aux(211) =< V1 aux(212) =< 2*V1 aux(213) =< 2*V1+1 aux(214) =< V1/2 aux(215) =< 2/3*V1 aux(216) =< 3/5*V1 aux(217) =< 4/5*V1 aux(218) =< V aux(219) =< 2*V aux(220) =< 2*V+1 aux(221) =< V/2 aux(222) =< 2/3*V aux(223) =< 3/5*V aux(224) =< 4/5*V s(2834) =< aux(210) s(2804) =< aux(218) s(2805) =< aux(218) s(2806) =< aux(218) s(2807) =< aux(218) s(2808) =< aux(221) s(2805) =< aux(222) s(2809) =< aux(223) s(2804) =< aux(224) s(2805) =< aux(224) s(2807) =< aux(224) s(2810) =< aux(219) s(2811) =< aux(219)-1 s(2812) =< aux(219)+1 s(2813) =< aux(219)+2 s(2804) =< aux(220)*(1/5)+aux(224) s(2805) =< aux(220)*(1/5)+aux(224) s(2806) =< aux(220)*(1/5)+aux(224) s(2807) =< aux(220)*(1/5)+aux(224) s(2805) =< aux(220)*(1/3)+aux(222) s(2806) =< aux(220)*(1/3)+aux(222) s(2807) =< aux(220)*(1/3)+aux(222) s(2809) =< aux(220)*(1/5)+aux(223) s(2808) =< aux(220)*(1/4)+aux(221) s(2809) =< aux(220)*(1/4)+aux(221) s(2814) =< s(2806)*s(2810) s(2815) =< s(2805)*s(2811) s(2816) =< s(2805)*s(2811) s(2817) =< s(2805)*s(2812) s(2818) =< s(2804)*s(2813) s(2819) =< s(2809)*s(2811) s(2820) =< s(2808)*s(2810) s(2821) =< s(2814) s(2822) =< s(2815) s(2823) =< s(2817) s(2824) =< s(2823)*s(2812) s(2825) =< s(2824) s(2826) =< s(2818) s(2827) =< s(2826)*s(2813) s(2828) =< s(2827) s(2829) =< s(2819) s(2830) =< s(2820) s(2831) =< s(2830)*aux(219) s(2832) =< s(2831) s(2768) =< aux(211) s(2769) =< aux(211) s(2770) =< aux(211) s(2771) =< aux(211) s(2772) =< aux(214) s(2769) =< aux(215) s(2773) =< aux(216) s(2768) =< aux(217) s(2769) =< aux(217) s(2771) =< aux(217) s(2774) =< aux(212) s(2775) =< aux(212)-1 s(2776) =< aux(212)+1 s(2777) =< aux(212)+2 s(2768) =< aux(213)*(1/5)+aux(217) s(2769) =< aux(213)*(1/5)+aux(217) s(2770) =< aux(213)*(1/5)+aux(217) s(2771) =< aux(213)*(1/5)+aux(217) s(2769) =< aux(213)*(1/3)+aux(215) s(2770) =< aux(213)*(1/3)+aux(215) s(2771) =< aux(213)*(1/3)+aux(215) s(2773) =< aux(213)*(1/5)+aux(216) s(2772) =< aux(213)*(1/4)+aux(214) s(2773) =< aux(213)*(1/4)+aux(214) s(2778) =< s(2770)*s(2774) s(2779) =< s(2769)*s(2775) s(2780) =< s(2769)*s(2775) s(2781) =< s(2769)*s(2776) s(2782) =< s(2768)*s(2777) s(2783) =< s(2773)*s(2775) s(2784) =< s(2772)*s(2774) s(2785) =< s(2778) s(2786) =< s(2779) s(2787) =< s(2781) s(2788) =< s(2787)*s(2776) s(2789) =< s(2788) s(2790) =< s(2782) s(2791) =< s(2790)*s(2777) s(2792) =< s(2791) s(2793) =< s(2783) s(2794) =< s(2784) s(2795) =< s(2794)*aux(212) s(2796) =< s(2795) with precondition: [V5=2,Out=1,V1>=1,V>=0] * Chain [63]: 7*s(2920)+5*s(2921)+21*s(2922)+1*s(2923)+4*s(2924)+4*s(2925)+2*s(2932)+11*s(2937)+3*s(2938)+14*s(2939)+3*s(2941)+14*s(2942)+3*s(2944)+10*s(2945)+14*s(2946)+3*s(2948)+14*s(2956)+10*s(2957)+42*s(2958)+2*s(2959)+8*s(2960)+8*s(2961)+4*s(2968)+22*s(2973)+6*s(2974)+28*s(2975)+6*s(2977)+28*s(2978)+6*s(2980)+20*s(2981)+28*s(2982)+6*s(2984)+8*s(2987)+20*s(2988)+6*s(2990)+4 Such that:s(2913) =< V1 s(2914) =< 2*V1 s(2915) =< 2*V1+1 s(2916) =< V1/2 s(2917) =< 2/3*V1 s(2918) =< 3/5*V1 s(2919) =< 4/5*V1 aux(229) =< V aux(230) =< 2*V aux(231) =< 2*V+1 aux(232) =< V/2 aux(233) =< 2/3*V aux(234) =< 3/5*V aux(235) =< 4/5*V s(2987) =< aux(230) s(2988) =< aux(231) s(2989) =< s(2987)*aux(231) s(2990) =< s(2989) s(2956) =< aux(229) s(2957) =< aux(229) s(2958) =< aux(229) s(2959) =< aux(229) s(2960) =< aux(232) s(2957) =< aux(233) s(2961) =< aux(234) s(2956) =< aux(235) s(2957) =< aux(235) s(2959) =< aux(235) s(2962) =< aux(230) s(2963) =< aux(230)-1 s(2964) =< aux(230)+1 s(2965) =< aux(230)+2 s(2956) =< aux(231)*(1/5)+aux(235) s(2957) =< aux(231)*(1/5)+aux(235) s(2958) =< aux(231)*(1/5)+aux(235) s(2959) =< aux(231)*(1/5)+aux(235) s(2957) =< aux(231)*(1/3)+aux(233) s(2958) =< aux(231)*(1/3)+aux(233) s(2959) =< aux(231)*(1/3)+aux(233) s(2961) =< aux(231)*(1/5)+aux(234) s(2960) =< aux(231)*(1/4)+aux(232) s(2961) =< aux(231)*(1/4)+aux(232) s(2966) =< s(2958)*s(2962) s(2967) =< s(2957)*s(2963) s(2968) =< s(2957)*s(2963) s(2969) =< s(2957)*s(2964) s(2970) =< s(2956)*s(2965) s(2971) =< s(2961)*s(2963) s(2972) =< s(2960)*s(2962) s(2973) =< s(2966) s(2974) =< s(2967) s(2975) =< s(2969) s(2976) =< s(2975)*s(2964) s(2977) =< s(2976) s(2978) =< s(2970) s(2979) =< s(2978)*s(2965) s(2980) =< s(2979) s(2981) =< s(2971) s(2982) =< s(2972) s(2983) =< s(2982)*aux(230) s(2984) =< s(2983) s(2920) =< s(2913) s(2921) =< s(2913) s(2922) =< s(2913) s(2923) =< s(2913) s(2924) =< s(2916) s(2921) =< s(2917) s(2925) =< s(2918) s(2920) =< s(2919) s(2921) =< s(2919) s(2923) =< s(2919) s(2926) =< s(2914) s(2927) =< s(2914)-1 s(2928) =< s(2914)+1 s(2929) =< s(2914)+2 s(2920) =< s(2915)*(1/5)+s(2919) s(2921) =< s(2915)*(1/5)+s(2919) s(2922) =< s(2915)*(1/5)+s(2919) s(2923) =< s(2915)*(1/5)+s(2919) s(2921) =< s(2915)*(1/3)+s(2917) s(2922) =< s(2915)*(1/3)+s(2917) s(2923) =< s(2915)*(1/3)+s(2917) s(2925) =< s(2915)*(1/5)+s(2918) s(2924) =< s(2915)*(1/4)+s(2916) s(2925) =< s(2915)*(1/4)+s(2916) s(2930) =< s(2922)*s(2926) s(2931) =< s(2921)*s(2927) s(2932) =< s(2921)*s(2927) s(2933) =< s(2921)*s(2928) s(2934) =< s(2920)*s(2929) s(2935) =< s(2925)*s(2927) s(2936) =< s(2924)*s(2926) s(2937) =< s(2930) s(2938) =< s(2931) s(2939) =< s(2933) s(2940) =< s(2939)*s(2928) s(2941) =< s(2940) s(2942) =< s(2934) s(2943) =< s(2942)*s(2929) s(2944) =< s(2943) s(2945) =< s(2935) s(2946) =< s(2936) s(2947) =< s(2946)*s(2914) s(2948) =< s(2947) with precondition: [V5=2,V1>=1,Out>=2,2*V>=Out+1] * Chain [62]: 21*s(3040)+15*s(3041)+63*s(3042)+3*s(3043)+12*s(3044)+12*s(3045)+6*s(3052)+33*s(3057)+9*s(3058)+42*s(3059)+9*s(3061)+42*s(3062)+9*s(3064)+30*s(3065)+42*s(3066)+9*s(3068)+14*s(3076)+10*s(3077)+42*s(3078)+2*s(3079)+8*s(3080)+8*s(3081)+4*s(3088)+22*s(3093)+6*s(3094)+28*s(3095)+6*s(3097)+28*s(3098)+6*s(3100)+20*s(3101)+28*s(3102)+6*s(3104)+0 Such that:aux(236) =< V1 aux(237) =< 2*V1 aux(238) =< 2*V1+1 aux(239) =< V1/2 aux(240) =< 2/3*V1 aux(241) =< 3/5*V1 aux(242) =< 4/5*V1 aux(243) =< V5 aux(244) =< 2*V5 aux(245) =< 2*V5+1 aux(246) =< V5/2 aux(247) =< 2/3*V5 aux(248) =< 3/5*V5 aux(249) =< 4/5*V5 s(3076) =< aux(243) s(3077) =< aux(243) s(3078) =< aux(243) s(3079) =< aux(243) s(3080) =< aux(246) s(3077) =< aux(247) s(3081) =< aux(248) s(3076) =< aux(249) s(3077) =< aux(249) s(3079) =< aux(249) s(3082) =< aux(244) s(3083) =< aux(244)-1 s(3084) =< aux(244)+1 s(3085) =< aux(244)+2 s(3076) =< aux(245)*(1/5)+aux(249) s(3077) =< aux(245)*(1/5)+aux(249) s(3078) =< aux(245)*(1/5)+aux(249) s(3079) =< aux(245)*(1/5)+aux(249) s(3077) =< aux(245)*(1/3)+aux(247) s(3078) =< aux(245)*(1/3)+aux(247) s(3079) =< aux(245)*(1/3)+aux(247) s(3081) =< aux(245)*(1/5)+aux(248) s(3080) =< aux(245)*(1/4)+aux(246) s(3081) =< aux(245)*(1/4)+aux(246) s(3086) =< s(3078)*s(3082) s(3087) =< s(3077)*s(3083) s(3088) =< s(3077)*s(3083) s(3089) =< s(3077)*s(3084) s(3090) =< s(3076)*s(3085) s(3091) =< s(3081)*s(3083) s(3092) =< s(3080)*s(3082) s(3093) =< s(3086) s(3094) =< s(3087) s(3095) =< s(3089) s(3096) =< s(3095)*s(3084) s(3097) =< s(3096) s(3098) =< s(3090) s(3099) =< s(3098)*s(3085) s(3100) =< s(3099) s(3101) =< s(3091) s(3102) =< s(3092) s(3103) =< s(3102)*aux(244) s(3104) =< s(3103) s(3040) =< aux(236) s(3041) =< aux(236) s(3042) =< aux(236) s(3043) =< aux(236) s(3044) =< aux(239) s(3041) =< aux(240) s(3045) =< aux(241) s(3040) =< aux(242) s(3041) =< aux(242) s(3043) =< aux(242) s(3046) =< aux(237) s(3047) =< aux(237)-1 s(3048) =< aux(237)+1 s(3049) =< aux(237)+2 s(3040) =< aux(238)*(1/5)+aux(242) s(3041) =< aux(238)*(1/5)+aux(242) s(3042) =< aux(238)*(1/5)+aux(242) s(3043) =< aux(238)*(1/5)+aux(242) s(3041) =< aux(238)*(1/3)+aux(240) s(3042) =< aux(238)*(1/3)+aux(240) s(3043) =< aux(238)*(1/3)+aux(240) s(3045) =< aux(238)*(1/5)+aux(241) s(3044) =< aux(238)*(1/4)+aux(239) s(3045) =< aux(238)*(1/4)+aux(239) s(3050) =< s(3042)*s(3046) s(3051) =< s(3041)*s(3047) s(3052) =< s(3041)*s(3047) s(3053) =< s(3041)*s(3048) s(3054) =< s(3040)*s(3049) s(3055) =< s(3045)*s(3047) s(3056) =< s(3044)*s(3046) s(3057) =< s(3050) s(3058) =< s(3051) s(3059) =< s(3053) s(3060) =< s(3059)*s(3048) s(3061) =< s(3060) s(3062) =< s(3054) s(3063) =< s(3062)*s(3049) s(3064) =< s(3063) s(3065) =< s(3055) s(3066) =< s(3056) s(3067) =< s(3066)*aux(237) s(3068) =< s(3067) with precondition: [V=2,Out=0,V1>=0,V5>=0] * Chain [61]: 21*s(3220)+15*s(3221)+63*s(3222)+3*s(3223)+12*s(3224)+12*s(3225)+6*s(3232)+33*s(3237)+9*s(3238)+42*s(3239)+9*s(3241)+42*s(3242)+9*s(3244)+30*s(3245)+42*s(3246)+9*s(3248)+7*s(3256)+5*s(3257)+21*s(3258)+1*s(3259)+4*s(3260)+4*s(3261)+2*s(3268)+11*s(3273)+3*s(3274)+14*s(3275)+3*s(3277)+14*s(3278)+3*s(3280)+10*s(3281)+14*s(3282)+3*s(3284)+10*s(3286)+10*s(3324)+10*s(3362)+4 Such that:s(3361) =< 1 s(3323) =< 3 s(3249) =< V5 s(3250) =< 2*V5 aux(250) =< 2*V5+1 s(3252) =< V5/2 s(3253) =< 2/3*V5 s(3254) =< 3/5*V5 s(3255) =< 4/5*V5 aux(251) =< V1 aux(252) =< 2*V1 aux(253) =< 2*V1+1 aux(254) =< V1/2 aux(255) =< 2/3*V1 aux(256) =< 3/5*V1 aux(257) =< 4/5*V1 s(3362) =< s(3361) s(3220) =< aux(251) s(3221) =< aux(251) s(3222) =< aux(251) s(3223) =< aux(251) s(3224) =< aux(254) s(3221) =< aux(255) s(3225) =< aux(256) s(3220) =< aux(257) s(3221) =< aux(257) s(3223) =< aux(257) s(3226) =< aux(252) s(3227) =< aux(252)-1 s(3228) =< aux(252)+1 s(3229) =< aux(252)+2 s(3220) =< aux(253)*(1/5)+aux(257) s(3221) =< aux(253)*(1/5)+aux(257) s(3222) =< aux(253)*(1/5)+aux(257) s(3223) =< aux(253)*(1/5)+aux(257) s(3221) =< aux(253)*(1/3)+aux(255) s(3222) =< aux(253)*(1/3)+aux(255) s(3223) =< aux(253)*(1/3)+aux(255) s(3225) =< aux(253)*(1/5)+aux(256) s(3224) =< aux(253)*(1/4)+aux(254) s(3225) =< aux(253)*(1/4)+aux(254) s(3230) =< s(3222)*s(3226) s(3231) =< s(3221)*s(3227) s(3232) =< s(3221)*s(3227) s(3233) =< s(3221)*s(3228) s(3234) =< s(3220)*s(3229) s(3235) =< s(3225)*s(3227) s(3236) =< s(3224)*s(3226) s(3237) =< s(3230) s(3238) =< s(3231) s(3239) =< s(3233) s(3240) =< s(3239)*s(3228) s(3241) =< s(3240) s(3242) =< s(3234) s(3243) =< s(3242)*s(3229) s(3244) =< s(3243) s(3245) =< s(3235) s(3246) =< s(3236) s(3247) =< s(3246)*aux(252) s(3248) =< s(3247) s(3324) =< s(3323) s(3286) =< aux(250) s(3256) =< s(3249) s(3257) =< s(3249) s(3258) =< s(3249) s(3259) =< s(3249) s(3260) =< s(3252) s(3257) =< s(3253) s(3261) =< s(3254) s(3256) =< s(3255) s(3257) =< s(3255) s(3259) =< s(3255) s(3262) =< s(3250) s(3263) =< s(3250)-1 s(3264) =< s(3250)+1 s(3265) =< s(3250)+2 s(3256) =< aux(250)*(1/5)+s(3255) s(3257) =< aux(250)*(1/5)+s(3255) s(3258) =< aux(250)*(1/5)+s(3255) s(3259) =< aux(250)*(1/5)+s(3255) s(3257) =< aux(250)*(1/3)+s(3253) s(3258) =< aux(250)*(1/3)+s(3253) s(3259) =< aux(250)*(1/3)+s(3253) s(3261) =< aux(250)*(1/5)+s(3254) s(3260) =< aux(250)*(1/4)+s(3252) s(3261) =< aux(250)*(1/4)+s(3252) s(3266) =< s(3258)*s(3262) s(3267) =< s(3257)*s(3263) s(3268) =< s(3257)*s(3263) s(3269) =< s(3257)*s(3264) s(3270) =< s(3256)*s(3265) s(3271) =< s(3261)*s(3263) s(3272) =< s(3260)*s(3262) s(3273) =< s(3266) s(3274) =< s(3267) s(3275) =< s(3269) s(3276) =< s(3275)*s(3264) s(3277) =< s(3276) s(3278) =< s(3270) s(3279) =< s(3278)*s(3265) s(3280) =< s(3279) s(3281) =< s(3271) s(3282) =< s(3272) s(3283) =< s(3282)*s(3250) s(3284) =< s(3283) with precondition: [V=2,Out=1,V1>=1,V5>=0] * Chain [60]: 14*s(3370)+10*s(3371)+42*s(3372)+2*s(3373)+8*s(3374)+8*s(3375)+4*s(3382)+22*s(3387)+6*s(3388)+28*s(3389)+6*s(3391)+28*s(3392)+6*s(3394)+20*s(3395)+28*s(3396)+6*s(3398)+7*s(3406)+5*s(3407)+21*s(3408)+1*s(3409)+4*s(3410)+4*s(3411)+2*s(3418)+11*s(3423)+3*s(3424)+14*s(3425)+3*s(3427)+14*s(3428)+3*s(3430)+10*s(3431)+14*s(3432)+3*s(3434)+8*s(3437)+20*s(3438)+6*s(3440)+4 Such that:s(3399) =< V5 s(3400) =< 2*V5 s(3401) =< 2*V5+1 s(3402) =< V5/2 s(3403) =< 2/3*V5 s(3404) =< 3/5*V5 s(3405) =< 4/5*V5 aux(260) =< 2 aux(261) =< 3 aux(262) =< V1 aux(263) =< 2*V1 aux(264) =< 2*V1+1 aux(265) =< V1/2 aux(266) =< 2/3*V1 aux(267) =< 3/5*V1 aux(268) =< 4/5*V1 s(3437) =< aux(260) s(3438) =< aux(261) s(3439) =< s(3437)*aux(261) s(3440) =< s(3439) s(3406) =< s(3399) s(3407) =< s(3399) s(3408) =< s(3399) s(3409) =< s(3399) s(3410) =< s(3402) s(3407) =< s(3403) s(3411) =< s(3404) s(3406) =< s(3405) s(3407) =< s(3405) s(3409) =< s(3405) s(3412) =< s(3400) s(3413) =< s(3400)-1 s(3414) =< s(3400)+1 s(3415) =< s(3400)+2 s(3406) =< s(3401)*(1/5)+s(3405) s(3407) =< s(3401)*(1/5)+s(3405) s(3408) =< s(3401)*(1/5)+s(3405) s(3409) =< s(3401)*(1/5)+s(3405) s(3407) =< s(3401)*(1/3)+s(3403) s(3408) =< s(3401)*(1/3)+s(3403) s(3409) =< s(3401)*(1/3)+s(3403) s(3411) =< s(3401)*(1/5)+s(3404) s(3410) =< s(3401)*(1/4)+s(3402) s(3411) =< s(3401)*(1/4)+s(3402) s(3416) =< s(3408)*s(3412) s(3417) =< s(3407)*s(3413) s(3418) =< s(3407)*s(3413) s(3419) =< s(3407)*s(3414) s(3420) =< s(3406)*s(3415) s(3421) =< s(3411)*s(3413) s(3422) =< s(3410)*s(3412) s(3423) =< s(3416) s(3424) =< s(3417) s(3425) =< s(3419) s(3426) =< s(3425)*s(3414) s(3427) =< s(3426) s(3428) =< s(3420) s(3429) =< s(3428)*s(3415) s(3430) =< s(3429) s(3431) =< s(3421) s(3432) =< s(3422) s(3433) =< s(3432)*s(3400) s(3434) =< s(3433) s(3370) =< aux(262) s(3371) =< aux(262) s(3372) =< aux(262) s(3373) =< aux(262) s(3374) =< aux(265) s(3371) =< aux(266) s(3375) =< aux(267) s(3370) =< aux(268) s(3371) =< aux(268) s(3373) =< aux(268) s(3376) =< aux(263) s(3377) =< aux(263)-1 s(3378) =< aux(263)+1 s(3379) =< aux(263)+2 s(3370) =< aux(264)*(1/5)+aux(268) s(3371) =< aux(264)*(1/5)+aux(268) s(3372) =< aux(264)*(1/5)+aux(268) s(3373) =< aux(264)*(1/5)+aux(268) s(3371) =< aux(264)*(1/3)+aux(266) s(3372) =< aux(264)*(1/3)+aux(266) s(3373) =< aux(264)*(1/3)+aux(266) s(3375) =< aux(264)*(1/5)+aux(267) s(3374) =< aux(264)*(1/4)+aux(265) s(3375) =< aux(264)*(1/4)+aux(265) s(3380) =< s(3372)*s(3376) s(3381) =< s(3371)*s(3377) s(3382) =< s(3371)*s(3377) s(3383) =< s(3371)*s(3378) s(3384) =< s(3370)*s(3379) s(3385) =< s(3375)*s(3377) s(3386) =< s(3374)*s(3376) s(3387) =< s(3380) s(3388) =< s(3381) s(3389) =< s(3383) s(3390) =< s(3389)*s(3378) s(3391) =< s(3390) s(3392) =< s(3384) s(3393) =< s(3392)*s(3379) s(3394) =< s(3393) s(3395) =< s(3385) s(3396) =< s(3386) s(3397) =< s(3396)*aux(263) s(3398) =< s(3397) with precondition: [V=2,3>=Out,V1>=1,V5>=0,Out>=2] #### Cost of chains of fun2(V1,V,Out): * Chain [74]: 14*s(4056)+10*s(4057)+42*s(4058)+2*s(4059)+8*s(4060)+8*s(4061)+4*s(4068)+22*s(4073)+6*s(4074)+28*s(4075)+6*s(4077)+28*s(4078)+6*s(4080)+20*s(4081)+28*s(4082)+6*s(4084)+21*s(4092)+15*s(4093)+63*s(4094)+3*s(4095)+12*s(4096)+12*s(4097)+6*s(4104)+33*s(4109)+9*s(4110)+42*s(4111)+9*s(4113)+42*s(4114)+9*s(4116)+30*s(4117)+42*s(4118)+9*s(4120)+3*s(4121)+1*s(4196)+0 Such that:s(4196) =< 2 aux(318) =< V1 aux(319) =< 2*V1 aux(320) =< 2*V1+1 aux(321) =< V1/2 aux(322) =< 2/3*V1 aux(323) =< 3/5*V1 aux(324) =< 4/5*V1 aux(325) =< V aux(326) =< 2*V aux(327) =< 2*V+1 aux(328) =< V/2 aux(329) =< 2/3*V aux(330) =< 3/5*V aux(331) =< 4/5*V s(4121) =< aux(326) s(4092) =< aux(325) s(4093) =< aux(325) s(4094) =< aux(325) s(4095) =< aux(325) s(4096) =< aux(328) s(4093) =< aux(329) s(4097) =< aux(330) s(4092) =< aux(331) s(4093) =< aux(331) s(4095) =< aux(331) s(4098) =< aux(326) s(4099) =< aux(326)-1 s(4100) =< aux(326)+1 s(4101) =< aux(326)+2 s(4092) =< aux(327)*(1/5)+aux(331) s(4093) =< aux(327)*(1/5)+aux(331) s(4094) =< aux(327)*(1/5)+aux(331) s(4095) =< aux(327)*(1/5)+aux(331) s(4093) =< aux(327)*(1/3)+aux(329) s(4094) =< aux(327)*(1/3)+aux(329) s(4095) =< aux(327)*(1/3)+aux(329) s(4097) =< aux(327)*(1/5)+aux(330) s(4096) =< aux(327)*(1/4)+aux(328) s(4097) =< aux(327)*(1/4)+aux(328) s(4102) =< s(4094)*s(4098) s(4103) =< s(4093)*s(4099) s(4104) =< s(4093)*s(4099) s(4105) =< s(4093)*s(4100) s(4106) =< s(4092)*s(4101) s(4107) =< s(4097)*s(4099) s(4108) =< s(4096)*s(4098) s(4109) =< s(4102) s(4110) =< s(4103) s(4111) =< s(4105) s(4112) =< s(4111)*s(4100) s(4113) =< s(4112) s(4114) =< s(4106) s(4115) =< s(4114)*s(4101) s(4116) =< s(4115) s(4117) =< s(4107) s(4118) =< s(4108) s(4119) =< s(4118)*aux(326) s(4120) =< s(4119) s(4056) =< aux(318) s(4057) =< aux(318) s(4058) =< aux(318) s(4059) =< aux(318) s(4060) =< aux(321) s(4057) =< aux(322) s(4061) =< aux(323) s(4056) =< aux(324) s(4057) =< aux(324) s(4059) =< aux(324) s(4062) =< aux(319) s(4063) =< aux(319)-1 s(4064) =< aux(319)+1 s(4065) =< aux(319)+2 s(4056) =< aux(320)*(1/5)+aux(324) s(4057) =< aux(320)*(1/5)+aux(324) s(4058) =< aux(320)*(1/5)+aux(324) s(4059) =< aux(320)*(1/5)+aux(324) s(4057) =< aux(320)*(1/3)+aux(322) s(4058) =< aux(320)*(1/3)+aux(322) s(4059) =< aux(320)*(1/3)+aux(322) s(4061) =< aux(320)*(1/5)+aux(323) s(4060) =< aux(320)*(1/4)+aux(321) s(4061) =< aux(320)*(1/4)+aux(321) s(4066) =< s(4058)*s(4062) s(4067) =< s(4057)*s(4063) s(4068) =< s(4057)*s(4063) s(4069) =< s(4057)*s(4064) s(4070) =< s(4056)*s(4065) s(4071) =< s(4061)*s(4063) s(4072) =< s(4060)*s(4062) s(4073) =< s(4066) s(4074) =< s(4067) s(4075) =< s(4069) s(4076) =< s(4075)*s(4064) s(4077) =< s(4076) s(4078) =< s(4070) s(4079) =< s(4078)*s(4065) s(4080) =< s(4079) s(4081) =< s(4071) s(4082) =< s(4072) s(4083) =< s(4082)*aux(319) s(4084) =< s(4083) with precondition: [Out=0,V1>=0,V>=0] * Chain [73]: 21*s(4243)+15*s(4244)+63*s(4245)+3*s(4246)+12*s(4247)+12*s(4248)+6*s(4255)+33*s(4260)+9*s(4261)+42*s(4262)+9*s(4264)+42*s(4265)+9*s(4267)+30*s(4268)+42*s(4269)+9*s(4271)+28*s(4279)+20*s(4280)+84*s(4281)+4*s(4282)+16*s(4283)+16*s(4284)+8*s(4291)+44*s(4296)+12*s(4297)+56*s(4298)+12*s(4300)+56*s(4301)+12*s(4303)+40*s(4304)+56*s(4305)+12*s(4307)+1*s(4380)+2*s(4453)+1 Such that:aux(333) =< 2 aux(334) =< V1 aux(335) =< 2*V1 aux(336) =< 2*V1+1 aux(337) =< V1/2 aux(338) =< 2/3*V1 aux(339) =< 3/5*V1 aux(340) =< 4/5*V1 aux(341) =< V aux(342) =< 2*V aux(343) =< 2*V+1 aux(344) =< V/2 aux(345) =< 2/3*V aux(346) =< 3/5*V aux(347) =< 4/5*V s(4453) =< aux(333) s(4279) =< aux(341) s(4280) =< aux(341) s(4281) =< aux(341) s(4282) =< aux(341) s(4283) =< aux(344) s(4280) =< aux(345) s(4284) =< aux(346) s(4279) =< aux(347) s(4280) =< aux(347) s(4282) =< aux(347) s(4285) =< aux(342) s(4286) =< aux(342)-1 s(4287) =< aux(342)+1 s(4288) =< aux(342)+2 s(4279) =< aux(343)*(1/5)+aux(347) s(4280) =< aux(343)*(1/5)+aux(347) s(4281) =< aux(343)*(1/5)+aux(347) s(4282) =< aux(343)*(1/5)+aux(347) s(4280) =< aux(343)*(1/3)+aux(345) s(4281) =< aux(343)*(1/3)+aux(345) s(4282) =< aux(343)*(1/3)+aux(345) s(4284) =< aux(343)*(1/5)+aux(346) s(4283) =< aux(343)*(1/4)+aux(344) s(4284) =< aux(343)*(1/4)+aux(344) s(4289) =< s(4281)*s(4285) s(4290) =< s(4280)*s(4286) s(4291) =< s(4280)*s(4286) s(4292) =< s(4280)*s(4287) s(4293) =< s(4279)*s(4288) s(4294) =< s(4284)*s(4286) s(4295) =< s(4283)*s(4285) s(4296) =< s(4289) s(4297) =< s(4290) s(4298) =< s(4292) s(4299) =< s(4298)*s(4287) s(4300) =< s(4299) s(4301) =< s(4293) s(4302) =< s(4301)*s(4288) s(4303) =< s(4302) s(4304) =< s(4294) s(4305) =< s(4295) s(4306) =< s(4305)*aux(342) s(4307) =< s(4306) s(4243) =< aux(334) s(4244) =< aux(334) s(4245) =< aux(334) s(4246) =< aux(334) s(4247) =< aux(337) s(4244) =< aux(338) s(4248) =< aux(339) s(4243) =< aux(340) s(4244) =< aux(340) s(4246) =< aux(340) s(4249) =< aux(335) s(4250) =< aux(335)-1 s(4251) =< aux(335)+1 s(4252) =< aux(335)+2 s(4243) =< aux(336)*(1/5)+aux(340) s(4244) =< aux(336)*(1/5)+aux(340) s(4245) =< aux(336)*(1/5)+aux(340) s(4246) =< aux(336)*(1/5)+aux(340) s(4244) =< aux(336)*(1/3)+aux(338) s(4245) =< aux(336)*(1/3)+aux(338) s(4246) =< aux(336)*(1/3)+aux(338) s(4248) =< aux(336)*(1/5)+aux(339) s(4247) =< aux(336)*(1/4)+aux(337) s(4248) =< aux(336)*(1/4)+aux(337) s(4253) =< s(4245)*s(4249) s(4254) =< s(4244)*s(4250) s(4255) =< s(4244)*s(4250) s(4256) =< s(4244)*s(4251) s(4257) =< s(4243)*s(4252) s(4258) =< s(4248)*s(4250) s(4259) =< s(4247)*s(4249) s(4260) =< s(4253) s(4261) =< s(4254) s(4262) =< s(4256) s(4263) =< s(4262)*s(4251) s(4264) =< s(4263) s(4265) =< s(4257) s(4266) =< s(4265)*s(4252) s(4267) =< s(4266) s(4268) =< s(4258) s(4269) =< s(4259) s(4270) =< s(4269)*aux(335) s(4271) =< s(4270) s(4380) =< aux(342) with precondition: [Out=2,V1>=0,V>=0] * Chain [72]: 35*s(4498)+25*s(4499)+105*s(4500)+5*s(4501)+20*s(4502)+20*s(4503)+10*s(4510)+55*s(4515)+15*s(4516)+70*s(4517)+15*s(4519)+70*s(4520)+15*s(4522)+50*s(4523)+70*s(4524)+15*s(4526)+49*s(4534)+35*s(4535)+147*s(4536)+7*s(4537)+28*s(4538)+28*s(4539)+14*s(4546)+77*s(4551)+21*s(4552)+98*s(4553)+21*s(4555)+98*s(4556)+21*s(4558)+70*s(4559)+98*s(4560)+21*s(4562)+1*s(4707)+1*s(4780)+1*s(4889)+1*s(4926)+1 Such that:s(4926) =< 1 s(4889) =< 2 aux(350) =< V1 aux(351) =< 2*V1 aux(352) =< 2*V1+1 aux(353) =< V1/2 aux(354) =< 2/3*V1 aux(355) =< 3/5*V1 aux(356) =< 4/5*V1 aux(357) =< V aux(358) =< 2*V aux(359) =< 2*V+1 aux(360) =< V/2 aux(361) =< 2/3*V aux(362) =< 3/5*V aux(363) =< 4/5*V s(4534) =< aux(357) s(4535) =< aux(357) s(4536) =< aux(357) s(4537) =< aux(357) s(4538) =< aux(360) s(4535) =< aux(361) s(4539) =< aux(362) s(4534) =< aux(363) s(4535) =< aux(363) s(4537) =< aux(363) s(4540) =< aux(358) s(4541) =< aux(358)-1 s(4542) =< aux(358)+1 s(4543) =< aux(358)+2 s(4534) =< aux(359)*(1/5)+aux(363) s(4535) =< aux(359)*(1/5)+aux(363) s(4536) =< aux(359)*(1/5)+aux(363) s(4537) =< aux(359)*(1/5)+aux(363) s(4535) =< aux(359)*(1/3)+aux(361) s(4536) =< aux(359)*(1/3)+aux(361) s(4537) =< aux(359)*(1/3)+aux(361) s(4539) =< aux(359)*(1/5)+aux(362) s(4538) =< aux(359)*(1/4)+aux(360) s(4539) =< aux(359)*(1/4)+aux(360) s(4544) =< s(4536)*s(4540) s(4545) =< s(4535)*s(4541) s(4546) =< s(4535)*s(4541) s(4547) =< s(4535)*s(4542) s(4548) =< s(4534)*s(4543) s(4549) =< s(4539)*s(4541) s(4550) =< s(4538)*s(4540) s(4551) =< s(4544) s(4552) =< s(4545) s(4553) =< s(4547) s(4554) =< s(4553)*s(4542) s(4555) =< s(4554) s(4556) =< s(4548) s(4557) =< s(4556)*s(4543) s(4558) =< s(4557) s(4559) =< s(4549) s(4560) =< s(4550) s(4561) =< s(4560)*aux(358) s(4562) =< s(4561) s(4498) =< aux(350) s(4499) =< aux(350) s(4500) =< aux(350) s(4501) =< aux(350) s(4502) =< aux(353) s(4499) =< aux(354) s(4503) =< aux(355) s(4498) =< aux(356) s(4499) =< aux(356) s(4501) =< aux(356) s(4504) =< aux(351) s(4505) =< aux(351)-1 s(4506) =< aux(351)+1 s(4507) =< aux(351)+2 s(4498) =< aux(352)*(1/5)+aux(356) s(4499) =< aux(352)*(1/5)+aux(356) s(4500) =< aux(352)*(1/5)+aux(356) s(4501) =< aux(352)*(1/5)+aux(356) s(4499) =< aux(352)*(1/3)+aux(354) s(4500) =< aux(352)*(1/3)+aux(354) s(4501) =< aux(352)*(1/3)+aux(354) s(4503) =< aux(352)*(1/5)+aux(355) s(4502) =< aux(352)*(1/4)+aux(353) s(4503) =< aux(352)*(1/4)+aux(353) s(4508) =< s(4500)*s(4504) s(4509) =< s(4499)*s(4505) s(4510) =< s(4499)*s(4505) s(4511) =< s(4499)*s(4506) s(4512) =< s(4498)*s(4507) s(4513) =< s(4503)*s(4505) s(4514) =< s(4502)*s(4504) s(4515) =< s(4508) s(4516) =< s(4509) s(4517) =< s(4511) s(4518) =< s(4517)*s(4506) s(4519) =< s(4518) s(4520) =< s(4512) s(4521) =< s(4520)*s(4507) s(4522) =< s(4521) s(4523) =< s(4513) s(4524) =< s(4514) s(4525) =< s(4524)*aux(351) s(4526) =< s(4525) s(4707) =< aux(358) s(4780) =< aux(351) with precondition: [Out=1,V1>=1,V>=0] * Chain [71]: 7*s(4934)+5*s(4935)+21*s(4936)+1*s(4937)+4*s(4938)+4*s(4939)+2*s(4946)+11*s(4951)+3*s(4952)+14*s(4953)+3*s(4955)+14*s(4956)+3*s(4958)+10*s(4959)+14*s(4960)+3*s(4962)+2*s(4963)+0 Such that:s(4927) =< V1 s(4928) =< 2*V1 s(4929) =< 2*V1+1 s(4930) =< V1/2 s(4931) =< 2/3*V1 s(4932) =< 3/5*V1 s(4933) =< 4/5*V1 aux(364) =< 2 s(4963) =< aux(364) s(4934) =< s(4927) s(4935) =< s(4927) s(4936) =< s(4927) s(4937) =< s(4927) s(4938) =< s(4930) s(4935) =< s(4931) s(4939) =< s(4932) s(4934) =< s(4933) s(4935) =< s(4933) s(4937) =< s(4933) s(4940) =< s(4928) s(4941) =< s(4928)-1 s(4942) =< s(4928)+1 s(4943) =< s(4928)+2 s(4934) =< s(4929)*(1/5)+s(4933) s(4935) =< s(4929)*(1/5)+s(4933) s(4936) =< s(4929)*(1/5)+s(4933) s(4937) =< s(4929)*(1/5)+s(4933) s(4935) =< s(4929)*(1/3)+s(4931) s(4936) =< s(4929)*(1/3)+s(4931) s(4937) =< s(4929)*(1/3)+s(4931) s(4939) =< s(4929)*(1/5)+s(4932) s(4938) =< s(4929)*(1/4)+s(4930) s(4939) =< s(4929)*(1/4)+s(4930) s(4944) =< s(4936)*s(4940) s(4945) =< s(4935)*s(4941) s(4946) =< s(4935)*s(4941) s(4947) =< s(4935)*s(4942) s(4948) =< s(4934)*s(4943) s(4949) =< s(4939)*s(4941) s(4950) =< s(4938)*s(4940) s(4951) =< s(4944) s(4952) =< s(4945) s(4953) =< s(4947) s(4954) =< s(4953)*s(4942) s(4955) =< s(4954) s(4956) =< s(4948) s(4957) =< s(4956)*s(4943) s(4958) =< s(4957) s(4959) =< s(4949) s(4960) =< s(4950) s(4961) =< s(4960)*s(4928) s(4962) =< s(4961) with precondition: [V=2,Out=0,V1>=0] * Chain [70]: 21*s(4972)+15*s(4973)+63*s(4974)+3*s(4975)+12*s(4976)+12*s(4977)+6*s(4984)+33*s(4989)+9*s(4990)+42*s(4991)+9*s(4993)+42*s(4994)+9*s(4996)+30*s(4997)+42*s(4998)+9*s(5000)+1*s(5037)+1*s(5074)+7*s(5082)+5*s(5083)+21*s(5084)+1*s(5085)+4*s(5086)+4*s(5087)+2*s(5094)+11*s(5099)+3*s(5100)+14*s(5101)+3*s(5103)+14*s(5104)+3*s(5106)+10*s(5107)+14*s(5108)+3*s(5110)+1 Such that:s(5037) =< 1 s(5074) =< 2 s(5075) =< V s(5076) =< 2*V s(5077) =< 2*V+1 s(5078) =< V/2 s(5079) =< 2/3*V s(5080) =< 3/5*V s(5081) =< 4/5*V aux(365) =< V1 aux(366) =< 2*V1 aux(367) =< 2*V1+1 aux(368) =< V1/2 aux(369) =< 2/3*V1 aux(370) =< 3/5*V1 aux(371) =< 4/5*V1 s(4972) =< aux(365) s(4973) =< aux(365) s(4974) =< aux(365) s(4975) =< aux(365) s(4976) =< aux(368) s(4973) =< aux(369) s(4977) =< aux(370) s(4972) =< aux(371) s(4973) =< aux(371) s(4975) =< aux(371) s(4978) =< aux(366) s(4979) =< aux(366)-1 s(4980) =< aux(366)+1 s(4981) =< aux(366)+2 s(4972) =< aux(367)*(1/5)+aux(371) s(4973) =< aux(367)*(1/5)+aux(371) s(4974) =< aux(367)*(1/5)+aux(371) s(4975) =< aux(367)*(1/5)+aux(371) s(4973) =< aux(367)*(1/3)+aux(369) s(4974) =< aux(367)*(1/3)+aux(369) s(4975) =< aux(367)*(1/3)+aux(369) s(4977) =< aux(367)*(1/5)+aux(370) s(4976) =< aux(367)*(1/4)+aux(368) s(4977) =< aux(367)*(1/4)+aux(368) s(4982) =< s(4974)*s(4978) s(4983) =< s(4973)*s(4979) s(4984) =< s(4973)*s(4979) s(4985) =< s(4973)*s(4980) s(4986) =< s(4972)*s(4981) s(4987) =< s(4977)*s(4979) s(4988) =< s(4976)*s(4978) s(4989) =< s(4982) s(4990) =< s(4983) s(4991) =< s(4985) s(4992) =< s(4991)*s(4980) s(4993) =< s(4992) s(4994) =< s(4986) s(4995) =< s(4994)*s(4981) s(4996) =< s(4995) s(4997) =< s(4987) s(4998) =< s(4988) s(4999) =< s(4998)*aux(366) s(5000) =< s(4999) s(5082) =< s(5075) s(5083) =< s(5075) s(5084) =< s(5075) s(5085) =< s(5075) s(5086) =< s(5078) s(5083) =< s(5079) s(5087) =< s(5080) s(5082) =< s(5081) s(5083) =< s(5081) s(5085) =< s(5081) s(5088) =< s(5076) s(5089) =< s(5076)-1 s(5090) =< s(5076)+1 s(5091) =< s(5076)+2 s(5082) =< s(5077)*(1/5)+s(5081) s(5083) =< s(5077)*(1/5)+s(5081) s(5084) =< s(5077)*(1/5)+s(5081) s(5085) =< s(5077)*(1/5)+s(5081) s(5083) =< s(5077)*(1/3)+s(5079) s(5084) =< s(5077)*(1/3)+s(5079) s(5085) =< s(5077)*(1/3)+s(5079) s(5087) =< s(5077)*(1/5)+s(5080) s(5086) =< s(5077)*(1/4)+s(5078) s(5087) =< s(5077)*(1/4)+s(5078) s(5092) =< s(5084)*s(5088) s(5093) =< s(5083)*s(5089) s(5094) =< s(5083)*s(5089) s(5095) =< s(5083)*s(5090) s(5096) =< s(5082)*s(5091) s(5097) =< s(5087)*s(5089) s(5098) =< s(5086)*s(5088) s(5099) =< s(5092) s(5100) =< s(5093) s(5101) =< s(5095) s(5102) =< s(5101)*s(5090) s(5103) =< s(5102) s(5104) =< s(5096) s(5105) =< s(5104)*s(5091) s(5106) =< s(5105) s(5107) =< s(5097) s(5108) =< s(5098) s(5109) =< s(5108)*s(5076) s(5110) =< s(5109) with precondition: [Out=1,V1>=0,V>=1] * Chain [69]: 7*s(5118)+5*s(5119)+21*s(5120)+1*s(5121)+4*s(5122)+4*s(5123)+2*s(5130)+11*s(5135)+3*s(5136)+14*s(5137)+3*s(5139)+14*s(5140)+3*s(5142)+10*s(5143)+14*s(5144)+3*s(5146)+1*s(5147)+1 Such that:s(5147) =< 2 s(5111) =< V1 s(5112) =< 2*V1 s(5113) =< 2*V1+1 s(5114) =< V1/2 s(5115) =< 2/3*V1 s(5116) =< 3/5*V1 s(5117) =< 4/5*V1 s(5118) =< s(5111) s(5119) =< s(5111) s(5120) =< s(5111) s(5121) =< s(5111) s(5122) =< s(5114) s(5119) =< s(5115) s(5123) =< s(5116) s(5118) =< s(5117) s(5119) =< s(5117) s(5121) =< s(5117) s(5124) =< s(5112) s(5125) =< s(5112)-1 s(5126) =< s(5112)+1 s(5127) =< s(5112)+2 s(5118) =< s(5113)*(1/5)+s(5117) s(5119) =< s(5113)*(1/5)+s(5117) s(5120) =< s(5113)*(1/5)+s(5117) s(5121) =< s(5113)*(1/5)+s(5117) s(5119) =< s(5113)*(1/3)+s(5115) s(5120) =< s(5113)*(1/3)+s(5115) s(5121) =< s(5113)*(1/3)+s(5115) s(5123) =< s(5113)*(1/5)+s(5116) s(5122) =< s(5113)*(1/4)+s(5114) s(5123) =< s(5113)*(1/4)+s(5114) s(5128) =< s(5120)*s(5124) s(5129) =< s(5119)*s(5125) s(5130) =< s(5119)*s(5125) s(5131) =< s(5119)*s(5126) s(5132) =< s(5118)*s(5127) s(5133) =< s(5123)*s(5125) s(5134) =< s(5122)*s(5124) s(5135) =< s(5128) s(5136) =< s(5129) s(5137) =< s(5131) s(5138) =< s(5137)*s(5126) s(5139) =< s(5138) s(5140) =< s(5132) s(5141) =< s(5140)*s(5127) s(5142) =< s(5141) s(5143) =< s(5133) s(5144) =< s(5134) s(5145) =< s(5144)*s(5112) s(5146) =< s(5145) with precondition: [V=2,Out=2,V1>=1] #### Cost of chains of fun3(V1,V,Out): * Chain [78]: 14*s(5379)+10*s(5380)+42*s(5381)+2*s(5382)+8*s(5383)+8*s(5384)+4*s(5391)+22*s(5396)+6*s(5397)+28*s(5398)+6*s(5400)+28*s(5401)+6*s(5403)+20*s(5404)+28*s(5405)+6*s(5407)+21*s(5415)+15*s(5416)+63*s(5417)+3*s(5418)+12*s(5419)+12*s(5420)+6*s(5427)+33*s(5432)+9*s(5433)+42*s(5434)+9*s(5436)+42*s(5437)+9*s(5439)+30*s(5440)+42*s(5441)+9*s(5443)+1 Such that:aux(388) =< V1 aux(389) =< 2*V1 aux(390) =< 2*V1+1 aux(391) =< V1/2 aux(392) =< 2/3*V1 aux(393) =< 3/5*V1 aux(394) =< 4/5*V1 aux(395) =< V aux(396) =< 2*V aux(397) =< 2*V+1 aux(398) =< V/2 aux(399) =< 2/3*V aux(400) =< 3/5*V aux(401) =< 4/5*V s(5415) =< aux(395) s(5416) =< aux(395) s(5417) =< aux(395) s(5418) =< aux(395) s(5419) =< aux(398) s(5416) =< aux(399) s(5420) =< aux(400) s(5415) =< aux(401) s(5416) =< aux(401) s(5418) =< aux(401) s(5421) =< aux(396) s(5422) =< aux(396)-1 s(5423) =< aux(396)+1 s(5424) =< aux(396)+2 s(5415) =< aux(397)*(1/5)+aux(401) s(5416) =< aux(397)*(1/5)+aux(401) s(5417) =< aux(397)*(1/5)+aux(401) s(5418) =< aux(397)*(1/5)+aux(401) s(5416) =< aux(397)*(1/3)+aux(399) s(5417) =< aux(397)*(1/3)+aux(399) s(5418) =< aux(397)*(1/3)+aux(399) s(5420) =< aux(397)*(1/5)+aux(400) s(5419) =< aux(397)*(1/4)+aux(398) s(5420) =< aux(397)*(1/4)+aux(398) s(5425) =< s(5417)*s(5421) s(5426) =< s(5416)*s(5422) s(5427) =< s(5416)*s(5422) s(5428) =< s(5416)*s(5423) s(5429) =< s(5415)*s(5424) s(5430) =< s(5420)*s(5422) s(5431) =< s(5419)*s(5421) s(5432) =< s(5425) s(5433) =< s(5426) s(5434) =< s(5428) s(5435) =< s(5434)*s(5423) s(5436) =< s(5435) s(5437) =< s(5429) s(5438) =< s(5437)*s(5424) s(5439) =< s(5438) s(5440) =< s(5430) s(5441) =< s(5431) s(5442) =< s(5441)*aux(396) s(5443) =< s(5442) s(5379) =< aux(388) s(5380) =< aux(388) s(5381) =< aux(388) s(5382) =< aux(388) s(5383) =< aux(391) s(5380) =< aux(392) s(5384) =< aux(393) s(5379) =< aux(394) s(5380) =< aux(394) s(5382) =< aux(394) s(5385) =< aux(389) s(5386) =< aux(389)-1 s(5387) =< aux(389)+1 s(5388) =< aux(389)+2 s(5379) =< aux(390)*(1/5)+aux(394) s(5380) =< aux(390)*(1/5)+aux(394) s(5381) =< aux(390)*(1/5)+aux(394) s(5382) =< aux(390)*(1/5)+aux(394) s(5380) =< aux(390)*(1/3)+aux(392) s(5381) =< aux(390)*(1/3)+aux(392) s(5382) =< aux(390)*(1/3)+aux(392) s(5384) =< aux(390)*(1/5)+aux(393) s(5383) =< aux(390)*(1/4)+aux(391) s(5384) =< aux(390)*(1/4)+aux(391) s(5389) =< s(5381)*s(5385) s(5390) =< s(5380)*s(5386) s(5391) =< s(5380)*s(5386) s(5392) =< s(5380)*s(5387) s(5393) =< s(5379)*s(5388) s(5394) =< s(5384)*s(5386) s(5395) =< s(5383)*s(5385) s(5396) =< s(5389) s(5397) =< s(5390) s(5398) =< s(5392) s(5399) =< s(5398)*s(5387) s(5400) =< s(5399) s(5401) =< s(5393) s(5402) =< s(5401)*s(5388) s(5403) =< s(5402) s(5404) =< s(5394) s(5405) =< s(5395) s(5406) =< s(5405)*aux(389) s(5407) =< s(5406) with precondition: [Out=0,V1>=0,V>=0] * Chain [77]: 7*s(5559)+5*s(5560)+21*s(5561)+1*s(5562)+4*s(5563)+4*s(5564)+2*s(5571)+11*s(5576)+3*s(5577)+14*s(5578)+3*s(5580)+14*s(5581)+3*s(5583)+10*s(5584)+14*s(5585)+3*s(5587)+14*s(5595)+10*s(5596)+42*s(5597)+2*s(5598)+8*s(5599)+8*s(5600)+4*s(5607)+22*s(5612)+6*s(5613)+28*s(5614)+6*s(5616)+28*s(5617)+6*s(5619)+20*s(5620)+28*s(5621)+6*s(5623)+2*s(5625)+4*s(5663)+1 Such that:s(5552) =< V1 s(5553) =< 2*V1 s(5554) =< 2*V1+1 s(5555) =< V1/2 s(5556) =< 2/3*V1 s(5557) =< 3/5*V1 s(5558) =< 4/5*V1 aux(403) =< 2 aux(404) =< V aux(405) =< 2*V aux(406) =< 2*V+1 aux(407) =< V/2 aux(408) =< 2/3*V aux(409) =< 3/5*V aux(410) =< 4/5*V s(5663) =< aux(403) s(5595) =< aux(404) s(5596) =< aux(404) s(5597) =< aux(404) s(5598) =< aux(404) s(5599) =< aux(407) s(5596) =< aux(408) s(5600) =< aux(409) s(5595) =< aux(410) s(5596) =< aux(410) s(5598) =< aux(410) s(5601) =< aux(405) s(5602) =< aux(405)-1 s(5603) =< aux(405)+1 s(5604) =< aux(405)+2 s(5595) =< aux(406)*(1/5)+aux(410) s(5596) =< aux(406)*(1/5)+aux(410) s(5597) =< aux(406)*(1/5)+aux(410) s(5598) =< aux(406)*(1/5)+aux(410) s(5596) =< aux(406)*(1/3)+aux(408) s(5597) =< aux(406)*(1/3)+aux(408) s(5598) =< aux(406)*(1/3)+aux(408) s(5600) =< aux(406)*(1/5)+aux(409) s(5599) =< aux(406)*(1/4)+aux(407) s(5600) =< aux(406)*(1/4)+aux(407) s(5605) =< s(5597)*s(5601) s(5606) =< s(5596)*s(5602) s(5607) =< s(5596)*s(5602) s(5608) =< s(5596)*s(5603) s(5609) =< s(5595)*s(5604) s(5610) =< s(5600)*s(5602) s(5611) =< s(5599)*s(5601) s(5612) =< s(5605) s(5613) =< s(5606) s(5614) =< s(5608) s(5615) =< s(5614)*s(5603) s(5616) =< s(5615) s(5617) =< s(5609) s(5618) =< s(5617)*s(5604) s(5619) =< s(5618) s(5620) =< s(5610) s(5621) =< s(5611) s(5622) =< s(5621)*aux(405) s(5623) =< s(5622) s(5625) =< aux(405) s(5559) =< s(5552) s(5560) =< s(5552) s(5561) =< s(5552) s(5562) =< s(5552) s(5563) =< s(5555) s(5560) =< s(5556) s(5564) =< s(5557) s(5559) =< s(5558) s(5560) =< s(5558) s(5562) =< s(5558) s(5565) =< s(5553) s(5566) =< s(5553)-1 s(5567) =< s(5553)+1 s(5568) =< s(5553)+2 s(5559) =< s(5554)*(1/5)+s(5558) s(5560) =< s(5554)*(1/5)+s(5558) s(5561) =< s(5554)*(1/5)+s(5558) s(5562) =< s(5554)*(1/5)+s(5558) s(5560) =< s(5554)*(1/3)+s(5556) s(5561) =< s(5554)*(1/3)+s(5556) s(5562) =< s(5554)*(1/3)+s(5556) s(5564) =< s(5554)*(1/5)+s(5557) s(5563) =< s(5554)*(1/4)+s(5555) s(5564) =< s(5554)*(1/4)+s(5555) s(5569) =< s(5561)*s(5565) s(5570) =< s(5560)*s(5566) s(5571) =< s(5560)*s(5566) s(5572) =< s(5560)*s(5567) s(5573) =< s(5559)*s(5568) s(5574) =< s(5564)*s(5566) s(5575) =< s(5563)*s(5565) s(5576) =< s(5569) s(5577) =< s(5570) s(5578) =< s(5572) s(5579) =< s(5578)*s(5567) s(5580) =< s(5579) s(5581) =< s(5573) s(5582) =< s(5581)*s(5568) s(5583) =< s(5582) s(5584) =< s(5574) s(5585) =< s(5575) s(5586) =< s(5585)*s(5553) s(5587) =< s(5586) with precondition: [V1>=1,V>=1,Out>=1,2*V1>=Out,2*V>=Out] * Chain [76]: 7*s(5673)+5*s(5674)+21*s(5675)+1*s(5676)+4*s(5677)+4*s(5678)+2*s(5685)+11*s(5690)+3*s(5691)+14*s(5692)+3*s(5694)+14*s(5695)+3*s(5697)+10*s(5698)+14*s(5699)+3*s(5701)+1 Such that:s(5666) =< V1 s(5667) =< 2*V1 s(5668) =< 2*V1+1 s(5669) =< V1/2 s(5670) =< 2/3*V1 s(5671) =< 3/5*V1 s(5672) =< 4/5*V1 s(5673) =< s(5666) s(5674) =< s(5666) s(5675) =< s(5666) s(5676) =< s(5666) s(5677) =< s(5669) s(5674) =< s(5670) s(5678) =< s(5671) s(5673) =< s(5672) s(5674) =< s(5672) s(5676) =< s(5672) s(5679) =< s(5667) s(5680) =< s(5667)-1 s(5681) =< s(5667)+1 s(5682) =< s(5667)+2 s(5673) =< s(5668)*(1/5)+s(5672) s(5674) =< s(5668)*(1/5)+s(5672) s(5675) =< s(5668)*(1/5)+s(5672) s(5676) =< s(5668)*(1/5)+s(5672) s(5674) =< s(5668)*(1/3)+s(5670) s(5675) =< s(5668)*(1/3)+s(5670) s(5676) =< s(5668)*(1/3)+s(5670) s(5678) =< s(5668)*(1/5)+s(5671) s(5677) =< s(5668)*(1/4)+s(5669) s(5678) =< s(5668)*(1/4)+s(5669) s(5683) =< s(5675)*s(5679) s(5684) =< s(5674)*s(5680) s(5685) =< s(5674)*s(5680) s(5686) =< s(5674)*s(5681) s(5687) =< s(5673)*s(5682) s(5688) =< s(5678)*s(5680) s(5689) =< s(5677)*s(5679) s(5690) =< s(5683) s(5691) =< s(5684) s(5692) =< s(5686) s(5693) =< s(5692)*s(5681) s(5694) =< s(5693) s(5695) =< s(5687) s(5696) =< s(5695)*s(5682) s(5697) =< s(5696) s(5698) =< s(5688) s(5699) =< s(5689) s(5700) =< s(5699)*s(5667) s(5701) =< s(5700) with precondition: [V=2,Out=0,V1>=0] * Chain [75]: 7*s(5709)+5*s(5710)+21*s(5711)+1*s(5712)+4*s(5713)+4*s(5714)+2*s(5721)+11*s(5726)+3*s(5727)+14*s(5728)+3*s(5730)+14*s(5731)+3*s(5733)+10*s(5734)+14*s(5735)+3*s(5737)+2*s(5739)+1 Such that:s(5738) =< 2 s(5702) =< V1 s(5703) =< 2*V1 s(5704) =< 2*V1+1 s(5705) =< V1/2 s(5706) =< 2/3*V1 s(5707) =< 3/5*V1 s(5708) =< 4/5*V1 s(5739) =< s(5738) s(5709) =< s(5702) s(5710) =< s(5702) s(5711) =< s(5702) s(5712) =< s(5702) s(5713) =< s(5705) s(5710) =< s(5706) s(5714) =< s(5707) s(5709) =< s(5708) s(5710) =< s(5708) s(5712) =< s(5708) s(5715) =< s(5703) s(5716) =< s(5703)-1 s(5717) =< s(5703)+1 s(5718) =< s(5703)+2 s(5709) =< s(5704)*(1/5)+s(5708) s(5710) =< s(5704)*(1/5)+s(5708) s(5711) =< s(5704)*(1/5)+s(5708) s(5712) =< s(5704)*(1/5)+s(5708) s(5710) =< s(5704)*(1/3)+s(5706) s(5711) =< s(5704)*(1/3)+s(5706) s(5712) =< s(5704)*(1/3)+s(5706) s(5714) =< s(5704)*(1/5)+s(5707) s(5713) =< s(5704)*(1/4)+s(5705) s(5714) =< s(5704)*(1/4)+s(5705) s(5719) =< s(5711)*s(5715) s(5720) =< s(5710)*s(5716) s(5721) =< s(5710)*s(5716) s(5722) =< s(5710)*s(5717) s(5723) =< s(5709)*s(5718) s(5724) =< s(5714)*s(5716) s(5725) =< s(5713)*s(5715) s(5726) =< s(5719) s(5727) =< s(5720) s(5728) =< s(5722) s(5729) =< s(5728)*s(5717) s(5730) =< s(5729) s(5731) =< s(5723) s(5732) =< s(5731)*s(5718) s(5733) =< s(5732) s(5734) =< s(5724) s(5735) =< s(5725) s(5736) =< s(5735)*s(5703) s(5737) =< s(5736) with precondition: [V=2,2>=Out,V1>=1,Out>=1] #### Cost of chains of fun4(Out): * Chain [80]: 0 with precondition: [Out=0] * Chain [79]: 0 with precondition: [Out=2] #### Cost of chains of fun5(V1,Out): * Chain [83]: 7*s(5968)+5*s(5969)+21*s(5970)+1*s(5971)+4*s(5972)+4*s(5973)+2*s(5980)+11*s(5985)+3*s(5986)+14*s(5987)+3*s(5989)+14*s(5990)+3*s(5992)+10*s(5993)+14*s(5994)+3*s(5996)+0 Such that:s(5961) =< V1 s(5962) =< 2*V1 s(5963) =< 2*V1+1 s(5964) =< V1/2 s(5965) =< 2/3*V1 s(5966) =< 3/5*V1 s(5967) =< 4/5*V1 s(5968) =< s(5961) s(5969) =< s(5961) s(5970) =< s(5961) s(5971) =< s(5961) s(5972) =< s(5964) s(5969) =< s(5965) s(5973) =< s(5966) s(5968) =< s(5967) s(5969) =< s(5967) s(5971) =< s(5967) s(5974) =< s(5962) s(5975) =< s(5962)-1 s(5976) =< s(5962)+1 s(5977) =< s(5962)+2 s(5968) =< s(5963)*(1/5)+s(5967) s(5969) =< s(5963)*(1/5)+s(5967) s(5970) =< s(5963)*(1/5)+s(5967) s(5971) =< s(5963)*(1/5)+s(5967) s(5969) =< s(5963)*(1/3)+s(5965) s(5970) =< s(5963)*(1/3)+s(5965) s(5971) =< s(5963)*(1/3)+s(5965) s(5973) =< s(5963)*(1/5)+s(5966) s(5972) =< s(5963)*(1/4)+s(5964) s(5973) =< s(5963)*(1/4)+s(5964) s(5978) =< s(5970)*s(5974) s(5979) =< s(5969)*s(5975) s(5980) =< s(5969)*s(5975) s(5981) =< s(5969)*s(5976) s(5982) =< s(5968)*s(5977) s(5983) =< s(5973)*s(5975) s(5984) =< s(5972)*s(5974) s(5985) =< s(5978) s(5986) =< s(5979) s(5987) =< s(5981) s(5988) =< s(5987)*s(5976) s(5989) =< s(5988) s(5990) =< s(5982) s(5991) =< s(5990)*s(5977) s(5992) =< s(5991) s(5993) =< s(5983) s(5994) =< s(5984) s(5995) =< s(5994)*s(5962) s(5996) =< s(5995) with precondition: [V1>=1,Out>=1,2*V1+1>=Out] * Chain [82]: 0 with precondition: [Out=0,V1>=0] * Chain [81]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun7(Out): * Chain [85]: 0 with precondition: [Out=0] * Chain [84]: 0 with precondition: [Out=1] #### Cost of chains of start(V1,V,V5): * Chain [86]: 10*s(5998)+4*s(6001)+10*s(6002)+3*s(6004)+136*s(6006)+24*s(6009)+3*s(6011)+15*s(6013)+4*s(6016)+3*s(6019)+1*s(6023)+378*s(6033)+270*s(6034)+1134*s(6035)+54*s(6036)+216*s(6037)+216*s(6038)+108*s(6045)+594*s(6050)+162*s(6051)+756*s(6052)+162*s(6054)+756*s(6055)+162*s(6057)+540*s(6058)+756*s(6059)+162*s(6061)+64*s(6077)+61*s(6078)+357*s(6079)+255*s(6080)+1071*s(6081)+51*s(6082)+204*s(6083)+204*s(6084)+102*s(6091)+561*s(6096)+153*s(6097)+714*s(6098)+153*s(6100)+714*s(6101)+153*s(6103)+510*s(6104)+714*s(6105)+153*s(6107)+148*s(6153)+15*s(6155)+9*s(6185)+48*s(6186)+6*s(6188)+3*s(6295)+6*s(6313)+6*s(6316)+133*s(6396)+95*s(6397)+399*s(6398)+19*s(6399)+76*s(6400)+76*s(6401)+38*s(6408)+209*s(6413)+57*s(6414)+266*s(6415)+57*s(6417)+266*s(6418)+57*s(6420)+190*s(6421)+266*s(6422)+57*s(6424)+60*s(6537)+60*s(6653)+18*s(6655)+7 Such that:s(6016) =< V1-V+1 aux(426) =< V+1 s(6001) =< V-V5 s(5997) =< V5+1 aux(429) =< 1 aux(430) =< 2 aux(431) =< 3 aux(432) =< V1 aux(433) =< V1+1 aux(434) =< 2*V1 aux(435) =< 2*V1+1 aux(436) =< V1/2 aux(437) =< 2/3*V1 aux(438) =< 3/5*V1 aux(439) =< 4/5*V1 aux(440) =< V aux(441) =< 2*V aux(442) =< 2*V+1 aux(443) =< V/2 aux(444) =< 2/3*V aux(445) =< 3/5*V aux(446) =< 4/5*V aux(447) =< V5 aux(448) =< 2*V5 aux(449) =< 2*V5+1 aux(450) =< V5/2 aux(451) =< 2/3*V5 aux(452) =< 3/5*V5 aux(453) =< 4/5*V5 s(6006) =< aux(429) s(6077) =< aux(430) s(6023) =< aux(432) s(6013) =< aux(440) s(6079) =< aux(440) s(6080) =< aux(440) s(6081) =< aux(440) s(6082) =< aux(440) s(6083) =< aux(443) s(6080) =< aux(444) s(6084) =< aux(445) s(6079) =< aux(446) s(6080) =< aux(446) s(6082) =< aux(446) s(6085) =< aux(441) s(6086) =< aux(441)-1 s(6087) =< aux(441)+1 s(6088) =< aux(441)+2 s(6079) =< aux(442)*(1/5)+aux(446) s(6080) =< aux(442)*(1/5)+aux(446) s(6081) =< aux(442)*(1/5)+aux(446) s(6082) =< aux(442)*(1/5)+aux(446) s(6080) =< aux(442)*(1/3)+aux(444) s(6081) =< aux(442)*(1/3)+aux(444) s(6082) =< aux(442)*(1/3)+aux(444) s(6084) =< aux(442)*(1/5)+aux(445) s(6083) =< aux(442)*(1/4)+aux(443) s(6084) =< aux(442)*(1/4)+aux(443) s(6089) =< s(6081)*s(6085) s(6090) =< s(6080)*s(6086) s(6091) =< s(6080)*s(6086) s(6092) =< s(6080)*s(6087) s(6093) =< s(6079)*s(6088) s(6094) =< s(6084)*s(6086) s(6095) =< s(6083)*s(6085) s(6096) =< s(6089) s(6097) =< s(6090) s(6098) =< s(6092) s(6099) =< s(6098)*s(6087) s(6100) =< s(6099) s(6101) =< s(6093) s(6102) =< s(6101)*s(6088) s(6103) =< s(6102) s(6104) =< s(6094) s(6105) =< s(6095) s(6106) =< s(6105)*aux(441) s(6107) =< s(6106) s(6033) =< aux(432) s(6034) =< aux(432) s(6035) =< aux(432) s(6036) =< aux(432) s(6037) =< aux(436) s(6034) =< aux(437) s(6038) =< aux(438) s(6033) =< aux(439) s(6034) =< aux(439) s(6036) =< aux(439) s(6039) =< aux(434) s(6040) =< aux(434)-1 s(6041) =< aux(434)+1 s(6042) =< aux(434)+2 s(6033) =< aux(435)*(1/5)+aux(439) s(6034) =< aux(435)*(1/5)+aux(439) s(6035) =< aux(435)*(1/5)+aux(439) s(6036) =< aux(435)*(1/5)+aux(439) s(6034) =< aux(435)*(1/3)+aux(437) s(6035) =< aux(435)*(1/3)+aux(437) s(6036) =< aux(435)*(1/3)+aux(437) s(6038) =< aux(435)*(1/5)+aux(438) s(6037) =< aux(435)*(1/4)+aux(436) s(6038) =< aux(435)*(1/4)+aux(436) s(6043) =< s(6035)*s(6039) s(6044) =< s(6034)*s(6040) s(6045) =< s(6034)*s(6040) s(6046) =< s(6034)*s(6041) s(6047) =< s(6033)*s(6042) s(6048) =< s(6038)*s(6040) s(6049) =< s(6037)*s(6039) s(6050) =< s(6043) s(6051) =< s(6044) s(6052) =< s(6046) s(6053) =< s(6052)*s(6041) s(6054) =< s(6053) s(6055) =< s(6047) s(6056) =< s(6055)*s(6042) s(6057) =< s(6056) s(6058) =< s(6048) s(6059) =< s(6049) s(6060) =< s(6059)*aux(434) s(6061) =< s(6060) s(6153) =< aux(431) s(6294) =< s(6006)*aux(431) s(6295) =< s(6294) s(6537) =< aux(449) s(6396) =< aux(447) s(6397) =< aux(447) s(6398) =< aux(447) s(6399) =< aux(447) s(6400) =< aux(450) s(6397) =< aux(451) s(6401) =< aux(452) s(6396) =< aux(453) s(6397) =< aux(453) s(6399) =< aux(453) s(6402) =< aux(448) s(6403) =< aux(448)-1 s(6404) =< aux(448)+1 s(6405) =< aux(448)+2 s(6396) =< aux(449)*(1/5)+aux(453) s(6397) =< aux(449)*(1/5)+aux(453) s(6398) =< aux(449)*(1/5)+aux(453) s(6399) =< aux(449)*(1/5)+aux(453) s(6397) =< aux(449)*(1/3)+aux(451) s(6398) =< aux(449)*(1/3)+aux(451) s(6399) =< aux(449)*(1/3)+aux(451) s(6401) =< aux(449)*(1/5)+aux(452) s(6400) =< aux(449)*(1/4)+aux(450) s(6401) =< aux(449)*(1/4)+aux(450) s(6406) =< s(6398)*s(6402) s(6407) =< s(6397)*s(6403) s(6408) =< s(6397)*s(6403) s(6409) =< s(6397)*s(6404) s(6410) =< s(6396)*s(6405) s(6411) =< s(6401)*s(6403) s(6412) =< s(6400)*s(6402) s(6413) =< s(6406) s(6414) =< s(6407) s(6415) =< s(6409) s(6416) =< s(6415)*s(6404) s(6417) =< s(6416) s(6418) =< s(6410) s(6419) =< s(6418)*s(6405) s(6420) =< s(6419) s(6421) =< s(6411) s(6422) =< s(6412) s(6423) =< s(6422)*aux(448) s(6424) =< s(6423) s(6078) =< aux(441) s(6185) =< aux(434) s(6154) =< s(6077)*aux(431) s(6155) =< s(6154) s(6186) =< aux(435) s(6187) =< s(6185)*aux(435) s(6188) =< s(6187) s(6653) =< aux(442) s(6654) =< s(6078)*aux(442) s(6655) =< s(6654) s(6312) =< s(6153)*aux(431) s(6313) =< s(6312) s(6315) =< s(6186)*aux(435) s(6316) =< s(6315) s(6009) =< aux(433) s(6010) =< s(6009)*aux(433) s(6011) =< s(6010) s(6018) =< s(6016)*aux(433) s(6019) =< s(6018) s(6002) =< aux(426) s(6003) =< s(6001)*aux(426) s(6004) =< s(6003) s(5998) =< s(5997) with precondition: [] Closed-form bounds of start(V1,V,V5): ------------------------------------- * Chain [86] with precondition: [] - Upper bound: nat(V1)*4915+868+nat(V1)*270*nat(nat(2*V1)+ -1)+nat(V1)*3078*nat(2*V1)+nat(V1)*324*nat(2*V1)*nat(2*V1)+nat(V)*4656+nat(V)*255*nat(nat(2*V)+ -1)+nat(V)*2907*nat(2*V)+nat(V)*306*nat(2*V)*nat(2*V)+nat(V5)*1729+nat(V5)*95*nat(nat(2*V5)+ -1)+nat(V5)*1083*nat(2*V5)+nat(V5)*114*nat(2*V5)*nat(2*V5)+nat(nat(2*V1)+ -1)*540*nat(3/5*V1)+nat(nat(2*V)+ -1)*510*nat(3/5*V)+nat(nat(2*V5)+ -1)*190*nat(3/5*V5)+nat(2*V1)*9+nat(2*V1)*162*nat(2*V1)*nat(V1/2)+nat(2*V1)*6*nat(2*V1+1)+nat(2*V1)*756*nat(V1/2)+nat(2*V)*61+nat(2*V)*153*nat(2*V)*nat(V/2)+nat(2*V)*18*nat(2*V+1)+nat(2*V)*714*nat(V/2)+nat(2*V5)*57*nat(2*V5)*nat(V5/2)+nat(2*V5)*266*nat(V5/2)+nat(3/5*V1)*216+nat(3/5*V)*204+nat(3/5*V5)*76+nat(V1+1)*24+nat(V1+1)*3*nat(V1+1)+nat(V1+1)*3*nat(V1-V+1)+nat(V+1)*10+nat(V+1)*3*nat(V-V5)+nat(V5+1)*10+nat(2*V1+1)*48+nat(2*V1+1)*6*nat(2*V1+1)+nat(2*V+1)*60+nat(2*V5+1)*60+nat(V1-V+1)*4+nat(V-V5)*4+nat(V1/2)*216+nat(V/2)*204+nat(V5/2)*76 - Complexity: n^3 ### Maximum cost of start(V1,V,V5): nat(V1)*4915+868+nat(V1)*270*nat(nat(2*V1)+ -1)+nat(V1)*3078*nat(2*V1)+nat(V1)*324*nat(2*V1)*nat(2*V1)+nat(V)*4656+nat(V)*255*nat(nat(2*V)+ -1)+nat(V)*2907*nat(2*V)+nat(V)*306*nat(2*V)*nat(2*V)+nat(V5)*1729+nat(V5)*95*nat(nat(2*V5)+ -1)+nat(V5)*1083*nat(2*V5)+nat(V5)*114*nat(2*V5)*nat(2*V5)+nat(nat(2*V1)+ -1)*540*nat(3/5*V1)+nat(nat(2*V)+ -1)*510*nat(3/5*V)+nat(nat(2*V5)+ -1)*190*nat(3/5*V5)+nat(2*V1)*9+nat(2*V1)*162*nat(2*V1)*nat(V1/2)+nat(2*V1)*6*nat(2*V1+1)+nat(2*V1)*756*nat(V1/2)+nat(2*V)*61+nat(2*V)*153*nat(2*V)*nat(V/2)+nat(2*V)*18*nat(2*V+1)+nat(2*V)*714*nat(V/2)+nat(2*V5)*57*nat(2*V5)*nat(V5/2)+nat(2*V5)*266*nat(V5/2)+nat(3/5*V1)*216+nat(3/5*V)*204+nat(3/5*V5)*76+nat(V1+1)*24+nat(V1+1)*3*nat(V1+1)+nat(V1+1)*3*nat(V1-V+1)+nat(V+1)*10+nat(V+1)*3*nat(V-V5)+nat(V5+1)*10+nat(2*V1+1)*48+nat(2*V1+1)*6*nat(2*V1+1)+nat(2*V+1)*60+nat(2*V5+1)*60+nat(V1-V+1)*4+nat(V-V5)*4+nat(V1/2)*216+nat(V/2)*204+nat(V5/2)*76 Asymptotic class: n^3 * Total analysis performed in 21055 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(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false encArg(cons_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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false 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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal 0' :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal hole_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal1_4 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4 :: Nat -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: minus, cond, equal, min, encArg They will be analysed ascendingly in the following order: minus = cond equal < minus min < minus minus < encArg cond < encArg equal < encArg min < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false 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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal 0' :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal hole_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal1_4 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4 :: Nat -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal Generator Equations: gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(0) <=> true gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(x)) The following defined symbols remain to be analysed: equal, minus, cond, min, encArg They will be analysed ascendingly in the following order: minus = cond equal < minus min < minus minus < encArg cond < encArg equal < encArg min < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, 0)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, 0))) Induction Step: equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, +(n4_4, 1))), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_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(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false 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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal 0' :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal hole_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal1_4 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4 :: Nat -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal Generator Equations: gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(0) <=> true gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(x)) The following defined symbols remain to be analysed: equal, minus, cond, min, encArg They will be analysed ascendingly in the following order: minus = cond equal < minus min < minus minus < encArg cond < encArg equal < encArg min < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false 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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal 0' :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal hole_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal1_4 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4 :: Nat -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal Lemmas: equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(0) <=> true gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(x)) The following defined symbols remain to be analysed: min, minus, cond, encArg They will be analysed ascendingly in the following order: minus = cond min < minus minus < encArg cond < encArg min < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: min(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4))) -> *3_4, rt in Omega(n2263_4) Induction Base: min(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, 0)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, 0))) Induction Step: min(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, +(n2263_4, 1))), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, +(n2263_4, 1)))) ->_R^Omega(1) s(min(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4)))) ->_IH s(*3_4) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(equal(min(x, y), y), x, y) cond(true, x, y) -> s(minus(x, s(y))) min(0', v) -> 0' min(u, 0') -> 0' min(s(u), s(v)) -> s(min(u, v)) equal(0', 0') -> true equal(s(x), 0') -> false equal(0', s(y)) -> false equal(s(x), s(y)) -> equal(x, y) encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(0') -> 0' encArg(false) -> false 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_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_equal(x_1, x_2)) -> equal(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_equal(x_1, x_2) -> equal(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0' encode_false -> false Types: minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal 0' :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encArg :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal cons_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_minus :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_cond :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_equal :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_min :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_true :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_s :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_0 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal encode_false :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal hole_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal1_4 :: true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4 :: Nat -> true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal Lemmas: equal(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) min(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4)), gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(1, n2263_4))) -> *3_4, rt in Omega(n2263_4) Generator Equations: gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(0) <=> true gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(x, 1)) <=> s(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_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 ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(n5272_4)) -> gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(n5272_4), rt in Omega(0) Induction Base: encArg(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(0)) ->_R^Omega(0) true Induction Step: encArg(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(+(n5272_4, 1))) ->_R^Omega(0) s(encArg(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(n5272_4))) ->_IH s(gen_true:s:0':false:cons_minus:cons_cond:cons_min:cons_equal2_4(c5273_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (30) BOUNDS(1, INF)