/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^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 223 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, 21.5 s] (14) BOUNDS(1, n^2) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 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(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) [1] if_quot(true, x, y) -> s(quot(minus(x, y), y)) [1] if_quot(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [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, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) [1] if_quot(true, x, y) -> s(quot(minus(x, y), y)) [1] if_quot(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [0] The TRS has the following type information: minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot 0 :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot s :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot true :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot false :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encArg :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot cons_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot cons_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot cons_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot cons_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_0 :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_s :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_true :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_false :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot encode_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot 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_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_quot(v0, v1) -> null_encode_quot [0] encode_if_quot(v0, v1, v2) -> null_encode_if_quot [0] minus(v0, v1) -> null_minus [0] le(v0, v1) -> null_le [0] quot(v0, v1) -> null_quot [0] if_quot(v0, v1, v2) -> null_if_quot [0] And the following fresh constants: null_encArg, null_encode_minus, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_quot, null_encode_if_quot, null_minus, null_le, null_quot, null_if_quot ---------------------------------------- (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, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) [1] if_quot(true, x, y) -> s(quot(minus(x, y), y)) [1] if_quot(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(v0) -> null_encArg [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_quot(v0, v1) -> null_encode_quot [0] encode_if_quot(v0, v1, v2) -> null_encode_if_quot [0] minus(v0, v1) -> null_minus [0] le(v0, v1) -> null_le [0] quot(v0, v1) -> null_quot [0] if_quot(v0, v1, v2) -> null_if_quot [0] The TRS has the following type information: minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot 0 :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot s :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot true :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot false :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encArg :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot cons_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot cons_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot cons_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot cons_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_0 :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_s :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_true :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_false :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot encode_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot -> 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encArg :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_0 :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_s :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_true :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_false :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_encode_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_minus :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_le :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot null_if_quot :: 0:s:true:false:cons_minus:cons_le:cons_quot:cons_if_quot:null_encArg:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_quot:null_encode_if_quot:null_minus:null_le:null_quot:null_if_quot 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: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_minus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_quot => 0 null_encode_if_quot => 0 null_minus => 0 null_le => 0 null_quot => 0 null_if_quot => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> quot(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> if_quot(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_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_if_quot(z, z', z'') -{ 0 }-> if_quot(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_if_quot(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_le(z, z') -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_le(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_quot(z, z') -{ 0 }-> quot(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_quot(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 :|: if_quot(z, z', z'') -{ 1 }-> 0 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 if_quot(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 if_quot(z, z', z'') -{ 1 }-> 1 + quot(minus(x, y), y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 le(z, z') -{ 1 }-> le(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x le(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y le(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 quot(z, z') -{ 1 }-> if_quot(le(1 + y, x), x, 1 + y) :|: z' = 1 + y, x >= 0, y >= 0, z = x quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 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, V12),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[le(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[quot(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[fun(V1, V, V12, Out)],[V1 >= 0,V >= 0,V12 >= 0]). eq(start(V1, V, V12),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V12),0,[fun1(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[fun2(Out)],[]). eq(start(V1, V, V12),0,[fun3(V1, Out)],[V1 >= 0]). eq(start(V1, V, V12),0,[fun4(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[fun5(Out)],[]). eq(start(V1, V, V12),0,[fun6(Out)],[]). eq(start(V1, V, V12),0,[fun7(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V12),0,[fun8(V1, V, V12, Out)],[V1 >= 0,V >= 0,V12 >= 0]). eq(minus(V1, V, Out),1,[],[Out = V2,V2 >= 0,V1 = V2,V = 0]). eq(minus(V1, V, Out),1,[minus(V3, V4, Ret)],[Out = Ret,V = 1 + V4,V3 >= 0,V4 >= 0,V1 = 1 + V3]). eq(le(V1, V, Out),1,[],[Out = 2,V5 >= 0,V1 = 0,V = V5]). eq(le(V1, V, Out),1,[],[Out = 1,V6 >= 0,V1 = 1 + V6,V = 0]). eq(le(V1, V, Out),1,[le(V7, V8, Ret1)],[Out = Ret1,V = 1 + V8,V7 >= 0,V8 >= 0,V1 = 1 + V7]). eq(quot(V1, V, Out),1,[le(1 + V10, V9, Ret0),fun(Ret0, V9, 1 + V10, Ret2)],[Out = Ret2,V = 1 + V10,V9 >= 0,V10 >= 0,V1 = V9]). eq(fun(V1, V, V12, Out),1,[minus(V13, V11, Ret10),quot(Ret10, V11, Ret11)],[Out = 1 + Ret11,V1 = 2,V = V13,V12 = V11,V13 >= 0,V11 >= 0]). eq(fun(V1, V, V12, Out),1,[],[Out = 0,V = V15,V12 = V14,V1 = 1,V15 >= 0,V14 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret12)],[Out = 1 + Ret12,V1 = 1 + V16,V16 >= 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V17, Ret01),encArg(V18, Ret13),minus(Ret01, Ret13, Ret3)],[Out = Ret3,V17 >= 0,V1 = 1 + V17 + V18,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V19, Ret02),encArg(V20, Ret14),le(Ret02, Ret14, Ret4)],[Out = Ret4,V19 >= 0,V1 = 1 + V19 + V20,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret03),encArg(V21, Ret15),quot(Ret03, Ret15, Ret5)],[Out = Ret5,V22 >= 0,V1 = 1 + V21 + V22,V21 >= 0]). eq(encArg(V1, Out),0,[encArg(V25, Ret04),encArg(V24, Ret16),encArg(V23, Ret21),fun(Ret04, Ret16, Ret21, Ret6)],[Out = Ret6,V25 >= 0,V1 = 1 + V23 + V24 + V25,V23 >= 0,V24 >= 0]). eq(fun1(V1, V, Out),0,[encArg(V26, Ret05),encArg(V27, Ret17),minus(Ret05, Ret17, Ret7)],[Out = Ret7,V26 >= 0,V27 >= 0,V1 = V26,V = V27]). eq(fun2(Out),0,[],[Out = 0]). eq(fun3(V1, Out),0,[encArg(V28, Ret18)],[Out = 1 + Ret18,V28 >= 0,V1 = V28]). eq(fun4(V1, V, Out),0,[encArg(V30, Ret06),encArg(V29, Ret19),le(Ret06, Ret19, Ret8)],[Out = Ret8,V30 >= 0,V29 >= 0,V1 = V30,V = V29]). eq(fun5(Out),0,[],[Out = 2]). eq(fun6(Out),0,[],[Out = 1]). eq(fun7(V1, V, Out),0,[encArg(V32, Ret07),encArg(V31, Ret110),quot(Ret07, Ret110, Ret9)],[Out = Ret9,V32 >= 0,V31 >= 0,V1 = V32,V = V31]). eq(fun8(V1, V, V12, Out),0,[encArg(V33, Ret08),encArg(V35, Ret111),encArg(V34, Ret22),fun(Ret08, Ret111, Ret22, Ret20)],[Out = Ret20,V33 >= 0,V34 >= 0,V35 >= 0,V1 = V33,V = V35,V12 = V34]). eq(encArg(V1, Out),0,[],[Out = 0,V36 >= 0,V1 = V36]). eq(fun1(V1, V, Out),0,[],[Out = 0,V38 >= 0,V37 >= 0,V1 = V38,V = V37]). eq(fun3(V1, Out),0,[],[Out = 0,V39 >= 0,V1 = V39]). eq(fun4(V1, V, Out),0,[],[Out = 0,V40 >= 0,V41 >= 0,V1 = V40,V = V41]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 0]). eq(fun7(V1, V, Out),0,[],[Out = 0,V42 >= 0,V43 >= 0,V1 = V42,V = V43]). eq(fun8(V1, V, V12, Out),0,[],[Out = 0,V44 >= 0,V12 = V46,V45 >= 0,V1 = V44,V = V45,V46 >= 0]). eq(minus(V1, V, Out),0,[],[Out = 0,V48 >= 0,V47 >= 0,V1 = V48,V = V47]). eq(le(V1, V, Out),0,[],[Out = 0,V49 >= 0,V50 >= 0,V1 = V49,V = V50]). eq(quot(V1, V, Out),0,[],[Out = 0,V51 >= 0,V52 >= 0,V1 = V51,V = V52]). eq(fun(V1, V, V12, Out),0,[],[Out = 0,V53 >= 0,V12 = V55,V54 >= 0,V1 = V53,V = V54,V55 >= 0]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(le(V1,V,Out),[V1,V],[Out]). input_output_vars(quot(V1,V,Out),[V1,V],[Out]). input_output_vars(fun(V1,V,V12,Out),[V1,V,V12],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun1(V1,V,Out),[V1,V],[Out]). input_output_vars(fun2(Out),[],[Out]). input_output_vars(fun3(V1,Out),[V1],[Out]). input_output_vars(fun4(V1,V,Out),[V1,V],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(Out),[],[Out]). input_output_vars(fun7(V1,V,Out),[V1,V],[Out]). input_output_vars(fun8(V1,V,V12,Out),[V1,V,V12],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [minus/3] 1. recursive : [le/3] 2. recursive : [fun/4,quot/3] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun1/3] 5. non_recursive : [fun2/1] 6. non_recursive : [fun3/2] 7. non_recursive : [fun4/3] 8. non_recursive : [fun5/1] 9. non_recursive : [fun6/1] 10. non_recursive : [fun7/3] 11. non_recursive : [fun8/4] 12. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into minus/3 1. SCC is partially evaluated into le/3 2. SCC is partially evaluated into quot/3 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun1/3 5. SCC is completely evaluated into other SCCs 6. SCC is partially evaluated into fun3/2 7. SCC is partially evaluated into fun4/3 8. SCC is partially evaluated into fun5/1 9. SCC is partially evaluated into fun6/1 10. SCC is partially evaluated into fun7/3 11. SCC is partially evaluated into fun8/4 12. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations minus/3 * CE 17 is refined into CE [52] * CE 15 is refined into CE [53] * CE 16 is refined into CE [54] ### Cost equations --> "Loop" of minus/3 * CEs [54] --> Loop 27 * CEs [52] --> Loop 28 * CEs [53] --> Loop 29 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [27]: [V,V1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [27]: - RF of loop [27:1]: V V1 ### Specialization of cost equations le/3 * CE 25 is refined into CE [55] * CE 23 is refined into CE [56] * CE 22 is refined into CE [57] * CE 24 is refined into CE [58] ### Cost equations --> "Loop" of le/3 * CEs [58] --> Loop 30 * CEs [55] --> Loop 31 * CEs [56] --> Loop 32 * CEs [57] --> Loop 33 ### Ranking functions of CR le(V1,V,Out) * RF of phase [30]: [V,V1] #### Partial ranking functions of CR le(V1,V,Out) * Partial RF of phase [30]: - RF of loop [30:1]: V V1 ### Specialization of cost equations quot/3 * CE 18 is refined into CE [59,60,61,62] * CE 19 is refined into CE [63,64] * CE 21 is refined into CE [65] * CE 20 is refined into CE [66,67] ### Cost equations --> "Loop" of quot/3 * CEs [67] --> Loop 34 * CEs [66] --> Loop 35 * CEs [59,60,61,62,63,64,65] --> Loop 36 ### Ranking functions of CR quot(V1,V,Out) * RF of phase [34]: [V1,V1-V+1] #### Partial ranking functions of CR quot(V1,V,Out) * Partial RF of phase [34]: - RF of loop [34:1]: V1 V1-V+1 ### Specialization of cost equations encArg/2 * CE 29 is refined into CE [68] * CE 31 is refined into CE [69] * CE 32 is refined into CE [70] * CE 33 is refined into CE [71,72,73] * CE 34 is refined into CE [74,75,76,77,78] * CE 35 is refined into CE [79,80] * CE 30 is refined into CE [81] * CE 28 is refined into CE [82,83,84,85] * CE 26 is refined into CE [86] * CE 27 is refined into CE [87] ### Cost equations --> "Loop" of encArg/2 * CEs [85] --> Loop 37 * CEs [82,83,84] --> Loop 38 * CEs [86,87] --> Loop 39 * CEs [81] --> Loop 40 * CEs [73] --> Loop 41 * CEs [71] --> Loop 42 * CEs [78] --> Loop 43 * CEs [74] --> Loop 44 * CEs [77,80] --> Loop 45 * CEs [75] --> Loop 46 * CEs [72,76,79] --> Loop 47 * CEs [68] --> Loop 48 * CEs [69] --> Loop 49 * CEs [70] --> Loop 50 ### Ranking functions of CR encArg(V1,Out) * RF of phase [37,38,39,40,41,42,43,44,45,46,47]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [37,38,39,40,41,42,43,44,45,46,47]: - RF of loop [37:1,37:2,37:3,38:1,38:2,38:3,39:1,39:2,39:3,40:1,41:1,41:2,42:1,42:2,43:1,43:2,44:1,44:2,45:1,45:2,46:1,46:2,47:1,47:2]: V1 ### Specialization of cost equations fun1/3 * CE 36 is refined into CE [88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106] * CE 37 is refined into CE [107] ### Cost equations --> "Loop" of fun1/3 * CEs [92] --> Loop 51 * CEs [91,104] --> Loop 52 * CEs [97] --> Loop 53 * CEs [88,90,93,95,100] --> Loop 54 * CEs [89,94,96,98,99,101,102,103,105,106,107] --> Loop 55 ### Ranking functions of CR fun1(V1,V,Out) #### Partial ranking functions of CR fun1(V1,V,Out) ### Specialization of cost equations fun3/2 * CE 38 is refined into CE [108,109,110] * CE 39 is refined into CE [111] ### Cost equations --> "Loop" of fun3/2 * CEs [110] --> Loop 56 * CEs [111] --> Loop 57 * CEs [108,109] --> Loop 58 ### Ranking functions of CR fun3(V1,Out) #### Partial ranking functions of CR fun3(V1,Out) ### Specialization of cost equations fun4/3 * CE 40 is refined into CE [112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137] * CE 41 is refined into CE [138] ### Cost equations --> "Loop" of fun4/3 * CEs [117,120,134] --> Loop 59 * CEs [119] --> Loop 60 * CEs [118,135] --> Loop 61 * CEs [113,115,122,124,126,130] --> Loop 62 * CEs [112,116,121,127,129,132,136] --> Loop 63 * CEs [114,123,125,128,131,133,137,138] --> Loop 64 ### Ranking functions of CR fun4(V1,V,Out) #### Partial ranking functions of CR fun4(V1,V,Out) ### Specialization of cost equations fun5/1 * CE 42 is refined into CE [139] * CE 43 is refined into CE [140] ### Cost equations --> "Loop" of fun5/1 * CEs [139] --> Loop 65 * CEs [140] --> Loop 66 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/1 * CE 44 is refined into CE [141] * CE 45 is refined into CE [142] ### Cost equations --> "Loop" of fun6/1 * CEs [141] --> Loop 67 * CEs [142] --> Loop 68 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations fun7/3 * CE 46 is refined into CE [143,144,145,146,147,148,149,150,151,152,153,154,155] * CE 47 is refined into CE [156] ### Cost equations --> "Loop" of fun7/3 * CEs [146] --> Loop 69 * CEs [145,154] --> Loop 70 * CEs [144,149,151] --> Loop 71 * CEs [143,147,148,150,152,153,155,156] --> Loop 72 ### Ranking functions of CR fun7(V1,V,Out) #### Partial ranking functions of CR fun7(V1,V,Out) ### Specialization of cost equations fun8/4 * CE 48 is refined into CE [157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183] * CE 49 is refined into CE [184,185,186,187,188,189,190,191,192] * CE 50 is refined into CE [193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236] * CE 51 is refined into CE [237] ### Cost equations --> "Loop" of fun8/4 * CEs [205] --> Loop 73 * CEs [202,203,204,206,207,208,209] --> Loop 74 * CEs [160,161,162,178,179,180,187,188,189] --> Loop 75 * CEs [199,221] --> Loop 76 * CEs [197,198,212,219,220,234] --> Loop 77 * CEs [158,164,167,173,176,182,185,191] --> Loop 78 * CEs [196,218,227] --> Loop 79 * CEs [193,194,195,200,201,210,211,213,214,215,216,217,222,223,224,225,226,228,229,230,231,232,233,235,236] --> Loop 80 * CEs [157,159,163,165,166,168,169,170,171,172,174,175,177,181,183,184,186,190,192,237] --> Loop 81 ### Ranking functions of CR fun8(V1,V,V12,Out) #### Partial ranking functions of CR fun8(V1,V,V12,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [238] * CE 2 is refined into CE [239] * CE 3 is refined into CE [240,241,242,243] * CE 4 is refined into CE [244,245,246] * CE 5 is refined into CE [247,248,249,250,251] * CE 6 is refined into CE [252,253] * CE 7 is refined into CE [254,255,256] * CE 8 is refined into CE [257,258,259] * CE 9 is refined into CE [260,261,262] * CE 10 is refined into CE [263,264,265] * CE 11 is refined into CE [266,267] * CE 12 is refined into CE [268,269] * CE 13 is refined into CE [270,271] * CE 14 is refined into CE [272,273,274,275,276,277] ### Cost equations --> "Loop" of start/3 * CEs [238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277] --> Loop 82 ### Ranking functions of CR start(V1,V,V12) #### Partial ranking functions of CR start(V1,V,V12) Computing Bounds ===================================== #### Cost of chains of minus(V1,V,Out): * Chain [[27],29]: 1*it(27)+1 Such that:it(27) =< V with precondition: [V1=Out+V,V>=1,V1>=V] * Chain [[27],28]: 1*it(27)+0 Such that:it(27) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [29]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [28]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of le(V1,V,Out): * Chain [[30],33]: 1*it(30)+1 Such that:it(30) =< V1 with precondition: [Out=2,V1>=1,V>=V1] * Chain [[30],32]: 1*it(30)+1 Such that:it(30) =< V with precondition: [Out=1,V>=1,V1>=V+1] * Chain [[30],31]: 1*it(30)+0 Such that:it(30) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [33]: 1 with precondition: [V1=0,Out=2,V>=0] * Chain [32]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [31]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of quot(V1,V,Out): * Chain [[34],36]: 9*it(34)+1*s(5)+3 Such that:s(5) =< V aux(5) =< V1 it(34) =< aux(5) with precondition: [V>=1,Out>=1,V1+1>=Out+V] * Chain [[34],35,36]: 4*it(34)+3*s(5)+2*s(11)+6 Such that:aux(3) =< V1 aux(7) =< V aux(8) =< V1-V it(34) =< aux(8) s(5) =< aux(7) it(34) =< aux(3) s(12) =< aux(3) s(12) =< aux(8) s(11) =< s(12) with precondition: [V>=1,Out>=2,V1+2>=2*V+Out] * Chain [36]: 3*s(3)+1*s(5)+3 Such that:s(5) =< V aux(1) =< V1 s(3) =< aux(1) with precondition: [Out=0,V1>=0,V>=0] * Chain [35,36]: 3*s(5)+6 Such that:aux(7) =< V s(5) =< aux(7) with precondition: [Out=1,V>=1,V1>=V] #### Cost of chains of encArg(V1,Out): * Chain [50]: 0 with precondition: [V1=1,Out=1] * Chain [49]: 0 with precondition: [V1=2,Out=2] * Chain [48]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([37,38,39,40,41,42,43,44,45,46,47],[[50],[49],[48]])]: 8*it(37)+5*it(38)+1*it(39)+8*it(41)+2*it(42)+1*it(46)+3*it(47)+23*s(81)+5*s(83)+5*s(85)+3*s(89)+22*s(92)+5*s(94)+1*s(95)+0 Such that:aux(17) =< 2*V1 aux(33) =< V1 aux(34) =< 2*V1+1 aux(35) =< 2/3*V1 aux(36) =< 3/5*V1 aux(37) =< 3/8*V1 aux(38) =< 4/5*V1 it(39) =< aux(33) it(41) =< aux(33) it(42) =< aux(33) it(46) =< aux(33) it(47) =< aux(33) it([48]) =< aux(34) it(41) =< aux(35) it(38) =< aux(36) it(37) =< aux(37) it(46) =< aux(38) aux(19) =< aux(17)+1 aux(30) =< aux(17)+3 aux(23) =< aux(17) aux(27) =< aux(17)+2 aux(20) =< aux(17)-1 it(46) =< it([48])*(1/5)+aux(38) it(47) =< it([48])*(1/5)+aux(38) it(41) =< it([48])*(1/3)+aux(35) it(42) =< it([48])*(1/3)+aux(35) it(46) =< it([48])*(1/3)+aux(35) it(47) =< it([48])*(1/3)+aux(35) it(38) =< it([48])*(1/5)+aux(36) it(39) =< it([48])*(1/5)+aux(36) it(37) =< it([48])*(5/16)+aux(37) it(38) =< it([48])*(5/16)+aux(37) it(39) =< it([48])*(5/16)+aux(37) s(97) =< it(47)*aux(19) s(95) =< it(47)*aux(30) s(89) =< it(41)*aux(23) s(93) =< it(41)*aux(27) s(86) =< it(38)*aux(20) s(88) =< it(38)*aux(19) s(82) =< it(37)*aux(17) s(94) =< s(97) s(92) =< s(93) s(85) =< s(88) s(83) =< s(86) s(81) =< s(82) with precondition: [V1>=1,Out>=0,2*V1>=Out] #### Cost of chains of fun1(V1,V,Out): * Chain [55]: 2*s(138)+16*s(139)+4*s(140)+2*s(141)+6*s(142)+10*s(143)+16*s(144)+2*s(151)+6*s(152)+10*s(157)+44*s(158)+10*s(159)+10*s(160)+46*s(161)+4*s(169)+32*s(170)+8*s(171)+4*s(172)+12*s(173)+20*s(174)+32*s(175)+4*s(182)+12*s(183)+20*s(188)+88*s(189)+20*s(190)+20*s(191)+92*s(192)+3*s(193)+2*s(258)+1 Such that:aux(42) =< 2 aux(43) =< V1 aux(44) =< 2*V1 aux(45) =< 2*V1+1 aux(46) =< 2/3*V1 aux(47) =< 3/5*V1 aux(48) =< 3/8*V1 aux(49) =< 4/5*V1 aux(50) =< V aux(51) =< 2*V aux(52) =< 2*V+1 aux(53) =< 2/3*V aux(54) =< 3/5*V aux(55) =< 3/8*V aux(56) =< 4/5*V s(258) =< aux(42) s(193) =< aux(51) s(169) =< aux(50) s(170) =< aux(50) s(171) =< aux(50) s(172) =< aux(50) s(173) =< aux(50) s(170) =< aux(53) s(174) =< aux(54) s(175) =< aux(55) s(172) =< aux(56) s(176) =< aux(51)+1 s(177) =< aux(51)+3 s(178) =< aux(51) s(179) =< aux(51)+2 s(180) =< aux(51)-1 s(172) =< aux(52)*(1/5)+aux(56) s(173) =< aux(52)*(1/5)+aux(56) s(170) =< aux(52)*(1/3)+aux(53) s(171) =< aux(52)*(1/3)+aux(53) s(172) =< aux(52)*(1/3)+aux(53) s(173) =< aux(52)*(1/3)+aux(53) s(174) =< aux(52)*(1/5)+aux(54) s(169) =< aux(52)*(1/5)+aux(54) s(175) =< aux(52)*(5/16)+aux(55) s(174) =< aux(52)*(5/16)+aux(55) s(169) =< aux(52)*(5/16)+aux(55) s(181) =< s(173)*s(176) s(182) =< s(173)*s(177) s(183) =< s(170)*s(178) s(184) =< s(170)*s(179) s(185) =< s(174)*s(180) s(186) =< s(174)*s(176) s(187) =< s(175)*aux(51) s(188) =< s(181) s(189) =< s(184) s(190) =< s(186) s(191) =< s(185) s(192) =< s(187) s(138) =< aux(43) s(139) =< aux(43) s(140) =< aux(43) s(141) =< aux(43) s(142) =< aux(43) s(139) =< aux(46) s(143) =< aux(47) s(144) =< aux(48) s(141) =< aux(49) s(145) =< aux(44)+1 s(146) =< aux(44)+3 s(147) =< aux(44) s(148) =< aux(44)+2 s(149) =< aux(44)-1 s(141) =< aux(45)*(1/5)+aux(49) s(142) =< aux(45)*(1/5)+aux(49) s(139) =< aux(45)*(1/3)+aux(46) s(140) =< aux(45)*(1/3)+aux(46) s(141) =< aux(45)*(1/3)+aux(46) s(142) =< aux(45)*(1/3)+aux(46) s(143) =< aux(45)*(1/5)+aux(47) s(138) =< aux(45)*(1/5)+aux(47) s(144) =< aux(45)*(5/16)+aux(48) s(143) =< aux(45)*(5/16)+aux(48) s(138) =< aux(45)*(5/16)+aux(48) s(150) =< s(142)*s(145) s(151) =< s(142)*s(146) s(152) =< s(139)*s(147) s(153) =< s(139)*s(148) s(154) =< s(143)*s(149) s(155) =< s(143)*s(145) s(156) =< s(144)*aux(44) s(157) =< s(150) s(158) =< s(153) s(159) =< s(155) s(160) =< s(154) s(161) =< s(156) with precondition: [Out=0,V1>=0,V>=0] * Chain [54]: 3*s(332)+24*s(333)+6*s(334)+3*s(335)+9*s(336)+15*s(337)+24*s(338)+3*s(345)+9*s(346)+15*s(351)+66*s(352)+15*s(353)+15*s(354)+69*s(355)+3*s(363)+24*s(364)+6*s(365)+3*s(366)+9*s(367)+15*s(368)+24*s(369)+3*s(376)+9*s(377)+15*s(382)+66*s(383)+15*s(384)+15*s(385)+69*s(386)+1*s(449)+1 Such that:aux(58) =< V1 aux(59) =< 2*V1 aux(60) =< 2*V1+1 aux(61) =< 2/3*V1 aux(62) =< 3/5*V1 aux(63) =< 3/8*V1 aux(64) =< 4/5*V1 aux(65) =< V aux(66) =< 2*V aux(67) =< 2*V+1 aux(68) =< 2/3*V aux(69) =< 3/5*V aux(70) =< 3/8*V aux(71) =< 4/5*V s(363) =< aux(65) s(364) =< aux(65) s(365) =< aux(65) s(366) =< aux(65) s(367) =< aux(65) s(364) =< aux(68) s(368) =< aux(69) s(369) =< aux(70) s(366) =< aux(71) s(370) =< aux(66)+1 s(371) =< aux(66)+3 s(372) =< aux(66) s(373) =< aux(66)+2 s(374) =< aux(66)-1 s(366) =< aux(67)*(1/5)+aux(71) s(367) =< aux(67)*(1/5)+aux(71) s(364) =< aux(67)*(1/3)+aux(68) s(365) =< aux(67)*(1/3)+aux(68) s(366) =< aux(67)*(1/3)+aux(68) s(367) =< aux(67)*(1/3)+aux(68) s(368) =< aux(67)*(1/5)+aux(69) s(363) =< aux(67)*(1/5)+aux(69) s(369) =< aux(67)*(5/16)+aux(70) s(368) =< aux(67)*(5/16)+aux(70) s(363) =< aux(67)*(5/16)+aux(70) s(375) =< s(367)*s(370) s(376) =< s(367)*s(371) s(377) =< s(364)*s(372) s(378) =< s(364)*s(373) s(379) =< s(368)*s(374) s(380) =< s(368)*s(370) s(381) =< s(369)*aux(66) s(382) =< s(375) s(383) =< s(378) s(384) =< s(380) s(385) =< s(379) s(386) =< s(381) s(332) =< aux(58) s(333) =< aux(58) s(334) =< aux(58) s(335) =< aux(58) s(336) =< aux(58) s(333) =< aux(61) s(337) =< aux(62) s(338) =< aux(63) s(335) =< aux(64) s(339) =< aux(59)+1 s(340) =< aux(59)+3 s(341) =< aux(59) s(342) =< aux(59)+2 s(343) =< aux(59)-1 s(335) =< aux(60)*(1/5)+aux(64) s(336) =< aux(60)*(1/5)+aux(64) s(333) =< aux(60)*(1/3)+aux(61) s(334) =< aux(60)*(1/3)+aux(61) s(335) =< aux(60)*(1/3)+aux(61) s(336) =< aux(60)*(1/3)+aux(61) s(337) =< aux(60)*(1/5)+aux(62) s(332) =< aux(60)*(1/5)+aux(62) s(338) =< aux(60)*(5/16)+aux(63) s(337) =< aux(60)*(5/16)+aux(63) s(332) =< aux(60)*(5/16)+aux(63) s(344) =< s(336)*s(339) s(345) =< s(336)*s(340) s(346) =< s(333)*s(341) s(347) =< s(333)*s(342) s(348) =< s(337)*s(343) s(349) =< s(337)*s(339) s(350) =< s(338)*aux(59) s(351) =< s(344) s(352) =< s(347) s(353) =< s(349) s(354) =< s(348) s(355) =< s(350) s(449) =< aux(66) with precondition: [V1>=1,V>=0,Out>=0,2*V1>=Out] * Chain [53]: 1*s(519)+8*s(520)+2*s(521)+1*s(522)+3*s(523)+5*s(524)+8*s(525)+1*s(532)+3*s(533)+5*s(538)+22*s(539)+5*s(540)+5*s(541)+23*s(542)+1*s(543)+1 Such that:s(543) =< 2 s(512) =< V s(513) =< 2*V s(514) =< 2*V+1 s(515) =< 2/3*V s(516) =< 3/5*V s(517) =< 3/8*V s(518) =< 4/5*V s(519) =< s(512) s(520) =< s(512) s(521) =< s(512) s(522) =< s(512) s(523) =< s(512) s(520) =< s(515) s(524) =< s(516) s(525) =< s(517) s(522) =< s(518) s(526) =< s(513)+1 s(527) =< s(513)+3 s(528) =< s(513) s(529) =< s(513)+2 s(530) =< s(513)-1 s(522) =< s(514)*(1/5)+s(518) s(523) =< s(514)*(1/5)+s(518) s(520) =< s(514)*(1/3)+s(515) s(521) =< s(514)*(1/3)+s(515) s(522) =< s(514)*(1/3)+s(515) s(523) =< s(514)*(1/3)+s(515) s(524) =< s(514)*(1/5)+s(516) s(519) =< s(514)*(1/5)+s(516) s(525) =< s(514)*(5/16)+s(517) s(524) =< s(514)*(5/16)+s(517) s(519) =< s(514)*(5/16)+s(517) s(531) =< s(523)*s(526) s(532) =< s(523)*s(527) s(533) =< s(520)*s(528) s(534) =< s(520)*s(529) s(535) =< s(524)*s(530) s(536) =< s(524)*s(526) s(537) =< s(525)*s(513) s(538) =< s(531) s(539) =< s(534) s(540) =< s(536) s(541) =< s(535) s(542) =< s(537) with precondition: [V1=2,1>=Out,V>=1,Out>=0] * Chain [52]: 1*s(551)+8*s(552)+2*s(553)+1*s(554)+3*s(555)+5*s(556)+8*s(557)+1*s(564)+3*s(565)+5*s(570)+22*s(571)+5*s(572)+5*s(573)+23*s(574)+2*s(575)+0 Such that:s(544) =< V1 s(545) =< 2*V1 s(546) =< 2*V1+1 s(547) =< 2/3*V1 s(548) =< 3/5*V1 s(549) =< 3/8*V1 s(550) =< 4/5*V1 aux(72) =< 2 s(575) =< aux(72) s(551) =< s(544) s(552) =< s(544) s(553) =< s(544) s(554) =< s(544) s(555) =< s(544) s(552) =< s(547) s(556) =< s(548) s(557) =< s(549) s(554) =< s(550) s(558) =< s(545)+1 s(559) =< s(545)+3 s(560) =< s(545) s(561) =< s(545)+2 s(562) =< s(545)-1 s(554) =< s(546)*(1/5)+s(550) s(555) =< s(546)*(1/5)+s(550) s(552) =< s(546)*(1/3)+s(547) s(553) =< s(546)*(1/3)+s(547) s(554) =< s(546)*(1/3)+s(547) s(555) =< s(546)*(1/3)+s(547) s(556) =< s(546)*(1/5)+s(548) s(551) =< s(546)*(1/5)+s(548) s(557) =< s(546)*(5/16)+s(549) s(556) =< s(546)*(5/16)+s(549) s(551) =< s(546)*(5/16)+s(549) s(563) =< s(555)*s(558) s(564) =< s(555)*s(559) s(565) =< s(552)*s(560) s(566) =< s(552)*s(561) s(567) =< s(556)*s(562) s(568) =< s(556)*s(558) s(569) =< s(557)*s(545) s(570) =< s(563) s(571) =< s(566) s(572) =< s(568) s(573) =< s(567) s(574) =< s(569) with precondition: [V=2,Out=0,V1>=0] * Chain [51]: 1*s(584)+8*s(585)+2*s(586)+1*s(587)+3*s(588)+5*s(589)+8*s(590)+1*s(597)+3*s(598)+5*s(603)+22*s(604)+5*s(605)+5*s(606)+23*s(607)+1*s(608)+1 Such that:s(608) =< 2 s(577) =< V1 s(578) =< 2*V1 s(579) =< 2*V1+1 s(580) =< 2/3*V1 s(581) =< 3/5*V1 s(582) =< 3/8*V1 s(583) =< 4/5*V1 s(584) =< s(577) s(585) =< s(577) s(586) =< s(577) s(587) =< s(577) s(588) =< s(577) s(585) =< s(580) s(589) =< s(581) s(590) =< s(582) s(587) =< s(583) s(591) =< s(578)+1 s(592) =< s(578)+3 s(593) =< s(578) s(594) =< s(578)+2 s(595) =< s(578)-1 s(587) =< s(579)*(1/5)+s(583) s(588) =< s(579)*(1/5)+s(583) s(585) =< s(579)*(1/3)+s(580) s(586) =< s(579)*(1/3)+s(580) s(587) =< s(579)*(1/3)+s(580) s(588) =< s(579)*(1/3)+s(580) s(589) =< s(579)*(1/5)+s(581) s(584) =< s(579)*(1/5)+s(581) s(590) =< s(579)*(5/16)+s(582) s(589) =< s(579)*(5/16)+s(582) s(584) =< s(579)*(5/16)+s(582) s(596) =< s(588)*s(591) s(597) =< s(588)*s(592) s(598) =< s(585)*s(593) s(599) =< s(585)*s(594) s(600) =< s(589)*s(595) s(601) =< s(589)*s(591) s(602) =< s(590)*s(578) s(603) =< s(596) s(604) =< s(599) s(605) =< s(601) s(606) =< s(600) s(607) =< s(602) with precondition: [V=2,Out>=0,2*V1>=Out+2] #### Cost of chains of fun3(V1,Out): * Chain [58]: 1*s(809)+8*s(810)+2*s(811)+1*s(812)+3*s(813)+5*s(814)+8*s(815)+1*s(822)+3*s(823)+5*s(828)+22*s(829)+5*s(830)+5*s(831)+23*s(832)+0 Such that:s(802) =< V1 s(803) =< 2*V1 s(804) =< 2*V1+1 s(805) =< 2/3*V1 s(806) =< 3/5*V1 s(807) =< 3/8*V1 s(808) =< 4/5*V1 s(809) =< s(802) s(810) =< s(802) s(811) =< s(802) s(812) =< s(802) s(813) =< s(802) s(810) =< s(805) s(814) =< s(806) s(815) =< s(807) s(812) =< s(808) s(816) =< s(803)+1 s(817) =< s(803)+3 s(818) =< s(803) s(819) =< s(803)+2 s(820) =< s(803)-1 s(812) =< s(804)*(1/5)+s(808) s(813) =< s(804)*(1/5)+s(808) s(810) =< s(804)*(1/3)+s(805) s(811) =< s(804)*(1/3)+s(805) s(812) =< s(804)*(1/3)+s(805) s(813) =< s(804)*(1/3)+s(805) s(814) =< s(804)*(1/5)+s(806) s(809) =< s(804)*(1/5)+s(806) s(815) =< s(804)*(5/16)+s(807) s(814) =< s(804)*(5/16)+s(807) s(809) =< s(804)*(5/16)+s(807) s(821) =< s(813)*s(816) s(822) =< s(813)*s(817) s(823) =< s(810)*s(818) s(824) =< s(810)*s(819) s(825) =< s(814)*s(820) s(826) =< s(814)*s(816) s(827) =< s(815)*s(803) s(828) =< s(821) s(829) =< s(824) s(830) =< s(826) s(831) =< s(825) s(832) =< s(827) with precondition: [V1>=1,Out>=1,2*V1+1>=Out] * Chain [57]: 0 with precondition: [Out=0,V1>=0] * Chain [56]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun4(V1,V,Out): * Chain [64]: 2*s(840)+16*s(841)+4*s(842)+2*s(843)+6*s(844)+10*s(845)+16*s(846)+2*s(853)+6*s(854)+10*s(859)+44*s(860)+10*s(861)+10*s(862)+46*s(863)+3*s(871)+24*s(872)+6*s(873)+3*s(874)+9*s(875)+15*s(876)+24*s(877)+3*s(884)+9*s(885)+15*s(890)+66*s(891)+15*s(892)+15*s(893)+69*s(894)+3*s(895)+1*s(960)+0 Such that:s(960) =< 2 aux(91) =< V1 aux(92) =< 2*V1 aux(93) =< 2*V1+1 aux(94) =< 2/3*V1 aux(95) =< 3/5*V1 aux(96) =< 3/8*V1 aux(97) =< 4/5*V1 aux(98) =< V aux(99) =< 2*V aux(100) =< 2*V+1 aux(101) =< 2/3*V aux(102) =< 3/5*V aux(103) =< 3/8*V aux(104) =< 4/5*V s(895) =< aux(99) s(871) =< aux(98) s(872) =< aux(98) s(873) =< aux(98) s(874) =< aux(98) s(875) =< aux(98) s(872) =< aux(101) s(876) =< aux(102) s(877) =< aux(103) s(874) =< aux(104) s(878) =< aux(99)+1 s(879) =< aux(99)+3 s(880) =< aux(99) s(881) =< aux(99)+2 s(882) =< aux(99)-1 s(874) =< aux(100)*(1/5)+aux(104) s(875) =< aux(100)*(1/5)+aux(104) s(872) =< aux(100)*(1/3)+aux(101) s(873) =< aux(100)*(1/3)+aux(101) s(874) =< aux(100)*(1/3)+aux(101) s(875) =< aux(100)*(1/3)+aux(101) s(876) =< aux(100)*(1/5)+aux(102) s(871) =< aux(100)*(1/5)+aux(102) s(877) =< aux(100)*(5/16)+aux(103) s(876) =< aux(100)*(5/16)+aux(103) s(871) =< aux(100)*(5/16)+aux(103) s(883) =< s(875)*s(878) s(884) =< s(875)*s(879) s(885) =< s(872)*s(880) s(886) =< s(872)*s(881) s(887) =< s(876)*s(882) s(888) =< s(876)*s(878) s(889) =< s(877)*aux(99) s(890) =< s(883) s(891) =< s(886) s(892) =< s(888) s(893) =< s(887) s(894) =< s(889) s(840) =< aux(91) s(841) =< aux(91) s(842) =< aux(91) s(843) =< aux(91) s(844) =< aux(91) s(841) =< aux(94) s(845) =< aux(95) s(846) =< aux(96) s(843) =< aux(97) s(847) =< aux(92)+1 s(848) =< aux(92)+3 s(849) =< aux(92) s(850) =< aux(92)+2 s(851) =< aux(92)-1 s(843) =< aux(93)*(1/5)+aux(97) s(844) =< aux(93)*(1/5)+aux(97) s(841) =< aux(93)*(1/3)+aux(94) s(842) =< aux(93)*(1/3)+aux(94) s(843) =< aux(93)*(1/3)+aux(94) s(844) =< aux(93)*(1/3)+aux(94) s(845) =< aux(93)*(1/5)+aux(95) s(840) =< aux(93)*(1/5)+aux(95) s(846) =< aux(93)*(5/16)+aux(96) s(845) =< aux(93)*(5/16)+aux(96) s(840) =< aux(93)*(5/16)+aux(96) s(852) =< s(844)*s(847) s(853) =< s(844)*s(848) s(854) =< s(841)*s(849) s(855) =< s(841)*s(850) s(856) =< s(845)*s(851) s(857) =< s(845)*s(847) s(858) =< s(846)*aux(92) s(859) =< s(852) s(860) =< s(855) s(861) =< s(857) s(862) =< s(856) s(863) =< s(858) with precondition: [Out=0,V1>=0,V>=0] * Chain [63]: 3*s(1002)+24*s(1003)+6*s(1004)+3*s(1005)+9*s(1006)+15*s(1007)+24*s(1008)+3*s(1015)+9*s(1016)+15*s(1021)+66*s(1022)+15*s(1023)+15*s(1024)+69*s(1025)+4*s(1033)+32*s(1034)+8*s(1035)+4*s(1036)+12*s(1037)+20*s(1038)+32*s(1039)+4*s(1046)+12*s(1047)+20*s(1052)+88*s(1053)+20*s(1054)+20*s(1055)+92*s(1056)+1*s(1119)+2*s(1182)+1 Such that:aux(106) =< 2 aux(107) =< V1 aux(108) =< 2*V1 aux(109) =< 2*V1+1 aux(110) =< 2/3*V1 aux(111) =< 3/5*V1 aux(112) =< 3/8*V1 aux(113) =< 4/5*V1 aux(114) =< V aux(115) =< 2*V aux(116) =< 2*V+1 aux(117) =< 2/3*V aux(118) =< 3/5*V aux(119) =< 3/8*V aux(120) =< 4/5*V s(1182) =< aux(106) s(1033) =< aux(114) s(1034) =< aux(114) s(1035) =< aux(114) s(1036) =< aux(114) s(1037) =< aux(114) s(1034) =< aux(117) s(1038) =< aux(118) s(1039) =< aux(119) s(1036) =< aux(120) s(1040) =< aux(115)+1 s(1041) =< aux(115)+3 s(1042) =< aux(115) s(1043) =< aux(115)+2 s(1044) =< aux(115)-1 s(1036) =< aux(116)*(1/5)+aux(120) s(1037) =< aux(116)*(1/5)+aux(120) s(1034) =< aux(116)*(1/3)+aux(117) s(1035) =< aux(116)*(1/3)+aux(117) s(1036) =< aux(116)*(1/3)+aux(117) s(1037) =< aux(116)*(1/3)+aux(117) s(1038) =< aux(116)*(1/5)+aux(118) s(1033) =< aux(116)*(1/5)+aux(118) s(1039) =< aux(116)*(5/16)+aux(119) s(1038) =< aux(116)*(5/16)+aux(119) s(1033) =< aux(116)*(5/16)+aux(119) s(1045) =< s(1037)*s(1040) s(1046) =< s(1037)*s(1041) s(1047) =< s(1034)*s(1042) s(1048) =< s(1034)*s(1043) s(1049) =< s(1038)*s(1044) s(1050) =< s(1038)*s(1040) s(1051) =< s(1039)*aux(115) s(1052) =< s(1045) s(1053) =< s(1048) s(1054) =< s(1050) s(1055) =< s(1049) s(1056) =< s(1051) s(1002) =< aux(107) s(1003) =< aux(107) s(1004) =< aux(107) s(1005) =< aux(107) s(1006) =< aux(107) s(1003) =< aux(110) s(1007) =< aux(111) s(1008) =< aux(112) s(1005) =< aux(113) s(1009) =< aux(108)+1 s(1010) =< aux(108)+3 s(1011) =< aux(108) s(1012) =< aux(108)+2 s(1013) =< aux(108)-1 s(1005) =< aux(109)*(1/5)+aux(113) s(1006) =< aux(109)*(1/5)+aux(113) s(1003) =< aux(109)*(1/3)+aux(110) s(1004) =< aux(109)*(1/3)+aux(110) s(1005) =< aux(109)*(1/3)+aux(110) s(1006) =< aux(109)*(1/3)+aux(110) s(1007) =< aux(109)*(1/5)+aux(111) s(1002) =< aux(109)*(1/5)+aux(111) s(1008) =< aux(109)*(5/16)+aux(112) s(1007) =< aux(109)*(5/16)+aux(112) s(1002) =< aux(109)*(5/16)+aux(112) s(1014) =< s(1006)*s(1009) s(1015) =< s(1006)*s(1010) s(1016) =< s(1003)*s(1011) s(1017) =< s(1003)*s(1012) s(1018) =< s(1007)*s(1013) s(1019) =< s(1007)*s(1009) s(1020) =< s(1008)*aux(108) s(1021) =< s(1014) s(1022) =< s(1017) s(1023) =< s(1019) s(1024) =< s(1018) s(1025) =< s(1020) s(1119) =< aux(115) with precondition: [Out=2,V1>=0,V>=0] * Chain [62]: 3*s(1222)+24*s(1223)+6*s(1224)+3*s(1225)+9*s(1226)+15*s(1227)+24*s(1228)+3*s(1235)+9*s(1236)+15*s(1241)+66*s(1242)+15*s(1243)+15*s(1244)+69*s(1245)+4*s(1253)+32*s(1254)+8*s(1255)+4*s(1256)+12*s(1257)+20*s(1258)+32*s(1259)+4*s(1266)+12*s(1267)+20*s(1272)+88*s(1273)+20*s(1274)+20*s(1275)+92*s(1276)+1*s(1339)+1*s(1433)+1 Such that:s(1433) =< 1 aux(122) =< V1 aux(123) =< 2*V1 aux(124) =< 2*V1+1 aux(125) =< 2/3*V1 aux(126) =< 3/5*V1 aux(127) =< 3/8*V1 aux(128) =< 4/5*V1 aux(129) =< V aux(130) =< 2*V aux(131) =< 2*V+1 aux(132) =< 2/3*V aux(133) =< 3/5*V aux(134) =< 3/8*V aux(135) =< 4/5*V s(1253) =< aux(129) s(1254) =< aux(129) s(1255) =< aux(129) s(1256) =< aux(129) s(1257) =< aux(129) s(1254) =< aux(132) s(1258) =< aux(133) s(1259) =< aux(134) s(1256) =< aux(135) s(1260) =< aux(130)+1 s(1261) =< aux(130)+3 s(1262) =< aux(130) s(1263) =< aux(130)+2 s(1264) =< aux(130)-1 s(1256) =< aux(131)*(1/5)+aux(135) s(1257) =< aux(131)*(1/5)+aux(135) s(1254) =< aux(131)*(1/3)+aux(132) s(1255) =< aux(131)*(1/3)+aux(132) s(1256) =< aux(131)*(1/3)+aux(132) s(1257) =< aux(131)*(1/3)+aux(132) s(1258) =< aux(131)*(1/5)+aux(133) s(1253) =< aux(131)*(1/5)+aux(133) s(1259) =< aux(131)*(5/16)+aux(134) s(1258) =< aux(131)*(5/16)+aux(134) s(1253) =< aux(131)*(5/16)+aux(134) s(1265) =< s(1257)*s(1260) s(1266) =< s(1257)*s(1261) s(1267) =< s(1254)*s(1262) s(1268) =< s(1254)*s(1263) s(1269) =< s(1258)*s(1264) s(1270) =< s(1258)*s(1260) s(1271) =< s(1259)*aux(130) s(1272) =< s(1265) s(1273) =< s(1268) s(1274) =< s(1270) s(1275) =< s(1269) s(1276) =< s(1271) s(1222) =< aux(122) s(1223) =< aux(122) s(1224) =< aux(122) s(1225) =< aux(122) s(1226) =< aux(122) s(1223) =< aux(125) s(1227) =< aux(126) s(1228) =< aux(127) s(1225) =< aux(128) s(1229) =< aux(123)+1 s(1230) =< aux(123)+3 s(1231) =< aux(123) s(1232) =< aux(123)+2 s(1233) =< aux(123)-1 s(1225) =< aux(124)*(1/5)+aux(128) s(1226) =< aux(124)*(1/5)+aux(128) s(1223) =< aux(124)*(1/3)+aux(125) s(1224) =< aux(124)*(1/3)+aux(125) s(1225) =< aux(124)*(1/3)+aux(125) s(1226) =< aux(124)*(1/3)+aux(125) s(1227) =< aux(124)*(1/5)+aux(126) s(1222) =< aux(124)*(1/5)+aux(126) s(1228) =< aux(124)*(5/16)+aux(127) s(1227) =< aux(124)*(5/16)+aux(127) s(1222) =< aux(124)*(5/16)+aux(127) s(1234) =< s(1226)*s(1229) s(1235) =< s(1226)*s(1230) s(1236) =< s(1223)*s(1231) s(1237) =< s(1223)*s(1232) s(1238) =< s(1227)*s(1233) s(1239) =< s(1227)*s(1229) s(1240) =< s(1228)*aux(123) s(1241) =< s(1234) s(1242) =< s(1237) s(1243) =< s(1239) s(1244) =< s(1238) s(1245) =< s(1240) s(1339) =< aux(123) with precondition: [Out=1,V1>=1,V>=0] * Chain [61]: 1*s(1441)+8*s(1442)+2*s(1443)+1*s(1444)+3*s(1445)+5*s(1446)+8*s(1447)+1*s(1454)+3*s(1455)+5*s(1460)+22*s(1461)+5*s(1462)+5*s(1463)+23*s(1464)+2*s(1465)+0 Such that:s(1434) =< V1 s(1435) =< 2*V1 s(1436) =< 2*V1+1 s(1437) =< 2/3*V1 s(1438) =< 3/5*V1 s(1439) =< 3/8*V1 s(1440) =< 4/5*V1 aux(136) =< 2 s(1465) =< aux(136) s(1441) =< s(1434) s(1442) =< s(1434) s(1443) =< s(1434) s(1444) =< s(1434) s(1445) =< s(1434) s(1442) =< s(1437) s(1446) =< s(1438) s(1447) =< s(1439) s(1444) =< s(1440) s(1448) =< s(1435)+1 s(1449) =< s(1435)+3 s(1450) =< s(1435) s(1451) =< s(1435)+2 s(1452) =< s(1435)-1 s(1444) =< s(1436)*(1/5)+s(1440) s(1445) =< s(1436)*(1/5)+s(1440) s(1442) =< s(1436)*(1/3)+s(1437) s(1443) =< s(1436)*(1/3)+s(1437) s(1444) =< s(1436)*(1/3)+s(1437) s(1445) =< s(1436)*(1/3)+s(1437) s(1446) =< s(1436)*(1/5)+s(1438) s(1441) =< s(1436)*(1/5)+s(1438) s(1447) =< s(1436)*(5/16)+s(1439) s(1446) =< s(1436)*(5/16)+s(1439) s(1441) =< s(1436)*(5/16)+s(1439) s(1453) =< s(1445)*s(1448) s(1454) =< s(1445)*s(1449) s(1455) =< s(1442)*s(1450) s(1456) =< s(1442)*s(1451) s(1457) =< s(1446)*s(1452) s(1458) =< s(1446)*s(1448) s(1459) =< s(1447)*s(1435) s(1460) =< s(1453) s(1461) =< s(1456) s(1462) =< s(1458) s(1463) =< s(1457) s(1464) =< s(1459) with precondition: [V=2,Out=0,V1>=0] * Chain [60]: 1*s(1474)+8*s(1475)+2*s(1476)+1*s(1477)+3*s(1478)+5*s(1479)+8*s(1480)+1*s(1487)+3*s(1488)+5*s(1493)+22*s(1494)+5*s(1495)+5*s(1496)+23*s(1497)+1*s(1498)+1 Such that:s(1498) =< 2 s(1467) =< V1 s(1468) =< 2*V1 s(1469) =< 2*V1+1 s(1470) =< 2/3*V1 s(1471) =< 3/5*V1 s(1472) =< 3/8*V1 s(1473) =< 4/5*V1 s(1474) =< s(1467) s(1475) =< s(1467) s(1476) =< s(1467) s(1477) =< s(1467) s(1478) =< s(1467) s(1475) =< s(1470) s(1479) =< s(1471) s(1480) =< s(1472) s(1477) =< s(1473) s(1481) =< s(1468)+1 s(1482) =< s(1468)+3 s(1483) =< s(1468) s(1484) =< s(1468)+2 s(1485) =< s(1468)-1 s(1477) =< s(1469)*(1/5)+s(1473) s(1478) =< s(1469)*(1/5)+s(1473) s(1475) =< s(1469)*(1/3)+s(1470) s(1476) =< s(1469)*(1/3)+s(1470) s(1477) =< s(1469)*(1/3)+s(1470) s(1478) =< s(1469)*(1/3)+s(1470) s(1479) =< s(1469)*(1/5)+s(1471) s(1474) =< s(1469)*(1/5)+s(1471) s(1480) =< s(1469)*(5/16)+s(1472) s(1479) =< s(1469)*(5/16)+s(1472) s(1474) =< s(1469)*(5/16)+s(1472) s(1486) =< s(1478)*s(1481) s(1487) =< s(1478)*s(1482) s(1488) =< s(1475)*s(1483) s(1489) =< s(1475)*s(1484) s(1490) =< s(1479)*s(1485) s(1491) =< s(1479)*s(1481) s(1492) =< s(1480)*s(1468) s(1493) =< s(1486) s(1494) =< s(1489) s(1495) =< s(1491) s(1496) =< s(1490) s(1497) =< s(1492) with precondition: [V=2,Out=1,2*V1>=3] * Chain [59]: 2*s(1506)+16*s(1507)+4*s(1508)+2*s(1509)+6*s(1510)+10*s(1511)+16*s(1512)+2*s(1519)+6*s(1520)+10*s(1525)+44*s(1526)+10*s(1527)+10*s(1528)+46*s(1529)+1*s(1561)+1 Such that:s(1561) =< 2 aux(137) =< V1 aux(138) =< 2*V1 aux(139) =< 2*V1+1 aux(140) =< 2/3*V1 aux(141) =< 3/5*V1 aux(142) =< 3/8*V1 aux(143) =< 4/5*V1 s(1506) =< aux(137) s(1507) =< aux(137) s(1508) =< aux(137) s(1509) =< aux(137) s(1510) =< aux(137) s(1507) =< aux(140) s(1511) =< aux(141) s(1512) =< aux(142) s(1509) =< aux(143) s(1513) =< aux(138)+1 s(1514) =< aux(138)+3 s(1515) =< aux(138) s(1516) =< aux(138)+2 s(1517) =< aux(138)-1 s(1509) =< aux(139)*(1/5)+aux(143) s(1510) =< aux(139)*(1/5)+aux(143) s(1507) =< aux(139)*(1/3)+aux(140) s(1508) =< aux(139)*(1/3)+aux(140) s(1509) =< aux(139)*(1/3)+aux(140) s(1510) =< aux(139)*(1/3)+aux(140) s(1511) =< aux(139)*(1/5)+aux(141) s(1506) =< aux(139)*(1/5)+aux(141) s(1512) =< aux(139)*(5/16)+aux(142) s(1511) =< aux(139)*(5/16)+aux(142) s(1506) =< aux(139)*(5/16)+aux(142) s(1518) =< s(1510)*s(1513) s(1519) =< s(1510)*s(1514) s(1520) =< s(1507)*s(1515) s(1521) =< s(1507)*s(1516) s(1522) =< s(1511)*s(1517) s(1523) =< s(1511)*s(1513) s(1524) =< s(1512)*aux(138) s(1525) =< s(1518) s(1526) =< s(1521) s(1527) =< s(1523) s(1528) =< s(1522) s(1529) =< s(1524) with precondition: [V=2,Out=2,V1>=0] #### Cost of chains of fun5(Out): * Chain [66]: 0 with precondition: [Out=0] * Chain [65]: 0 with precondition: [Out=2] #### Cost of chains of fun6(Out): * Chain [68]: 0 with precondition: [Out=0] * Chain [67]: 0 with precondition: [Out=1] #### Cost of chains of fun7(V1,V,Out): * Chain [72]: 2*s(1859)+16*s(1860)+4*s(1861)+2*s(1862)+6*s(1863)+10*s(1864)+16*s(1865)+2*s(1872)+6*s(1873)+10*s(1878)+44*s(1879)+10*s(1880)+10*s(1881)+46*s(1882)+3*s(1890)+24*s(1891)+6*s(1892)+3*s(1893)+9*s(1894)+15*s(1895)+24*s(1896)+3*s(1903)+9*s(1904)+15*s(1909)+66*s(1910)+15*s(1911)+15*s(1912)+69*s(1913)+3*s(1914)+6*s(1916)+10*s(1984)+3 Such that:aux(174) =< 2 aux(175) =< V1 aux(176) =< 2*V1 aux(177) =< 2*V1+1 aux(178) =< 2/3*V1 aux(179) =< 3/5*V1 aux(180) =< 3/8*V1 aux(181) =< 4/5*V1 aux(182) =< V aux(183) =< 2*V aux(184) =< 2*V+1 aux(185) =< 2/3*V aux(186) =< 3/5*V aux(187) =< 3/8*V aux(188) =< 4/5*V s(1984) =< aux(174) s(1914) =< aux(183) s(1890) =< aux(182) s(1891) =< aux(182) s(1892) =< aux(182) s(1893) =< aux(182) s(1894) =< aux(182) s(1891) =< aux(185) s(1895) =< aux(186) s(1896) =< aux(187) s(1893) =< aux(188) s(1897) =< aux(183)+1 s(1898) =< aux(183)+3 s(1899) =< aux(183) s(1900) =< aux(183)+2 s(1901) =< aux(183)-1 s(1893) =< aux(184)*(1/5)+aux(188) s(1894) =< aux(184)*(1/5)+aux(188) s(1891) =< aux(184)*(1/3)+aux(185) s(1892) =< aux(184)*(1/3)+aux(185) s(1893) =< aux(184)*(1/3)+aux(185) s(1894) =< aux(184)*(1/3)+aux(185) s(1895) =< aux(184)*(1/5)+aux(186) s(1890) =< aux(184)*(1/5)+aux(186) s(1896) =< aux(184)*(5/16)+aux(187) s(1895) =< aux(184)*(5/16)+aux(187) s(1890) =< aux(184)*(5/16)+aux(187) s(1902) =< s(1894)*s(1897) s(1903) =< s(1894)*s(1898) s(1904) =< s(1891)*s(1899) s(1905) =< s(1891)*s(1900) s(1906) =< s(1895)*s(1901) s(1907) =< s(1895)*s(1897) s(1908) =< s(1896)*aux(183) s(1909) =< s(1902) s(1910) =< s(1905) s(1911) =< s(1907) s(1912) =< s(1906) s(1913) =< s(1908) s(1916) =< aux(176) s(1859) =< aux(175) s(1860) =< aux(175) s(1861) =< aux(175) s(1862) =< aux(175) s(1863) =< aux(175) s(1860) =< aux(178) s(1864) =< aux(179) s(1865) =< aux(180) s(1862) =< aux(181) s(1866) =< aux(176)+1 s(1867) =< aux(176)+3 s(1868) =< aux(176) s(1869) =< aux(176)+2 s(1870) =< aux(176)-1 s(1862) =< aux(177)*(1/5)+aux(181) s(1863) =< aux(177)*(1/5)+aux(181) s(1860) =< aux(177)*(1/3)+aux(178) s(1861) =< aux(177)*(1/3)+aux(178) s(1862) =< aux(177)*(1/3)+aux(178) s(1863) =< aux(177)*(1/3)+aux(178) s(1864) =< aux(177)*(1/5)+aux(179) s(1859) =< aux(177)*(1/5)+aux(179) s(1865) =< aux(177)*(5/16)+aux(180) s(1864) =< aux(177)*(5/16)+aux(180) s(1859) =< aux(177)*(5/16)+aux(180) s(1871) =< s(1863)*s(1866) s(1872) =< s(1863)*s(1867) s(1873) =< s(1860)*s(1868) s(1874) =< s(1860)*s(1869) s(1875) =< s(1864)*s(1870) s(1876) =< s(1864)*s(1866) s(1877) =< s(1865)*aux(176) s(1878) =< s(1871) s(1879) =< s(1874) s(1880) =< s(1876) s(1881) =< s(1875) s(1882) =< s(1877) with precondition: [Out=0,V1>=0,V>=0] * Chain [71]: 1*s(2035)+8*s(2036)+2*s(2037)+1*s(2038)+3*s(2039)+5*s(2040)+8*s(2041)+1*s(2048)+3*s(2049)+5*s(2054)+22*s(2055)+5*s(2056)+5*s(2057)+23*s(2058)+2*s(2066)+16*s(2067)+4*s(2068)+2*s(2069)+6*s(2070)+10*s(2071)+16*s(2072)+2*s(2079)+6*s(2080)+10*s(2085)+44*s(2086)+10*s(2087)+10*s(2088)+46*s(2089)+22*s(2093)+32*s(2132)+4*s(2133)+2*s(2135)+6 Such that:s(2129) =< 1 s(2028) =< V1 aux(189) =< 2*V1 s(2030) =< 2*V1+1 s(2031) =< 2/3*V1 s(2032) =< 3/5*V1 s(2033) =< 3/8*V1 s(2034) =< 4/5*V1 aux(192) =< 2 aux(193) =< V aux(194) =< 2*V aux(195) =< 2*V+1 aux(196) =< 2/3*V aux(197) =< 3/5*V aux(198) =< 3/8*V aux(199) =< 4/5*V s(2132) =< aux(192) s(2133) =< s(2129) s(2133) =< aux(192) s(2134) =< aux(192) s(2134) =< s(2129) s(2135) =< s(2134) s(2066) =< aux(193) s(2067) =< aux(193) s(2068) =< aux(193) s(2069) =< aux(193) s(2070) =< aux(193) s(2067) =< aux(196) s(2071) =< aux(197) s(2072) =< aux(198) s(2069) =< aux(199) s(2073) =< aux(194)+1 s(2074) =< aux(194)+3 s(2075) =< aux(194) s(2076) =< aux(194)+2 s(2077) =< aux(194)-1 s(2069) =< aux(195)*(1/5)+aux(199) s(2070) =< aux(195)*(1/5)+aux(199) s(2067) =< aux(195)*(1/3)+aux(196) s(2068) =< aux(195)*(1/3)+aux(196) s(2069) =< aux(195)*(1/3)+aux(196) s(2070) =< aux(195)*(1/3)+aux(196) s(2071) =< aux(195)*(1/5)+aux(197) s(2066) =< aux(195)*(1/5)+aux(197) s(2072) =< aux(195)*(5/16)+aux(198) s(2071) =< aux(195)*(5/16)+aux(198) s(2066) =< aux(195)*(5/16)+aux(198) s(2078) =< s(2070)*s(2073) s(2079) =< s(2070)*s(2074) s(2080) =< s(2067)*s(2075) s(2081) =< s(2067)*s(2076) s(2082) =< s(2071)*s(2077) s(2083) =< s(2071)*s(2073) s(2084) =< s(2072)*aux(194) s(2085) =< s(2078) s(2086) =< s(2081) s(2087) =< s(2083) s(2088) =< s(2082) s(2089) =< s(2084) s(2093) =< aux(189) s(2035) =< s(2028) s(2036) =< s(2028) s(2037) =< s(2028) s(2038) =< s(2028) s(2039) =< s(2028) s(2036) =< s(2031) s(2040) =< s(2032) s(2041) =< s(2033) s(2038) =< s(2034) s(2042) =< aux(189)+1 s(2043) =< aux(189)+3 s(2044) =< aux(189) s(2045) =< aux(189)+2 s(2046) =< aux(189)-1 s(2038) =< s(2030)*(1/5)+s(2034) s(2039) =< s(2030)*(1/5)+s(2034) s(2036) =< s(2030)*(1/3)+s(2031) s(2037) =< s(2030)*(1/3)+s(2031) s(2038) =< s(2030)*(1/3)+s(2031) s(2039) =< s(2030)*(1/3)+s(2031) s(2040) =< s(2030)*(1/5)+s(2032) s(2035) =< s(2030)*(1/5)+s(2032) s(2041) =< s(2030)*(5/16)+s(2033) s(2040) =< s(2030)*(5/16)+s(2033) s(2035) =< s(2030)*(5/16)+s(2033) s(2047) =< s(2039)*s(2042) s(2048) =< s(2039)*s(2043) s(2049) =< s(2036)*s(2044) s(2050) =< s(2036)*s(2045) s(2051) =< s(2040)*s(2046) s(2052) =< s(2040)*s(2042) s(2053) =< s(2041)*aux(189) s(2054) =< s(2047) s(2055) =< s(2050) s(2056) =< s(2052) s(2057) =< s(2051) s(2058) =< s(2053) with precondition: [V1>=1,V>=1,Out>=1,2*V1>=Out] * Chain [70]: 1*s(2152)+8*s(2153)+2*s(2154)+1*s(2155)+3*s(2156)+5*s(2157)+8*s(2158)+1*s(2165)+3*s(2166)+5*s(2171)+22*s(2172)+5*s(2173)+5*s(2174)+23*s(2175)+2*s(2176)+3*s(2178)+3 Such that:s(2145) =< V1 aux(200) =< 2*V1 s(2147) =< 2*V1+1 s(2148) =< 2/3*V1 s(2149) =< 3/5*V1 s(2150) =< 3/8*V1 s(2151) =< 4/5*V1 aux(201) =< 2 s(2176) =< aux(201) s(2178) =< aux(200) s(2152) =< s(2145) s(2153) =< s(2145) s(2154) =< s(2145) s(2155) =< s(2145) s(2156) =< s(2145) s(2153) =< s(2148) s(2157) =< s(2149) s(2158) =< s(2150) s(2155) =< s(2151) s(2159) =< aux(200)+1 s(2160) =< aux(200)+3 s(2161) =< aux(200) s(2162) =< aux(200)+2 s(2163) =< aux(200)-1 s(2155) =< s(2147)*(1/5)+s(2151) s(2156) =< s(2147)*(1/5)+s(2151) s(2153) =< s(2147)*(1/3)+s(2148) s(2154) =< s(2147)*(1/3)+s(2148) s(2155) =< s(2147)*(1/3)+s(2148) s(2156) =< s(2147)*(1/3)+s(2148) s(2157) =< s(2147)*(1/5)+s(2149) s(2152) =< s(2147)*(1/5)+s(2149) s(2158) =< s(2147)*(5/16)+s(2150) s(2157) =< s(2147)*(5/16)+s(2150) s(2152) =< s(2147)*(5/16)+s(2150) s(2164) =< s(2156)*s(2159) s(2165) =< s(2156)*s(2160) s(2166) =< s(2153)*s(2161) s(2167) =< s(2153)*s(2162) s(2168) =< s(2157)*s(2163) s(2169) =< s(2157)*s(2159) s(2170) =< s(2158)*aux(200) s(2171) =< s(2164) s(2172) =< s(2167) s(2173) =< s(2169) s(2174) =< s(2168) s(2175) =< s(2170) with precondition: [V=2,Out=0,V1>=0] * Chain [69]: 1*s(2189)+8*s(2190)+2*s(2191)+1*s(2192)+3*s(2193)+5*s(2194)+8*s(2195)+1*s(2202)+3*s(2203)+5*s(2208)+22*s(2209)+5*s(2210)+5*s(2211)+23*s(2212)+7*s(2216)+15*s(2217)+6 Such that:s(2215) =< 2 s(2182) =< V1 s(2184) =< 2*V1+1 s(2185) =< 2/3*V1 s(2186) =< 3/5*V1 s(2187) =< 3/8*V1 s(2188) =< 4/5*V1 aux(202) =< 2*V1 s(2216) =< s(2215) s(2217) =< aux(202) s(2189) =< s(2182) s(2190) =< s(2182) s(2191) =< s(2182) s(2192) =< s(2182) s(2193) =< s(2182) s(2190) =< s(2185) s(2194) =< s(2186) s(2195) =< s(2187) s(2192) =< s(2188) s(2196) =< aux(202)+1 s(2197) =< aux(202)+3 s(2198) =< aux(202) s(2199) =< aux(202)+2 s(2200) =< aux(202)-1 s(2192) =< s(2184)*(1/5)+s(2188) s(2193) =< s(2184)*(1/5)+s(2188) s(2190) =< s(2184)*(1/3)+s(2185) s(2191) =< s(2184)*(1/3)+s(2185) s(2192) =< s(2184)*(1/3)+s(2185) s(2193) =< s(2184)*(1/3)+s(2185) s(2194) =< s(2184)*(1/5)+s(2186) s(2189) =< s(2184)*(1/5)+s(2186) s(2195) =< s(2184)*(5/16)+s(2187) s(2194) =< s(2184)*(5/16)+s(2187) s(2189) =< s(2184)*(5/16)+s(2187) s(2201) =< s(2193)*s(2196) s(2202) =< s(2193)*s(2197) s(2203) =< s(2190)*s(2198) s(2204) =< s(2190)*s(2199) s(2205) =< s(2194)*s(2200) s(2206) =< s(2194)*s(2196) s(2207) =< s(2195)*aux(202) s(2208) =< s(2201) s(2209) =< s(2204) s(2210) =< s(2206) s(2211) =< s(2205) s(2212) =< s(2207) with precondition: [V=2,Out>=1,2*V1>=Out+1] #### Cost of chains of fun8(V1,V,V12,Out): * Chain [81]: 8*s(2431)+64*s(2432)+16*s(2433)+8*s(2434)+24*s(2435)+40*s(2436)+64*s(2437)+8*s(2444)+24*s(2445)+40*s(2450)+176*s(2451)+40*s(2452)+40*s(2453)+184*s(2454)+8*s(2462)+64*s(2463)+16*s(2464)+8*s(2465)+24*s(2466)+40*s(2467)+64*s(2468)+8*s(2475)+24*s(2476)+40*s(2481)+176*s(2482)+40*s(2483)+40*s(2484)+184*s(2485)+9*s(2493)+72*s(2494)+18*s(2495)+9*s(2496)+27*s(2497)+45*s(2498)+72*s(2499)+9*s(2506)+27*s(2507)+45*s(2512)+198*s(2513)+45*s(2514)+45*s(2515)+207*s(2516)+1 Such that:aux(219) =< V1 aux(220) =< 2*V1 aux(221) =< 2*V1+1 aux(222) =< 2/3*V1 aux(223) =< 3/5*V1 aux(224) =< 3/8*V1 aux(225) =< 4/5*V1 aux(226) =< V aux(227) =< 2*V aux(228) =< 2*V+1 aux(229) =< 2/3*V aux(230) =< 3/5*V aux(231) =< 3/8*V aux(232) =< 4/5*V aux(233) =< V12 aux(234) =< 2*V12 aux(235) =< 2*V12+1 aux(236) =< 2/3*V12 aux(237) =< 3/5*V12 aux(238) =< 3/8*V12 aux(239) =< 4/5*V12 s(2493) =< aux(233) s(2494) =< aux(233) s(2495) =< aux(233) s(2496) =< aux(233) s(2497) =< aux(233) s(2494) =< aux(236) s(2498) =< aux(237) s(2499) =< aux(238) s(2496) =< aux(239) s(2500) =< aux(234)+1 s(2501) =< aux(234)+3 s(2502) =< aux(234) s(2503) =< aux(234)+2 s(2504) =< aux(234)-1 s(2496) =< aux(235)*(1/5)+aux(239) s(2497) =< aux(235)*(1/5)+aux(239) s(2494) =< aux(235)*(1/3)+aux(236) s(2495) =< aux(235)*(1/3)+aux(236) s(2496) =< aux(235)*(1/3)+aux(236) s(2497) =< aux(235)*(1/3)+aux(236) s(2498) =< aux(235)*(1/5)+aux(237) s(2493) =< aux(235)*(1/5)+aux(237) s(2499) =< aux(235)*(5/16)+aux(238) s(2498) =< aux(235)*(5/16)+aux(238) s(2493) =< aux(235)*(5/16)+aux(238) s(2505) =< s(2497)*s(2500) s(2506) =< s(2497)*s(2501) s(2507) =< s(2494)*s(2502) s(2508) =< s(2494)*s(2503) s(2509) =< s(2498)*s(2504) s(2510) =< s(2498)*s(2500) s(2511) =< s(2499)*aux(234) s(2512) =< s(2505) s(2513) =< s(2508) s(2514) =< s(2510) s(2515) =< s(2509) s(2516) =< s(2511) s(2462) =< aux(226) s(2463) =< aux(226) s(2464) =< aux(226) s(2465) =< aux(226) s(2466) =< aux(226) s(2463) =< aux(229) s(2467) =< aux(230) s(2468) =< aux(231) s(2465) =< aux(232) s(2469) =< aux(227)+1 s(2470) =< aux(227)+3 s(2471) =< aux(227) s(2472) =< aux(227)+2 s(2473) =< aux(227)-1 s(2465) =< aux(228)*(1/5)+aux(232) s(2466) =< aux(228)*(1/5)+aux(232) s(2463) =< aux(228)*(1/3)+aux(229) s(2464) =< aux(228)*(1/3)+aux(229) s(2465) =< aux(228)*(1/3)+aux(229) s(2466) =< aux(228)*(1/3)+aux(229) s(2467) =< aux(228)*(1/5)+aux(230) s(2462) =< aux(228)*(1/5)+aux(230) s(2468) =< aux(228)*(5/16)+aux(231) s(2467) =< aux(228)*(5/16)+aux(231) s(2462) =< aux(228)*(5/16)+aux(231) s(2474) =< s(2466)*s(2469) s(2475) =< s(2466)*s(2470) s(2476) =< s(2463)*s(2471) s(2477) =< s(2463)*s(2472) s(2478) =< s(2467)*s(2473) s(2479) =< s(2467)*s(2469) s(2480) =< s(2468)*aux(227) s(2481) =< s(2474) s(2482) =< s(2477) s(2483) =< s(2479) s(2484) =< s(2478) s(2485) =< s(2480) s(2431) =< aux(219) s(2432) =< aux(219) s(2433) =< aux(219) s(2434) =< aux(219) s(2435) =< aux(219) s(2432) =< aux(222) s(2436) =< aux(223) s(2437) =< aux(224) s(2434) =< aux(225) s(2438) =< aux(220)+1 s(2439) =< aux(220)+3 s(2440) =< aux(220) s(2441) =< aux(220)+2 s(2442) =< aux(220)-1 s(2434) =< aux(221)*(1/5)+aux(225) s(2435) =< aux(221)*(1/5)+aux(225) s(2432) =< aux(221)*(1/3)+aux(222) s(2433) =< aux(221)*(1/3)+aux(222) s(2434) =< aux(221)*(1/3)+aux(222) s(2435) =< aux(221)*(1/3)+aux(222) s(2436) =< aux(221)*(1/5)+aux(223) s(2431) =< aux(221)*(1/5)+aux(223) s(2437) =< aux(221)*(5/16)+aux(224) s(2436) =< aux(221)*(5/16)+aux(224) s(2431) =< aux(221)*(5/16)+aux(224) s(2443) =< s(2435)*s(2438) s(2444) =< s(2435)*s(2439) s(2445) =< s(2432)*s(2440) s(2446) =< s(2432)*s(2441) s(2447) =< s(2436)*s(2442) s(2448) =< s(2436)*s(2438) s(2449) =< s(2437)*aux(220) s(2450) =< s(2443) s(2451) =< s(2446) s(2452) =< s(2448) s(2453) =< s(2447) s(2454) =< s(2449) with precondition: [Out=0,V1>=0,V>=0,V12>=0] * Chain [80]: 9*s(3206)+72*s(3207)+18*s(3208)+9*s(3209)+27*s(3210)+45*s(3211)+72*s(3212)+9*s(3219)+27*s(3220)+45*s(3225)+198*s(3226)+45*s(3227)+45*s(3228)+207*s(3229)+10*s(3237)+80*s(3238)+20*s(3239)+10*s(3240)+30*s(3241)+50*s(3242)+80*s(3243)+10*s(3250)+30*s(3251)+50*s(3256)+220*s(3257)+50*s(3258)+50*s(3259)+230*s(3260)+13*s(3268)+104*s(3269)+26*s(3270)+13*s(3271)+39*s(3272)+65*s(3273)+104*s(3274)+13*s(3281)+39*s(3282)+65*s(3287)+286*s(3288)+65*s(3289)+65*s(3290)+299*s(3291)+22*s(3294)+10*s(3388)+12*s(4119)+3*s(4189)+5 Such that:s(4188) =< 1 aux(263) =< 2 aux(264) =< V1 aux(265) =< 2*V1 aux(266) =< 2*V1+1 aux(267) =< 2/3*V1 aux(268) =< 3/5*V1 aux(269) =< 3/8*V1 aux(270) =< 4/5*V1 aux(271) =< V aux(272) =< 2*V aux(273) =< 2*V+1 aux(274) =< 2/3*V aux(275) =< 3/5*V aux(276) =< 3/8*V aux(277) =< 4/5*V aux(278) =< V12 aux(279) =< 2*V12 aux(280) =< 2*V12+1 aux(281) =< 2/3*V12 aux(282) =< 3/5*V12 aux(283) =< 3/8*V12 aux(284) =< 4/5*V12 s(4119) =< aux(263) s(4189) =< s(4188) s(3268) =< aux(278) s(3269) =< aux(278) s(3270) =< aux(278) s(3271) =< aux(278) s(3272) =< aux(278) s(3269) =< aux(281) s(3273) =< aux(282) s(3274) =< aux(283) s(3271) =< aux(284) s(3275) =< aux(279)+1 s(3276) =< aux(279)+3 s(3277) =< aux(279) s(3278) =< aux(279)+2 s(3279) =< aux(279)-1 s(3271) =< aux(280)*(1/5)+aux(284) s(3272) =< aux(280)*(1/5)+aux(284) s(3269) =< aux(280)*(1/3)+aux(281) s(3270) =< aux(280)*(1/3)+aux(281) s(3271) =< aux(280)*(1/3)+aux(281) s(3272) =< aux(280)*(1/3)+aux(281) s(3273) =< aux(280)*(1/5)+aux(282) s(3268) =< aux(280)*(1/5)+aux(282) s(3274) =< aux(280)*(5/16)+aux(283) s(3273) =< aux(280)*(5/16)+aux(283) s(3268) =< aux(280)*(5/16)+aux(283) s(3280) =< s(3272)*s(3275) s(3281) =< s(3272)*s(3276) s(3282) =< s(3269)*s(3277) s(3283) =< s(3269)*s(3278) s(3284) =< s(3273)*s(3279) s(3285) =< s(3273)*s(3275) s(3286) =< s(3274)*aux(279) s(3287) =< s(3280) s(3288) =< s(3283) s(3289) =< s(3285) s(3290) =< s(3284) s(3291) =< s(3286) s(3294) =< aux(272) s(3237) =< aux(271) s(3238) =< aux(271) s(3239) =< aux(271) s(3240) =< aux(271) s(3241) =< aux(271) s(3238) =< aux(274) s(3242) =< aux(275) s(3243) =< aux(276) s(3240) =< aux(277) s(3244) =< aux(272)+1 s(3245) =< aux(272)+3 s(3246) =< aux(272) s(3247) =< aux(272)+2 s(3248) =< aux(272)-1 s(3240) =< aux(273)*(1/5)+aux(277) s(3241) =< aux(273)*(1/5)+aux(277) s(3238) =< aux(273)*(1/3)+aux(274) s(3239) =< aux(273)*(1/3)+aux(274) s(3240) =< aux(273)*(1/3)+aux(274) s(3241) =< aux(273)*(1/3)+aux(274) s(3242) =< aux(273)*(1/5)+aux(275) s(3237) =< aux(273)*(1/5)+aux(275) s(3243) =< aux(273)*(5/16)+aux(276) s(3242) =< aux(273)*(5/16)+aux(276) s(3237) =< aux(273)*(5/16)+aux(276) s(3249) =< s(3241)*s(3244) s(3250) =< s(3241)*s(3245) s(3251) =< s(3238)*s(3246) s(3252) =< s(3238)*s(3247) s(3253) =< s(3242)*s(3248) s(3254) =< s(3242)*s(3244) s(3255) =< s(3243)*aux(272) s(3256) =< s(3249) s(3257) =< s(3252) s(3258) =< s(3254) s(3259) =< s(3253) s(3260) =< s(3255) s(3206) =< aux(264) s(3207) =< aux(264) s(3208) =< aux(264) s(3209) =< aux(264) s(3210) =< aux(264) s(3207) =< aux(267) s(3211) =< aux(268) s(3212) =< aux(269) s(3209) =< aux(270) s(3213) =< aux(265)+1 s(3214) =< aux(265)+3 s(3215) =< aux(265) s(3216) =< aux(265)+2 s(3217) =< aux(265)-1 s(3209) =< aux(266)*(1/5)+aux(270) s(3210) =< aux(266)*(1/5)+aux(270) s(3207) =< aux(266)*(1/3)+aux(267) s(3208) =< aux(266)*(1/3)+aux(267) s(3209) =< aux(266)*(1/3)+aux(267) s(3210) =< aux(266)*(1/3)+aux(267) s(3211) =< aux(266)*(1/5)+aux(268) s(3206) =< aux(266)*(1/5)+aux(268) s(3212) =< aux(266)*(5/16)+aux(269) s(3211) =< aux(266)*(5/16)+aux(269) s(3206) =< aux(266)*(5/16)+aux(269) s(3218) =< s(3210)*s(3213) s(3219) =< s(3210)*s(3214) s(3220) =< s(3207)*s(3215) s(3221) =< s(3207)*s(3216) s(3222) =< s(3211)*s(3217) s(3223) =< s(3211)*s(3213) s(3224) =< s(3212)*aux(265) s(3225) =< s(3218) s(3226) =< s(3221) s(3227) =< s(3223) s(3228) =< s(3222) s(3229) =< s(3224) s(3388) =< aux(279) with precondition: [Out=1,V1>=1,V>=0,V12>=0] * Chain [79]: 1*s(4288)+8*s(4289)+2*s(4290)+1*s(4291)+3*s(4292)+5*s(4293)+8*s(4294)+1*s(4301)+3*s(4302)+5*s(4307)+22*s(4308)+5*s(4309)+5*s(4310)+23*s(4311)+2*s(4319)+16*s(4320)+4*s(4321)+2*s(4322)+6*s(4323)+10*s(4324)+16*s(4325)+2*s(4332)+6*s(4333)+10*s(4338)+44*s(4339)+10*s(4340)+10*s(4341)+46*s(4342)+3*s(4350)+24*s(4351)+6*s(4352)+3*s(4353)+9*s(4354)+15*s(4355)+24*s(4356)+3*s(4363)+9*s(4364)+15*s(4369)+66*s(4370)+15*s(4371)+15*s(4372)+69*s(4373)+46*s(4374)+17*s(4485)+8 Such that:aux(287) =< 1 s(4281) =< V1 s(4282) =< 2*V1 s(4283) =< 2*V1+1 s(4284) =< 2/3*V1 s(4285) =< 3/5*V1 s(4286) =< 3/8*V1 s(4287) =< 4/5*V1 aux(288) =< V aux(289) =< 2*V aux(290) =< 2*V+1 aux(291) =< 2/3*V aux(292) =< 3/5*V aux(293) =< 3/8*V aux(294) =< 4/5*V aux(295) =< V12 aux(296) =< 2*V12 aux(297) =< 2*V12+1 aux(298) =< 2/3*V12 aux(299) =< 3/5*V12 aux(300) =< 3/8*V12 aux(301) =< 4/5*V12 s(4374) =< aux(289) s(4350) =< aux(295) s(4351) =< aux(295) s(4352) =< aux(295) s(4353) =< aux(295) s(4354) =< aux(295) s(4351) =< aux(298) s(4355) =< aux(299) s(4356) =< aux(300) s(4353) =< aux(301) s(4357) =< aux(296)+1 s(4358) =< aux(296)+3 s(4359) =< aux(296) s(4360) =< aux(296)+2 s(4361) =< aux(296)-1 s(4353) =< aux(297)*(1/5)+aux(301) s(4354) =< aux(297)*(1/5)+aux(301) s(4351) =< aux(297)*(1/3)+aux(298) s(4352) =< aux(297)*(1/3)+aux(298) s(4353) =< aux(297)*(1/3)+aux(298) s(4354) =< aux(297)*(1/3)+aux(298) s(4355) =< aux(297)*(1/5)+aux(299) s(4350) =< aux(297)*(1/5)+aux(299) s(4356) =< aux(297)*(5/16)+aux(300) s(4355) =< aux(297)*(5/16)+aux(300) s(4350) =< aux(297)*(5/16)+aux(300) s(4362) =< s(4354)*s(4357) s(4363) =< s(4354)*s(4358) s(4364) =< s(4351)*s(4359) s(4365) =< s(4351)*s(4360) s(4366) =< s(4355)*s(4361) s(4367) =< s(4355)*s(4357) s(4368) =< s(4356)*aux(296) s(4369) =< s(4362) s(4370) =< s(4365) s(4371) =< s(4367) s(4372) =< s(4366) s(4373) =< s(4368) s(4319) =< aux(288) s(4320) =< aux(288) s(4321) =< aux(288) s(4322) =< aux(288) s(4323) =< aux(288) s(4320) =< aux(291) s(4324) =< aux(292) s(4325) =< aux(293) s(4322) =< aux(294) s(4326) =< aux(289)+1 s(4327) =< aux(289)+3 s(4328) =< aux(289) s(4329) =< aux(289)+2 s(4330) =< aux(289)-1 s(4322) =< aux(290)*(1/5)+aux(294) s(4323) =< aux(290)*(1/5)+aux(294) s(4320) =< aux(290)*(1/3)+aux(291) s(4321) =< aux(290)*(1/3)+aux(291) s(4322) =< aux(290)*(1/3)+aux(291) s(4323) =< aux(290)*(1/3)+aux(291) s(4324) =< aux(290)*(1/5)+aux(292) s(4319) =< aux(290)*(1/5)+aux(292) s(4325) =< aux(290)*(5/16)+aux(293) s(4324) =< aux(290)*(5/16)+aux(293) s(4319) =< aux(290)*(5/16)+aux(293) s(4331) =< s(4323)*s(4326) s(4332) =< s(4323)*s(4327) s(4333) =< s(4320)*s(4328) s(4334) =< s(4320)*s(4329) s(4335) =< s(4324)*s(4330) s(4336) =< s(4324)*s(4326) s(4337) =< s(4325)*aux(289) s(4338) =< s(4331) s(4339) =< s(4334) s(4340) =< s(4336) s(4341) =< s(4335) s(4342) =< s(4337) s(4288) =< s(4281) s(4289) =< s(4281) s(4290) =< s(4281) s(4291) =< s(4281) s(4292) =< s(4281) s(4289) =< s(4284) s(4293) =< s(4285) s(4294) =< s(4286) s(4291) =< s(4287) s(4295) =< s(4282)+1 s(4296) =< s(4282)+3 s(4297) =< s(4282) s(4298) =< s(4282)+2 s(4299) =< s(4282)-1 s(4291) =< s(4283)*(1/5)+s(4287) s(4292) =< s(4283)*(1/5)+s(4287) s(4289) =< s(4283)*(1/3)+s(4284) s(4290) =< s(4283)*(1/3)+s(4284) s(4291) =< s(4283)*(1/3)+s(4284) s(4292) =< s(4283)*(1/3)+s(4284) s(4293) =< s(4283)*(1/5)+s(4285) s(4288) =< s(4283)*(1/5)+s(4285) s(4294) =< s(4283)*(5/16)+s(4286) s(4293) =< s(4283)*(5/16)+s(4286) s(4288) =< s(4283)*(5/16)+s(4286) s(4300) =< s(4292)*s(4295) s(4301) =< s(4292)*s(4296) s(4302) =< s(4289)*s(4297) s(4303) =< s(4289)*s(4298) s(4304) =< s(4293)*s(4299) s(4305) =< s(4293)*s(4295) s(4306) =< s(4294)*s(4282) s(4307) =< s(4300) s(4308) =< s(4303) s(4309) =< s(4305) s(4310) =< s(4304) s(4311) =< s(4306) s(4485) =< aux(287) with precondition: [V1>=1,V12>=1,Out>=2,2*V>=Out] * Chain [78]: 4*s(4501)+32*s(4502)+8*s(4503)+4*s(4504)+12*s(4505)+20*s(4506)+32*s(4507)+4*s(4514)+12*s(4515)+20*s(4520)+88*s(4521)+20*s(4522)+20*s(4523)+92*s(4524)+4*s(4532)+32*s(4533)+8*s(4534)+4*s(4535)+12*s(4536)+20*s(4537)+32*s(4538)+4*s(4545)+12*s(4546)+20*s(4551)+88*s(4552)+20*s(4553)+20*s(4554)+92*s(4555)+1 Such that:aux(302) =< V1 aux(303) =< 2*V1 aux(304) =< 2*V1+1 aux(305) =< 2/3*V1 aux(306) =< 3/5*V1 aux(307) =< 3/8*V1 aux(308) =< 4/5*V1 aux(309) =< V aux(310) =< 2*V aux(311) =< 2*V+1 aux(312) =< 2/3*V aux(313) =< 3/5*V aux(314) =< 3/8*V aux(315) =< 4/5*V s(4532) =< aux(309) s(4533) =< aux(309) s(4534) =< aux(309) s(4535) =< aux(309) s(4536) =< aux(309) s(4533) =< aux(312) s(4537) =< aux(313) s(4538) =< aux(314) s(4535) =< aux(315) s(4539) =< aux(310)+1 s(4540) =< aux(310)+3 s(4541) =< aux(310) s(4542) =< aux(310)+2 s(4543) =< aux(310)-1 s(4535) =< aux(311)*(1/5)+aux(315) s(4536) =< aux(311)*(1/5)+aux(315) s(4533) =< aux(311)*(1/3)+aux(312) s(4534) =< aux(311)*(1/3)+aux(312) s(4535) =< aux(311)*(1/3)+aux(312) s(4536) =< aux(311)*(1/3)+aux(312) s(4537) =< aux(311)*(1/5)+aux(313) s(4532) =< aux(311)*(1/5)+aux(313) s(4538) =< aux(311)*(5/16)+aux(314) s(4537) =< aux(311)*(5/16)+aux(314) s(4532) =< aux(311)*(5/16)+aux(314) s(4544) =< s(4536)*s(4539) s(4545) =< s(4536)*s(4540) s(4546) =< s(4533)*s(4541) s(4547) =< s(4533)*s(4542) s(4548) =< s(4537)*s(4543) s(4549) =< s(4537)*s(4539) s(4550) =< s(4538)*aux(310) s(4551) =< s(4544) s(4552) =< s(4547) s(4553) =< s(4549) s(4554) =< s(4548) s(4555) =< s(4550) s(4501) =< aux(302) s(4502) =< aux(302) s(4503) =< aux(302) s(4504) =< aux(302) s(4505) =< aux(302) s(4502) =< aux(305) s(4506) =< aux(306) s(4507) =< aux(307) s(4504) =< aux(308) s(4508) =< aux(303)+1 s(4509) =< aux(303)+3 s(4510) =< aux(303) s(4511) =< aux(303)+2 s(4512) =< aux(303)-1 s(4504) =< aux(304)*(1/5)+aux(308) s(4505) =< aux(304)*(1/5)+aux(308) s(4502) =< aux(304)*(1/3)+aux(305) s(4503) =< aux(304)*(1/3)+aux(305) s(4504) =< aux(304)*(1/3)+aux(305) s(4505) =< aux(304)*(1/3)+aux(305) s(4506) =< aux(304)*(1/5)+aux(306) s(4501) =< aux(304)*(1/5)+aux(306) s(4507) =< aux(304)*(5/16)+aux(307) s(4506) =< aux(304)*(5/16)+aux(307) s(4501) =< aux(304)*(5/16)+aux(307) s(4513) =< s(4505)*s(4508) s(4514) =< s(4505)*s(4509) s(4515) =< s(4502)*s(4510) s(4516) =< s(4502)*s(4511) s(4517) =< s(4506)*s(4512) s(4518) =< s(4506)*s(4508) s(4519) =< s(4507)*aux(303) s(4520) =< s(4513) s(4521) =< s(4516) s(4522) =< s(4518) s(4523) =< s(4517) s(4524) =< s(4519) with precondition: [V12=2,Out=0,V1>=0,V>=0] * Chain [77]: 3*s(4749)+24*s(4750)+6*s(4751)+3*s(4752)+9*s(4753)+15*s(4754)+24*s(4755)+3*s(4762)+9*s(4763)+15*s(4768)+66*s(4769)+15*s(4770)+15*s(4771)+69*s(4772)+4*s(4780)+32*s(4781)+8*s(4782)+4*s(4783)+12*s(4784)+20*s(4785)+32*s(4786)+4*s(4793)+12*s(4794)+20*s(4799)+88*s(4800)+20*s(4801)+20*s(4802)+92*s(4803)+12*s(4804)+6*s(4873)+5 Such that:aux(324) =< 2 aux(325) =< V1 aux(326) =< 2*V1 aux(327) =< 2*V1+1 aux(328) =< 2/3*V1 aux(329) =< 3/5*V1 aux(330) =< 3/8*V1 aux(331) =< 4/5*V1 aux(332) =< V aux(333) =< 2*V aux(334) =< 2*V+1 aux(335) =< 2/3*V aux(336) =< 3/5*V aux(337) =< 3/8*V aux(338) =< 4/5*V s(4804) =< aux(324) s(4780) =< aux(332) s(4781) =< aux(332) s(4782) =< aux(332) s(4783) =< aux(332) s(4784) =< aux(332) s(4781) =< aux(335) s(4785) =< aux(336) s(4786) =< aux(337) s(4783) =< aux(338) s(4787) =< aux(333)+1 s(4788) =< aux(333)+3 s(4789) =< aux(333) s(4790) =< aux(333)+2 s(4791) =< aux(333)-1 s(4783) =< aux(334)*(1/5)+aux(338) s(4784) =< aux(334)*(1/5)+aux(338) s(4781) =< aux(334)*(1/3)+aux(335) s(4782) =< aux(334)*(1/3)+aux(335) s(4783) =< aux(334)*(1/3)+aux(335) s(4784) =< aux(334)*(1/3)+aux(335) s(4785) =< aux(334)*(1/5)+aux(336) s(4780) =< aux(334)*(1/5)+aux(336) s(4786) =< aux(334)*(5/16)+aux(337) s(4785) =< aux(334)*(5/16)+aux(337) s(4780) =< aux(334)*(5/16)+aux(337) s(4792) =< s(4784)*s(4787) s(4793) =< s(4784)*s(4788) s(4794) =< s(4781)*s(4789) s(4795) =< s(4781)*s(4790) s(4796) =< s(4785)*s(4791) s(4797) =< s(4785)*s(4787) s(4798) =< s(4786)*aux(333) s(4799) =< s(4792) s(4800) =< s(4795) s(4801) =< s(4797) s(4802) =< s(4796) s(4803) =< s(4798) s(4749) =< aux(325) s(4750) =< aux(325) s(4751) =< aux(325) s(4752) =< aux(325) s(4753) =< aux(325) s(4750) =< aux(328) s(4754) =< aux(329) s(4755) =< aux(330) s(4752) =< aux(331) s(4756) =< aux(326)+1 s(4757) =< aux(326)+3 s(4758) =< aux(326) s(4759) =< aux(326)+2 s(4760) =< aux(326)-1 s(4752) =< aux(327)*(1/5)+aux(331) s(4753) =< aux(327)*(1/5)+aux(331) s(4750) =< aux(327)*(1/3)+aux(328) s(4751) =< aux(327)*(1/3)+aux(328) s(4752) =< aux(327)*(1/3)+aux(328) s(4753) =< aux(327)*(1/3)+aux(328) s(4754) =< aux(327)*(1/5)+aux(329) s(4749) =< aux(327)*(1/5)+aux(329) s(4755) =< aux(327)*(5/16)+aux(330) s(4754) =< aux(327)*(5/16)+aux(330) s(4749) =< aux(327)*(5/16)+aux(330) s(4761) =< s(4753)*s(4756) s(4762) =< s(4753)*s(4757) s(4763) =< s(4750)*s(4758) s(4764) =< s(4750)*s(4759) s(4765) =< s(4754)*s(4760) s(4766) =< s(4754)*s(4756) s(4767) =< s(4755)*aux(326) s(4768) =< s(4761) s(4769) =< s(4764) s(4770) =< s(4766) s(4771) =< s(4765) s(4772) =< s(4767) s(4873) =< aux(333) with precondition: [V12=2,Out=1,V1>=1,V>=0] * Chain [76]: 1*s(4990)+8*s(4991)+2*s(4992)+1*s(4993)+3*s(4994)+5*s(4995)+8*s(4996)+1*s(5003)+3*s(5004)+5*s(5009)+22*s(5010)+5*s(5011)+5*s(5012)+23*s(5013)+2*s(5021)+16*s(5022)+4*s(5023)+2*s(5024)+6*s(5025)+10*s(5026)+16*s(5027)+2*s(5034)+6*s(5035)+10*s(5040)+44*s(5041)+10*s(5042)+10*s(5043)+46*s(5044)+16*s(5045)+30*s(5050)+8 Such that:s(4983) =< V1 s(4984) =< 2*V1 s(4985) =< 2*V1+1 s(4986) =< 2/3*V1 s(4987) =< 3/5*V1 s(4988) =< 3/8*V1 s(4989) =< 4/5*V1 aux(343) =< 2 aux(344) =< V aux(345) =< 2*V aux(346) =< 2*V+1 aux(347) =< 2/3*V aux(348) =< 3/5*V aux(349) =< 3/8*V aux(350) =< 4/5*V s(5045) =< aux(343) s(5050) =< aux(345) s(5021) =< aux(344) s(5022) =< aux(344) s(5023) =< aux(344) s(5024) =< aux(344) s(5025) =< aux(344) s(5022) =< aux(347) s(5026) =< aux(348) s(5027) =< aux(349) s(5024) =< aux(350) s(5028) =< aux(345)+1 s(5029) =< aux(345)+3 s(5030) =< aux(345) s(5031) =< aux(345)+2 s(5032) =< aux(345)-1 s(5024) =< aux(346)*(1/5)+aux(350) s(5025) =< aux(346)*(1/5)+aux(350) s(5022) =< aux(346)*(1/3)+aux(347) s(5023) =< aux(346)*(1/3)+aux(347) s(5024) =< aux(346)*(1/3)+aux(347) s(5025) =< aux(346)*(1/3)+aux(347) s(5026) =< aux(346)*(1/5)+aux(348) s(5021) =< aux(346)*(1/5)+aux(348) s(5027) =< aux(346)*(5/16)+aux(349) s(5026) =< aux(346)*(5/16)+aux(349) s(5021) =< aux(346)*(5/16)+aux(349) s(5033) =< s(5025)*s(5028) s(5034) =< s(5025)*s(5029) s(5035) =< s(5022)*s(5030) s(5036) =< s(5022)*s(5031) s(5037) =< s(5026)*s(5032) s(5038) =< s(5026)*s(5028) s(5039) =< s(5027)*aux(345) s(5040) =< s(5033) s(5041) =< s(5036) s(5042) =< s(5038) s(5043) =< s(5037) s(5044) =< s(5039) s(4990) =< s(4983) s(4991) =< s(4983) s(4992) =< s(4983) s(4993) =< s(4983) s(4994) =< s(4983) s(4991) =< s(4986) s(4995) =< s(4987) s(4996) =< s(4988) s(4993) =< s(4989) s(4997) =< s(4984)+1 s(4998) =< s(4984)+3 s(4999) =< s(4984) s(5000) =< s(4984)+2 s(5001) =< s(4984)-1 s(4993) =< s(4985)*(1/5)+s(4989) s(4994) =< s(4985)*(1/5)+s(4989) s(4991) =< s(4985)*(1/3)+s(4986) s(4992) =< s(4985)*(1/3)+s(4986) s(4993) =< s(4985)*(1/3)+s(4986) s(4994) =< s(4985)*(1/3)+s(4986) s(4995) =< s(4985)*(1/5)+s(4987) s(4990) =< s(4985)*(1/5)+s(4987) s(4996) =< s(4985)*(5/16)+s(4988) s(4995) =< s(4985)*(5/16)+s(4988) s(4990) =< s(4985)*(5/16)+s(4988) s(5002) =< s(4994)*s(4997) s(5003) =< s(4994)*s(4998) s(5004) =< s(4991)*s(4999) s(5005) =< s(4991)*s(5000) s(5006) =< s(4995)*s(5001) s(5007) =< s(4995)*s(4997) s(5008) =< s(4996)*s(4984) s(5009) =< s(5002) s(5010) =< s(5005) s(5011) =< s(5007) s(5012) =< s(5006) s(5013) =< s(5008) with precondition: [V12=2,V1>=1,Out>=2,2*V>=Out+2] * Chain [75]: 6*s(5101)+48*s(5102)+12*s(5103)+6*s(5104)+18*s(5105)+30*s(5106)+48*s(5107)+6*s(5114)+18*s(5115)+30*s(5120)+132*s(5121)+30*s(5122)+30*s(5123)+138*s(5124)+3*s(5132)+24*s(5133)+6*s(5134)+3*s(5135)+9*s(5136)+15*s(5137)+24*s(5138)+3*s(5145)+9*s(5146)+15*s(5151)+66*s(5152)+15*s(5153)+15*s(5154)+69*s(5155)+1 Such that:aux(351) =< V1 aux(352) =< 2*V1 aux(353) =< 2*V1+1 aux(354) =< 2/3*V1 aux(355) =< 3/5*V1 aux(356) =< 3/8*V1 aux(357) =< 4/5*V1 aux(358) =< V12 aux(359) =< 2*V12 aux(360) =< 2*V12+1 aux(361) =< 2/3*V12 aux(362) =< 3/5*V12 aux(363) =< 3/8*V12 aux(364) =< 4/5*V12 s(5132) =< aux(358) s(5133) =< aux(358) s(5134) =< aux(358) s(5135) =< aux(358) s(5136) =< aux(358) s(5133) =< aux(361) s(5137) =< aux(362) s(5138) =< aux(363) s(5135) =< aux(364) s(5139) =< aux(359)+1 s(5140) =< aux(359)+3 s(5141) =< aux(359) s(5142) =< aux(359)+2 s(5143) =< aux(359)-1 s(5135) =< aux(360)*(1/5)+aux(364) s(5136) =< aux(360)*(1/5)+aux(364) s(5133) =< aux(360)*(1/3)+aux(361) s(5134) =< aux(360)*(1/3)+aux(361) s(5135) =< aux(360)*(1/3)+aux(361) s(5136) =< aux(360)*(1/3)+aux(361) s(5137) =< aux(360)*(1/5)+aux(362) s(5132) =< aux(360)*(1/5)+aux(362) s(5138) =< aux(360)*(5/16)+aux(363) s(5137) =< aux(360)*(5/16)+aux(363) s(5132) =< aux(360)*(5/16)+aux(363) s(5144) =< s(5136)*s(5139) s(5145) =< s(5136)*s(5140) s(5146) =< s(5133)*s(5141) s(5147) =< s(5133)*s(5142) s(5148) =< s(5137)*s(5143) s(5149) =< s(5137)*s(5139) s(5150) =< s(5138)*aux(359) s(5151) =< s(5144) s(5152) =< s(5147) s(5153) =< s(5149) s(5154) =< s(5148) s(5155) =< s(5150) s(5101) =< aux(351) s(5102) =< aux(351) s(5103) =< aux(351) s(5104) =< aux(351) s(5105) =< aux(351) s(5102) =< aux(354) s(5106) =< aux(355) s(5107) =< aux(356) s(5104) =< aux(357) s(5108) =< aux(352)+1 s(5109) =< aux(352)+3 s(5110) =< aux(352) s(5111) =< aux(352)+2 s(5112) =< aux(352)-1 s(5104) =< aux(353)*(1/5)+aux(357) s(5105) =< aux(353)*(1/5)+aux(357) s(5102) =< aux(353)*(1/3)+aux(354) s(5103) =< aux(353)*(1/3)+aux(354) s(5104) =< aux(353)*(1/3)+aux(354) s(5105) =< aux(353)*(1/3)+aux(354) s(5106) =< aux(353)*(1/5)+aux(355) s(5101) =< aux(353)*(1/5)+aux(355) s(5107) =< aux(353)*(5/16)+aux(356) s(5106) =< aux(353)*(5/16)+aux(356) s(5101) =< aux(353)*(5/16)+aux(356) s(5113) =< s(5105)*s(5108) s(5114) =< s(5105)*s(5109) s(5115) =< s(5102)*s(5110) s(5116) =< s(5102)*s(5111) s(5117) =< s(5106)*s(5112) s(5118) =< s(5106)*s(5108) s(5119) =< s(5107)*aux(352) s(5120) =< s(5113) s(5121) =< s(5116) s(5122) =< s(5118) s(5123) =< s(5117) s(5124) =< s(5119) with precondition: [V=2,Out=0,V1>=0,V12>=0] * Chain [74]: 7*s(5380)+56*s(5381)+14*s(5382)+7*s(5383)+21*s(5384)+35*s(5385)+56*s(5386)+7*s(5393)+21*s(5394)+35*s(5399)+154*s(5400)+35*s(5401)+35*s(5402)+161*s(5403)+3*s(5411)+24*s(5412)+6*s(5413)+3*s(5414)+9*s(5415)+15*s(5416)+24*s(5417)+3*s(5424)+9*s(5425)+15*s(5430)+66*s(5431)+15*s(5432)+15*s(5433)+69*s(5434)+12*s(5437)+2*s(5500)+3*s(5569)+5 Such that:s(5568) =< 1 aux(370) =< 2 aux(371) =< V1 aux(372) =< 2*V1 aux(373) =< 2*V1+1 aux(374) =< 2/3*V1 aux(375) =< 3/5*V1 aux(376) =< 3/8*V1 aux(377) =< 4/5*V1 aux(378) =< V12 aux(379) =< 2*V12 aux(380) =< 2*V12+1 aux(381) =< 2/3*V12 aux(382) =< 3/5*V12 aux(383) =< 3/8*V12 aux(384) =< 4/5*V12 s(5437) =< aux(370) s(5569) =< s(5568) s(5411) =< aux(378) s(5412) =< aux(378) s(5413) =< aux(378) s(5414) =< aux(378) s(5415) =< aux(378) s(5412) =< aux(381) s(5416) =< aux(382) s(5417) =< aux(383) s(5414) =< aux(384) s(5418) =< aux(379)+1 s(5419) =< aux(379)+3 s(5420) =< aux(379) s(5421) =< aux(379)+2 s(5422) =< aux(379)-1 s(5414) =< aux(380)*(1/5)+aux(384) s(5415) =< aux(380)*(1/5)+aux(384) s(5412) =< aux(380)*(1/3)+aux(381) s(5413) =< aux(380)*(1/3)+aux(381) s(5414) =< aux(380)*(1/3)+aux(381) s(5415) =< aux(380)*(1/3)+aux(381) s(5416) =< aux(380)*(1/5)+aux(382) s(5411) =< aux(380)*(1/5)+aux(382) s(5417) =< aux(380)*(5/16)+aux(383) s(5416) =< aux(380)*(5/16)+aux(383) s(5411) =< aux(380)*(5/16)+aux(383) s(5423) =< s(5415)*s(5418) s(5424) =< s(5415)*s(5419) s(5425) =< s(5412)*s(5420) s(5426) =< s(5412)*s(5421) s(5427) =< s(5416)*s(5422) s(5428) =< s(5416)*s(5418) s(5429) =< s(5417)*aux(379) s(5430) =< s(5423) s(5431) =< s(5426) s(5432) =< s(5428) s(5433) =< s(5427) s(5434) =< s(5429) s(5380) =< aux(371) s(5381) =< aux(371) s(5382) =< aux(371) s(5383) =< aux(371) s(5384) =< aux(371) s(5381) =< aux(374) s(5385) =< aux(375) s(5386) =< aux(376) s(5383) =< aux(377) s(5387) =< aux(372)+1 s(5388) =< aux(372)+3 s(5389) =< aux(372) s(5390) =< aux(372)+2 s(5391) =< aux(372)-1 s(5383) =< aux(373)*(1/5)+aux(377) s(5384) =< aux(373)*(1/5)+aux(377) s(5381) =< aux(373)*(1/3)+aux(374) s(5382) =< aux(373)*(1/3)+aux(374) s(5383) =< aux(373)*(1/3)+aux(374) s(5384) =< aux(373)*(1/3)+aux(374) s(5385) =< aux(373)*(1/5)+aux(375) s(5380) =< aux(373)*(1/5)+aux(375) s(5386) =< aux(373)*(5/16)+aux(376) s(5385) =< aux(373)*(5/16)+aux(376) s(5380) =< aux(373)*(5/16)+aux(376) s(5392) =< s(5384)*s(5387) s(5393) =< s(5384)*s(5388) s(5394) =< s(5381)*s(5389) s(5395) =< s(5381)*s(5390) s(5396) =< s(5385)*s(5391) s(5397) =< s(5385)*s(5387) s(5398) =< s(5386)*aux(372) s(5399) =< s(5392) s(5400) =< s(5395) s(5401) =< s(5397) s(5402) =< s(5396) s(5403) =< s(5398) s(5500) =< aux(379) with precondition: [V=2,Out=1,V1>=1,V12>=0] * Chain [73]: 1*s(5716)+8*s(5717)+2*s(5718)+1*s(5719)+3*s(5720)+5*s(5721)+8*s(5722)+1*s(5729)+3*s(5730)+5*s(5735)+22*s(5736)+5*s(5737)+5*s(5738)+23*s(5739)+1*s(5747)+8*s(5748)+2*s(5749)+1*s(5750)+3*s(5751)+5*s(5752)+8*s(5753)+1*s(5760)+3*s(5761)+5*s(5766)+22*s(5767)+5*s(5768)+5*s(5769)+23*s(5770)+17*s(5771)+8 Such that:s(5709) =< V1 s(5710) =< 2*V1 s(5711) =< 2*V1+1 s(5712) =< 2/3*V1 s(5713) =< 3/5*V1 s(5714) =< 3/8*V1 s(5715) =< 4/5*V1 s(5740) =< V12 s(5741) =< 2*V12 s(5742) =< 2*V12+1 s(5743) =< 2/3*V12 s(5744) =< 3/5*V12 s(5745) =< 3/8*V12 s(5746) =< 4/5*V12 aux(385) =< 1 s(5771) =< aux(385) s(5747) =< s(5740) s(5748) =< s(5740) s(5749) =< s(5740) s(5750) =< s(5740) s(5751) =< s(5740) s(5748) =< s(5743) s(5752) =< s(5744) s(5753) =< s(5745) s(5750) =< s(5746) s(5754) =< s(5741)+1 s(5755) =< s(5741)+3 s(5756) =< s(5741) s(5757) =< s(5741)+2 s(5758) =< s(5741)-1 s(5750) =< s(5742)*(1/5)+s(5746) s(5751) =< s(5742)*(1/5)+s(5746) s(5748) =< s(5742)*(1/3)+s(5743) s(5749) =< s(5742)*(1/3)+s(5743) s(5750) =< s(5742)*(1/3)+s(5743) s(5751) =< s(5742)*(1/3)+s(5743) s(5752) =< s(5742)*(1/5)+s(5744) s(5747) =< s(5742)*(1/5)+s(5744) s(5753) =< s(5742)*(5/16)+s(5745) s(5752) =< s(5742)*(5/16)+s(5745) s(5747) =< s(5742)*(5/16)+s(5745) s(5759) =< s(5751)*s(5754) s(5760) =< s(5751)*s(5755) s(5761) =< s(5748)*s(5756) s(5762) =< s(5748)*s(5757) s(5763) =< s(5752)*s(5758) s(5764) =< s(5752)*s(5754) s(5765) =< s(5753)*s(5741) s(5766) =< s(5759) s(5767) =< s(5762) s(5768) =< s(5764) s(5769) =< s(5763) s(5770) =< s(5765) s(5716) =< s(5709) s(5717) =< s(5709) s(5718) =< s(5709) s(5719) =< s(5709) s(5720) =< s(5709) s(5717) =< s(5712) s(5721) =< s(5713) s(5722) =< s(5714) s(5719) =< s(5715) s(5723) =< s(5710)+1 s(5724) =< s(5710)+3 s(5725) =< s(5710) s(5726) =< s(5710)+2 s(5727) =< s(5710)-1 s(5719) =< s(5711)*(1/5)+s(5715) s(5720) =< s(5711)*(1/5)+s(5715) s(5717) =< s(5711)*(1/3)+s(5712) s(5718) =< s(5711)*(1/3)+s(5712) s(5719) =< s(5711)*(1/3)+s(5712) s(5720) =< s(5711)*(1/3)+s(5712) s(5721) =< s(5711)*(1/5)+s(5713) s(5716) =< s(5711)*(1/5)+s(5713) s(5722) =< s(5711)*(5/16)+s(5714) s(5721) =< s(5711)*(5/16)+s(5714) s(5716) =< s(5711)*(5/16)+s(5714) s(5728) =< s(5720)*s(5723) s(5729) =< s(5720)*s(5724) s(5730) =< s(5717)*s(5725) s(5731) =< s(5717)*s(5726) s(5732) =< s(5721)*s(5727) s(5733) =< s(5721)*s(5723) s(5734) =< s(5722)*s(5710) s(5735) =< s(5728) s(5736) =< s(5731) s(5737) =< s(5733) s(5738) =< s(5732) s(5739) =< s(5734) with precondition: [V=2,Out=2,V1>=1,V12>=1] #### Cost of chains of start(V1,V,V12): * Chain [82]: 15*s(6263)+12*s(6264)+12*s(6271)+4*s(6277)+2*s(6279)+13*s(6285)+4*s(6293)+2*s(6295)+66*s(6304)+528*s(6305)+132*s(6306)+66*s(6307)+198*s(6308)+330*s(6309)+528*s(6310)+66*s(6317)+198*s(6318)+330*s(6323)+1452*s(6324)+330*s(6325)+330*s(6326)+1518*s(6327)+116*s(6328)+54*s(6343)+432*s(6344)+108*s(6345)+54*s(6346)+162*s(6347)+270*s(6348)+432*s(6349)+54*s(6356)+162*s(6357)+270*s(6362)+1188*s(6363)+270*s(6364)+270*s(6365)+1242*s(6366)+115*s(6391)+41*s(6585)+47*s(6649)+4*s(6798)+2*s(6800)+32*s(6871)+256*s(6872)+64*s(6873)+32*s(6874)+96*s(6875)+160*s(6876)+256*s(6877)+32*s(6884)+96*s(6885)+160*s(6890)+704*s(6891)+160*s(6892)+160*s(6893)+736*s(6894)+12*s(7016)+8 Such that:s(6289) =< V1-V s(6273) =< V-2*V12 aux(434) =< 1 aux(435) =< 2 aux(436) =< V1 aux(437) =< 2*V1 aux(438) =< 2*V1+1 aux(439) =< 2/3*V1 aux(440) =< 3/5*V1 aux(441) =< 3/8*V1 aux(442) =< 4/5*V1 aux(443) =< V aux(444) =< V-V12 aux(445) =< 2*V aux(446) =< 2*V+1 aux(447) =< 2/3*V aux(448) =< 3/5*V aux(449) =< 3/8*V aux(450) =< 4/5*V aux(451) =< V12 aux(452) =< 2*V12 aux(453) =< 2*V12+1 aux(454) =< 2/3*V12 aux(455) =< 3/5*V12 aux(456) =< 3/8*V12 aux(457) =< 4/5*V12 s(6585) =< aux(434) s(6328) =< aux(435) s(6285) =< aux(436) s(6263) =< aux(443) s(6343) =< aux(443) s(6344) =< aux(443) s(6345) =< aux(443) s(6346) =< aux(443) s(6347) =< aux(443) s(6344) =< aux(447) s(6348) =< aux(448) s(6349) =< aux(449) s(6346) =< aux(450) s(6350) =< aux(445)+1 s(6351) =< aux(445)+3 s(6352) =< aux(445) s(6353) =< aux(445)+2 s(6354) =< aux(445)-1 s(6346) =< aux(446)*(1/5)+aux(450) s(6347) =< aux(446)*(1/5)+aux(450) s(6344) =< aux(446)*(1/3)+aux(447) s(6345) =< aux(446)*(1/3)+aux(447) s(6346) =< aux(446)*(1/3)+aux(447) s(6347) =< aux(446)*(1/3)+aux(447) s(6348) =< aux(446)*(1/5)+aux(448) s(6343) =< aux(446)*(1/5)+aux(448) s(6349) =< aux(446)*(5/16)+aux(449) s(6348) =< aux(446)*(5/16)+aux(449) s(6343) =< aux(446)*(5/16)+aux(449) s(6355) =< s(6347)*s(6350) s(6356) =< s(6347)*s(6351) s(6357) =< s(6344)*s(6352) s(6358) =< s(6344)*s(6353) s(6359) =< s(6348)*s(6354) s(6360) =< s(6348)*s(6350) s(6361) =< s(6349)*aux(445) s(6362) =< s(6355) s(6363) =< s(6358) s(6364) =< s(6360) s(6365) =< s(6359) s(6366) =< s(6361) s(6304) =< aux(436) s(6305) =< aux(436) s(6306) =< aux(436) s(6307) =< aux(436) s(6308) =< aux(436) s(6305) =< aux(439) s(6309) =< aux(440) s(6310) =< aux(441) s(6307) =< aux(442) s(6311) =< aux(437)+1 s(6312) =< aux(437)+3 s(6313) =< aux(437) s(6314) =< aux(437)+2 s(6315) =< aux(437)-1 s(6307) =< aux(438)*(1/5)+aux(442) s(6308) =< aux(438)*(1/5)+aux(442) s(6305) =< aux(438)*(1/3)+aux(439) s(6306) =< aux(438)*(1/3)+aux(439) s(6307) =< aux(438)*(1/3)+aux(439) s(6308) =< aux(438)*(1/3)+aux(439) s(6309) =< aux(438)*(1/5)+aux(440) s(6304) =< aux(438)*(1/5)+aux(440) s(6310) =< aux(438)*(5/16)+aux(441) s(6309) =< aux(438)*(5/16)+aux(441) s(6304) =< aux(438)*(5/16)+aux(441) s(6316) =< s(6308)*s(6311) s(6317) =< s(6308)*s(6312) s(6318) =< s(6305)*s(6313) s(6319) =< s(6305)*s(6314) s(6320) =< s(6309)*s(6315) s(6321) =< s(6309)*s(6311) s(6322) =< s(6310)*aux(437) s(6323) =< s(6316) s(6324) =< s(6319) s(6325) =< s(6321) s(6326) =< s(6320) s(6327) =< s(6322) s(6649) =< aux(437) s(6798) =< aux(434) s(6798) =< aux(435) s(6799) =< aux(435) s(6799) =< aux(434) s(6800) =< s(6799) s(6871) =< aux(451) s(6872) =< aux(451) s(6873) =< aux(451) s(6874) =< aux(451) s(6875) =< aux(451) s(6872) =< aux(454) s(6876) =< aux(455) s(6877) =< aux(456) s(6874) =< aux(457) s(6878) =< aux(452)+1 s(6879) =< aux(452)+3 s(6880) =< aux(452) s(6881) =< aux(452)+2 s(6882) =< aux(452)-1 s(6874) =< aux(453)*(1/5)+aux(457) s(6875) =< aux(453)*(1/5)+aux(457) s(6872) =< aux(453)*(1/3)+aux(454) s(6873) =< aux(453)*(1/3)+aux(454) s(6874) =< aux(453)*(1/3)+aux(454) s(6875) =< aux(453)*(1/3)+aux(454) s(6876) =< aux(453)*(1/5)+aux(455) s(6871) =< aux(453)*(1/5)+aux(455) s(6877) =< aux(453)*(5/16)+aux(456) s(6876) =< aux(453)*(5/16)+aux(456) s(6871) =< aux(453)*(5/16)+aux(456) s(6883) =< s(6875)*s(6878) s(6884) =< s(6875)*s(6879) s(6885) =< s(6872)*s(6880) s(6886) =< s(6872)*s(6881) s(6887) =< s(6876)*s(6882) s(6888) =< s(6876)*s(6878) s(6889) =< s(6877)*aux(452) s(6890) =< s(6883) s(6891) =< s(6886) s(6892) =< s(6888) s(6893) =< s(6887) s(6894) =< s(6889) s(7016) =< aux(452) s(6391) =< aux(445) s(6293) =< s(6289) s(6293) =< aux(436) s(6294) =< aux(436) s(6294) =< s(6289) s(6295) =< s(6294) s(6264) =< aux(451) s(6277) =< s(6273) s(6277) =< aux(444) s(6278) =< aux(444) s(6278) =< s(6273) s(6279) =< s(6278) s(6271) =< aux(444) with precondition: [] Closed-form bounds of start(V1,V,V12): ------------------------------------- * Chain [82] with precondition: [] - Upper bound: nat(V1)*4437+289+nat(V1)*2046*nat(2*V1)+nat(V)*3633+nat(V)*1674*nat(2*V)+nat(V12)*2156+nat(V12)*992*nat(2*V12)+nat(nat(2*V1)+ -1)*330*nat(3/5*V1)+nat(nat(2*V)+ -1)*270*nat(3/5*V)+nat(nat(2*V12)+ -1)*160*nat(3/5*V12)+nat(2*V1)*47+nat(2*V1)*330*nat(3/5*V1)+nat(2*V1)*1518*nat(3/8*V1)+nat(2*V)*115+nat(2*V)*270*nat(3/5*V)+nat(2*V)*1242*nat(3/8*V)+nat(2*V12)*12+nat(2*V12)*160*nat(3/5*V12)+nat(2*V12)*736*nat(3/8*V12)+nat(3/5*V1)*660+nat(3/5*V)*540+nat(3/5*V12)*320+nat(3/8*V1)*528+nat(3/8*V)*432+nat(3/8*V12)*256+nat(V1-V)*4+nat(V-V12)*14+nat(V-2*V12)*4 - Complexity: n^2 ### Maximum cost of start(V1,V,V12): nat(V1)*4437+289+nat(V1)*2046*nat(2*V1)+nat(V)*3633+nat(V)*1674*nat(2*V)+nat(V12)*2156+nat(V12)*992*nat(2*V12)+nat(nat(2*V1)+ -1)*330*nat(3/5*V1)+nat(nat(2*V)+ -1)*270*nat(3/5*V)+nat(nat(2*V12)+ -1)*160*nat(3/5*V12)+nat(2*V1)*47+nat(2*V1)*330*nat(3/5*V1)+nat(2*V1)*1518*nat(3/8*V1)+nat(2*V)*115+nat(2*V)*270*nat(3/5*V)+nat(2*V)*1242*nat(3/8*V)+nat(2*V12)*12+nat(2*V12)*160*nat(3/5*V12)+nat(2*V12)*736*nat(3/8*V12)+nat(3/5*V1)*660+nat(3/5*V)*540+nat(3/5*V12)*320+nat(3/8*V1)*528+nat(3/8*V)*432+nat(3/8*V12)*256+nat(V1-V)*4+nat(V-V12)*14+nat(V-2*V12)*4 Asymptotic class: n^2 * Total analysis performed in 19086 ms. ---------------------------------------- (14) BOUNDS(1, n^2) ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence minus(s(x), s(y)) ->^+ minus(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [x / s(x), y / s(y)]. The result substitution is [ ]. ---------------------------------------- (18) Complex Obligation (BEST) ---------------------------------------- (19) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) if_quot(true, x, y) -> s(quot(minus(x, y), y)) if_quot(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_if_quot(x_1, x_2, x_3)) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_if_quot(x_1, x_2, x_3) -> if_quot(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST