/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^5)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 52.3 s] (10) BOUNDS(1, n^5) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) [1] ifPlus(true, x, y) -> p(y) [1] ifPlus(false, x, y) -> plus(p(x), y) [1] times(x, y) -> timesIter(0, x, y, 0) [1] timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) [1] ifTimes(true, i, x, y, z) -> z [1] ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) [1] isZero(0) -> true [1] isZero(s(0)) -> false [1] isZero(s(s(x))) -> isZero(s(x)) [1] inc(0) -> s(0) [1] inc(s(x)) -> s(inc(x)) [1] inc(x) -> s(x) [1] p(0) -> 0 [1] p(s(x)) -> x [1] p(s(s(x))) -> s(p(s(x))) [1] ge(x, 0) -> true [1] ge(0, s(y)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] f0(0, y, x) -> f1(x, y, x) [1] f1(x, y, z) -> f2(x, y, z) [1] f2(x, 1, z) -> f0(x, z, z) [1] f0(x, y, z) -> d [1] f1(x, y, z) -> c [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) [1] ifPlus(true, x, y) -> p(y) [1] ifPlus(false, x, y) -> plus(p(x), y) [1] times(x, y) -> timesIter(0, x, y, 0) [1] timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) [1] ifTimes(true, i, x, y, z) -> z [1] ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) [1] isZero(0) -> true [1] isZero(s(0)) -> false [1] isZero(s(s(x))) -> isZero(s(x)) [1] inc(0) -> s(0) [1] inc(s(x)) -> s(inc(x)) [1] inc(x) -> s(x) [1] p(0) -> 0 [1] p(s(x)) -> x [1] p(s(s(x))) -> s(p(s(x))) [1] ge(x, 0) -> true [1] ge(0, s(y)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] f0(0, y, x) -> f1(x, y, x) [1] f1(x, y, z) -> f2(x, y, z) [1] f2(x, 1, z) -> f0(x, z, z) [1] f0(x, y, z) -> d [1] f1(x, y, z) -> c [1] The TRS has the following type information: plus :: 0:s:1 -> 0:s:1 -> 0:s:1 ifPlus :: true:false -> 0:s:1 -> 0:s:1 -> 0:s:1 isZero :: 0:s:1 -> true:false inc :: 0:s:1 -> 0:s:1 true :: true:false p :: 0:s:1 -> 0:s:1 false :: true:false times :: 0:s:1 -> 0:s:1 -> 0:s:1 timesIter :: 0:s:1 -> 0:s:1 -> 0:s:1 -> 0:s:1 -> 0:s:1 0 :: 0:s:1 ifTimes :: true:false -> 0:s:1 -> 0:s:1 -> 0:s:1 -> 0:s:1 -> 0:s:1 ge :: 0:s:1 -> 0:s:1 -> true:false s :: 0:s:1 -> 0:s:1 f0 :: 0:s:1 -> 0:s:1 -> 0:s:1 -> d:c f1 :: 0:s:1 -> 0:s:1 -> 0:s:1 -> d:c f2 :: 0:s:1 -> 0:s:1 -> 0:s:1 -> d:c 1 :: 0:s:1 d :: d:c c :: d:c Rewrite Strategy: INNERMOST ---------------------------------------- (5) 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: isZero(v0) -> null_isZero [0] p(v0) -> null_p [0] ge(v0, v1) -> null_ge [0] f2(v0, v1, v2) -> null_f2 [0] ifPlus(v0, v1, v2) -> null_ifPlus [0] ifTimes(v0, v1, v2, v3, v4) -> null_ifTimes [0] And the following fresh constants: null_isZero, null_p, null_ge, null_f2, null_ifPlus, null_ifTimes ---------------------------------------- (6) 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: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) [1] ifPlus(true, x, y) -> p(y) [1] ifPlus(false, x, y) -> plus(p(x), y) [1] times(x, y) -> timesIter(0, x, y, 0) [1] timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) [1] ifTimes(true, i, x, y, z) -> z [1] ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) [1] isZero(0) -> true [1] isZero(s(0)) -> false [1] isZero(s(s(x))) -> isZero(s(x)) [1] inc(0) -> s(0) [1] inc(s(x)) -> s(inc(x)) [1] inc(x) -> s(x) [1] p(0) -> 0 [1] p(s(x)) -> x [1] p(s(s(x))) -> s(p(s(x))) [1] ge(x, 0) -> true [1] ge(0, s(y)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] f0(0, y, x) -> f1(x, y, x) [1] f1(x, y, z) -> f2(x, y, z) [1] f2(x, 1, z) -> f0(x, z, z) [1] f0(x, y, z) -> d [1] f1(x, y, z) -> c [1] isZero(v0) -> null_isZero [0] p(v0) -> null_p [0] ge(v0, v1) -> null_ge [0] f2(v0, v1, v2) -> null_f2 [0] ifPlus(v0, v1, v2) -> null_ifPlus [0] ifTimes(v0, v1, v2, v3, v4) -> null_ifTimes [0] The TRS has the following type information: plus :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes ifPlus :: true:false:null_isZero:null_ge -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes isZero :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> true:false:null_isZero:null_ge inc :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes true :: true:false:null_isZero:null_ge p :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes false :: true:false:null_isZero:null_ge times :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes timesIter :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes 0 :: 0:s:1:null_p:null_ifPlus:null_ifTimes ifTimes :: true:false:null_isZero:null_ge -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes ge :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> true:false:null_isZero:null_ge s :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes f0 :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> d:c:null_f2 f1 :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> d:c:null_f2 f2 :: 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> 0:s:1:null_p:null_ifPlus:null_ifTimes -> d:c:null_f2 1 :: 0:s:1:null_p:null_ifPlus:null_ifTimes d :: d:c:null_f2 c :: d:c:null_f2 null_isZero :: true:false:null_isZero:null_ge null_p :: 0:s:1:null_p:null_ifPlus:null_ifTimes null_ge :: true:false:null_isZero:null_ge null_f2 :: d:c:null_f2 null_ifPlus :: 0:s:1:null_p:null_ifPlus:null_ifTimes null_ifTimes :: 0:s:1:null_p:null_ifPlus:null_ifTimes Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: true => 2 false => 1 0 => 0 1 => 1 d => 2 c => 1 null_isZero => 0 null_p => 0 null_ge => 0 null_f2 => 0 null_ifPlus => 0 null_ifTimes => 0 ---------------------------------------- (8) Obligation: Complexity RNTS consisting of the following rules: f0(z', z'', z1) -{ 1 }-> f1(x, y, x) :|: z'' = y, y >= 0, x >= 0, z1 = x, z' = 0 f0(z', z'', z1) -{ 1 }-> 2 :|: z1 = z, z >= 0, z' = x, z'' = y, x >= 0, y >= 0 f1(z', z'', z1) -{ 1 }-> f2(x, y, z) :|: z1 = z, z >= 0, z' = x, z'' = y, x >= 0, y >= 0 f1(z', z'', z1) -{ 1 }-> 1 :|: z1 = z, z >= 0, z' = x, z'' = y, x >= 0, y >= 0 f2(z', z'', z1) -{ 1 }-> f0(x, z, z) :|: z1 = z, z >= 0, z' = x, x >= 0, z'' = 1 f2(z', z'', z1) -{ 0 }-> 0 :|: v0 >= 0, z1 = v2, v1 >= 0, z'' = v1, v2 >= 0, z' = v0 ge(z', z'') -{ 1 }-> ge(x, y) :|: z' = 1 + x, x >= 0, y >= 0, z'' = 1 + y ge(z', z'') -{ 1 }-> 2 :|: z'' = 0, z' = x, x >= 0 ge(z', z'') -{ 1 }-> 1 :|: y >= 0, z'' = 1 + y, z' = 0 ge(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 ifPlus(z', z'', z1) -{ 1 }-> plus(p(x), y) :|: z1 = y, x >= 0, y >= 0, z'' = x, z' = 1 ifPlus(z', z'', z1) -{ 1 }-> p(y) :|: z1 = y, z' = 2, x >= 0, y >= 0, z'' = x ifPlus(z', z'', z1) -{ 0 }-> 0 :|: v0 >= 0, z1 = v2, v1 >= 0, z'' = v1, v2 >= 0, z' = v0 ifTimes(z', z'', z1, z2, z3) -{ 1 }-> z :|: z2 = y, z >= 0, z' = 2, z'' = i, z3 = z, x >= 0, y >= 0, i >= 0, z1 = x ifTimes(z', z'', z1, z2, z3) -{ 1 }-> timesIter(inc(i), x, y, plus(z, y)) :|: z2 = y, z >= 0, z'' = i, z3 = z, x >= 0, y >= 0, i >= 0, z' = 1, z1 = x ifTimes(z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z2 = v3, v0 >= 0, v4 >= 0, z1 = v2, v1 >= 0, z'' = v1, z3 = v4, v2 >= 0, v3 >= 0, z' = v0 inc(z') -{ 1 }-> 1 + x :|: z' = x, x >= 0 inc(z') -{ 1 }-> 1 + inc(x) :|: z' = 1 + x, x >= 0 inc(z') -{ 1 }-> 1 + 0 :|: z' = 0 isZero(z') -{ 1 }-> isZero(1 + x) :|: x >= 0, z' = 1 + (1 + x) isZero(z') -{ 1 }-> 2 :|: z' = 0 isZero(z') -{ 1 }-> 1 :|: z' = 1 + 0 isZero(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0 p(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0 p(z') -{ 1 }-> 0 :|: z' = 0 p(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0 p(z') -{ 1 }-> 1 + p(1 + x) :|: x >= 0, z' = 1 + (1 + x) plus(z', z'') -{ 1 }-> ifPlus(isZero(x), x, inc(y)) :|: z' = x, z'' = y, x >= 0, y >= 0 times(z', z'') -{ 1 }-> timesIter(0, x, y, 0) :|: z' = x, z'' = y, x >= 0, y >= 0 timesIter(z', z'', z1, z2) -{ 1 }-> ifTimes(ge(i, x), i, x, y, z) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, i >= 0, z'' = x, z' = i Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (9) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V, V1, V6, V14, V19),0,[plus(V, V1, Out)],[V >= 0,V1 >= 0]). eq(start(V, V1, V6, V14, V19),0,[ifPlus(V, V1, V6, Out)],[V >= 0,V1 >= 0,V6 >= 0]). eq(start(V, V1, V6, V14, V19),0,[times(V, V1, Out)],[V >= 0,V1 >= 0]). eq(start(V, V1, V6, V14, V19),0,[timesIter(V, V1, V6, V14, Out)],[V >= 0,V1 >= 0,V6 >= 0,V14 >= 0]). eq(start(V, V1, V6, V14, V19),0,[ifTimes(V, V1, V6, V14, V19, Out)],[V >= 0,V1 >= 0,V6 >= 0,V14 >= 0,V19 >= 0]). eq(start(V, V1, V6, V14, V19),0,[isZero(V, Out)],[V >= 0]). eq(start(V, V1, V6, V14, V19),0,[inc(V, Out)],[V >= 0]). eq(start(V, V1, V6, V14, V19),0,[p(V, Out)],[V >= 0]). eq(start(V, V1, V6, V14, V19),0,[ge(V, V1, Out)],[V >= 0,V1 >= 0]). eq(start(V, V1, V6, V14, V19),0,[f0(V, V1, V6, Out)],[V >= 0,V1 >= 0,V6 >= 0]). eq(start(V, V1, V6, V14, V19),0,[f1(V, V1, V6, Out)],[V >= 0,V1 >= 0,V6 >= 0]). eq(start(V, V1, V6, V14, V19),0,[f2(V, V1, V6, Out)],[V >= 0,V1 >= 0,V6 >= 0]). eq(plus(V, V1, Out),1,[isZero(V3, Ret0),inc(V2, Ret2),ifPlus(Ret0, V3, Ret2, Ret)],[Out = Ret,V = V3,V1 = V2,V3 >= 0,V2 >= 0]). eq(ifPlus(V, V1, V6, Out),1,[p(V5, Ret1)],[Out = Ret1,V6 = V5,V = 2,V4 >= 0,V5 >= 0,V1 = V4]). eq(ifPlus(V, V1, V6, Out),1,[p(V8, Ret01),plus(Ret01, V7, Ret3)],[Out = Ret3,V6 = V7,V8 >= 0,V7 >= 0,V1 = V8,V = 1]). eq(times(V, V1, Out),1,[timesIter(0, V9, V10, 0, Ret4)],[Out = Ret4,V = V9,V1 = V10,V9 >= 0,V10 >= 0]). eq(timesIter(V, V1, V6, V14, Out),1,[ge(V15, V12, Ret02),ifTimes(Ret02, V15, V12, V11, V13, Ret5)],[Out = Ret5,V6 = V11,V13 >= 0,V14 = V13,V12 >= 0,V11 >= 0,V15 >= 0,V1 = V12,V = V15]). eq(ifTimes(V, V1, V6, V14, V19, Out),1,[],[Out = V17,V14 = V16,V17 >= 0,V = 2,V1 = V20,V19 = V17,V18 >= 0,V16 >= 0,V20 >= 0,V6 = V18]). eq(ifTimes(V, V1, V6, V14, V19, Out),1,[inc(V22, Ret03),plus(V21, V23, Ret31),timesIter(Ret03, V24, V23, Ret31, Ret6)],[Out = Ret6,V14 = V23,V21 >= 0,V1 = V22,V19 = V21,V24 >= 0,V23 >= 0,V22 >= 0,V = 1,V6 = V24]). eq(isZero(V, Out),1,[],[Out = 2,V = 0]). eq(isZero(V, Out),1,[],[Out = 1,V = 1]). eq(isZero(V, Out),1,[isZero(1 + V25, Ret7)],[Out = Ret7,V25 >= 0,V = 2 + V25]). eq(inc(V, Out),1,[],[Out = 1,V = 0]). eq(inc(V, Out),1,[inc(V26, Ret11)],[Out = 1 + Ret11,V = 1 + V26,V26 >= 0]). eq(inc(V, Out),1,[],[Out = 1 + V27,V = V27,V27 >= 0]). eq(p(V, Out),1,[],[Out = 0,V = 0]). eq(p(V, Out),1,[],[Out = V28,V = 1 + V28,V28 >= 0]). eq(p(V, Out),1,[p(1 + V29, Ret12)],[Out = 1 + Ret12,V29 >= 0,V = 2 + V29]). eq(ge(V, V1, Out),1,[],[Out = 2,V1 = 0,V = V30,V30 >= 0]). eq(ge(V, V1, Out),1,[],[Out = 1,V31 >= 0,V1 = 1 + V31,V = 0]). eq(ge(V, V1, Out),1,[ge(V33, V32, Ret8)],[Out = Ret8,V = 1 + V33,V33 >= 0,V32 >= 0,V1 = 1 + V32]). eq(f0(V, V1, V6, Out),1,[f1(V34, V35, V34, Ret9)],[Out = Ret9,V1 = V35,V35 >= 0,V34 >= 0,V6 = V34,V = 0]). eq(f1(V, V1, V6, Out),1,[f2(V37, V38, V36, Ret10)],[Out = Ret10,V6 = V36,V36 >= 0,V = V37,V1 = V38,V37 >= 0,V38 >= 0]). eq(f2(V, V1, V6, Out),1,[f0(V39, V40, V40, Ret13)],[Out = Ret13,V6 = V40,V40 >= 0,V = V39,V39 >= 0,V1 = 1]). eq(f0(V, V1, V6, Out),1,[],[Out = 2,V6 = V43,V43 >= 0,V = V41,V1 = V42,V41 >= 0,V42 >= 0]). eq(f1(V, V1, V6, Out),1,[],[Out = 1,V6 = V46,V46 >= 0,V = V44,V1 = V45,V44 >= 0,V45 >= 0]). eq(isZero(V, Out),0,[],[Out = 0,V47 >= 0,V = V47]). eq(p(V, Out),0,[],[Out = 0,V48 >= 0,V = V48]). eq(ge(V, V1, Out),0,[],[Out = 0,V50 >= 0,V49 >= 0,V1 = V49,V = V50]). eq(f2(V, V1, V6, Out),0,[],[Out = 0,V51 >= 0,V6 = V53,V52 >= 0,V1 = V52,V53 >= 0,V = V51]). eq(ifPlus(V, V1, V6, Out),0,[],[Out = 0,V54 >= 0,V6 = V55,V56 >= 0,V1 = V56,V55 >= 0,V = V54]). eq(ifTimes(V, V1, V6, V14, V19, Out),0,[],[Out = 0,V14 = V61,V57 >= 0,V60 >= 0,V6 = V58,V59 >= 0,V1 = V59,V19 = V60,V58 >= 0,V61 >= 0,V = V57]). input_output_vars(plus(V,V1,Out),[V,V1],[Out]). input_output_vars(ifPlus(V,V1,V6,Out),[V,V1,V6],[Out]). input_output_vars(times(V,V1,Out),[V,V1],[Out]). input_output_vars(timesIter(V,V1,V6,V14,Out),[V,V1,V6,V14],[Out]). input_output_vars(ifTimes(V,V1,V6,V14,V19,Out),[V,V1,V6,V14,V19],[Out]). input_output_vars(isZero(V,Out),[V],[Out]). input_output_vars(inc(V,Out),[V],[Out]). input_output_vars(p(V,Out),[V],[Out]). input_output_vars(ge(V,V1,Out),[V,V1],[Out]). input_output_vars(f0(V,V1,V6,Out),[V,V1,V6],[Out]). input_output_vars(f1(V,V1,V6,Out),[V,V1,V6],[Out]). input_output_vars(f2(V,V1,V6,Out),[V,V1,V6],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [f0/4,f1/4,f2/4] 1. recursive : [ge/3] 2. recursive : [p/2] 3. recursive : [inc/2] 4. recursive : [isZero/2] 5. recursive : [ifPlus/4,plus/3] 6. recursive : [ifTimes/6,timesIter/5] 7. non_recursive : [times/3] 8. non_recursive : [start/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into f2/4 1. SCC is partially evaluated into ge/3 2. SCC is partially evaluated into p/2 3. SCC is partially evaluated into inc/2 4. SCC is partially evaluated into isZero/2 5. SCC is partially evaluated into plus/3 6. SCC is partially evaluated into timesIter/5 7. SCC is completely evaluated into other SCCs 8. SCC is partially evaluated into start/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations f2/4 * CE 32 is refined into CE [41] * CE 29 is refined into CE [42] * CE 31 is refined into CE [43] * CE 30 is refined into CE [44] ### Cost equations --> "Loop" of f2/4 * CEs [44] --> Loop 26 * CEs [41] --> Loop 27 * CEs [42] --> Loop 28 * CEs [43] --> Loop 29 ### Ranking functions of CR f2(V,V1,V6,Out) #### Partial ranking functions of CR f2(V,V1,V6,Out) ### Specialization of cost equations ge/3 * CE 40 is refined into CE [45] * CE 37 is refined into CE [46] * CE 38 is refined into CE [47] * CE 39 is refined into CE [48] ### Cost equations --> "Loop" of ge/3 * CEs [48] --> Loop 30 * CEs [45] --> Loop 31 * CEs [46] --> Loop 32 * CEs [47] --> Loop 33 ### Ranking functions of CR ge(V,V1,Out) * RF of phase [30]: [V,V1] #### Partial ranking functions of CR ge(V,V1,Out) * Partial RF of phase [30]: - RF of loop [30:1]: V V1 ### Specialization of cost equations p/2 * CE 26 is refined into CE [49] * CE 25 is refined into CE [50] * CE 28 is refined into CE [51] * CE 27 is refined into CE [52] ### Cost equations --> "Loop" of p/2 * CEs [52] --> Loop 34 * CEs [49] --> Loop 35 * CEs [50,51] --> Loop 36 ### Ranking functions of CR p(V,Out) * RF of phase [34]: [V-1] #### Partial ranking functions of CR p(V,Out) * Partial RF of phase [34]: - RF of loop [34:1]: V-1 ### Specialization of cost equations inc/2 * CE 17 is refined into CE [53] * CE 18 is refined into CE [54] ### Cost equations --> "Loop" of inc/2 * CEs [54] --> Loop 37 * CEs [53] --> Loop 38 ### Ranking functions of CR inc(V,Out) * RF of phase [37]: [V] #### Partial ranking functions of CR inc(V,Out) * Partial RF of phase [37]: - RF of loop [37:1]: V ### Specialization of cost equations isZero/2 * CE 36 is refined into CE [55] * CE 34 is refined into CE [56] * CE 33 is refined into CE [57] * CE 35 is refined into CE [58] ### Cost equations --> "Loop" of isZero/2 * CEs [58] --> Loop 39 * CEs [55] --> Loop 40 * CEs [56] --> Loop 41 * CEs [57] --> Loop 42 ### Ranking functions of CR isZero(V,Out) * RF of phase [39]: [V-1] #### Partial ranking functions of CR isZero(V,Out) * Partial RF of phase [39]: - RF of loop [39:1]: V-1 ### Specialization of cost equations plus/3 * CE 19 is refined into CE [59,60,61,62] * CE 21 is refined into CE [63,64,65] * CE 20 is refined into CE [66,67,68,69,70] ### Cost equations --> "Loop" of plus/3 * CEs [69,70] --> Loop 43 * CEs [68] --> Loop 44 * CEs [66,67] --> Loop 45 * CEs [60] --> Loop 46 * CEs [65] --> Loop 47 * CEs [64] --> Loop 48 * CEs [59,61,62,63] --> Loop 49 ### Ranking functions of CR plus(V,V1,Out) * RF of phase [43]: [V-1] #### Partial ranking functions of CR plus(V,V1,Out) * Partial RF of phase [43]: - RF of loop [43:1]: V-1 ### Specialization of cost equations timesIter/5 * CE 24 is refined into CE [71,72] * CE 22 is refined into CE [73,74,75,76,77] * CE 23 is refined into CE [78,79,80,81,82,83,84,85,86,87] ### Cost equations --> "Loop" of timesIter/5 * CEs [87] --> Loop 50 * CEs [85] --> Loop 51 * CEs [86] --> Loop 52 * CEs [84] --> Loop 53 * CEs [83] --> Loop 54 * CEs [82] --> Loop 55 * CEs [80] --> Loop 56 * CEs [81] --> Loop 57 * CEs [79] --> Loop 58 * CEs [78] --> Loop 59 * CEs [72] --> Loop 60 * CEs [71] --> Loop 61 * CEs [74] --> Loop 62 * CEs [73,75,76,77] --> Loop 63 ### Ranking functions of CR timesIter(V,V1,V6,V14,Out) * RF of phase [50,51,52,53,54]: [-V+V1] #### Partial ranking functions of CR timesIter(V,V1,V6,V14,Out) * Partial RF of phase [50,51,52,53,54]: - RF of loop [50:1,51:1,52:1,53:1,54:1]: -V+V1 - RF of loop [53:1]: -V14+1 depends on loops [50:1,51:1] ### Specialization of cost equations start/5 * CE 5 is refined into CE [88,89,90] * CE 2 is refined into CE [91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115] * CE 4 is refined into CE [116,117,118,119,120,121,122,123,124,125,126] * CE 1 is refined into CE [127] * CE 3 is refined into CE [128] * CE 6 is refined into CE [129,130,131] * CE 7 is refined into CE [132] * CE 8 is refined into CE [133,134,135] * CE 9 is refined into CE [136,137,138,139,140] * CE 10 is refined into CE [141,142,143,144,145,146,147] * CE 11 is refined into CE [148,149,150,151,152,153,154,155,156,157,158,159,160] * CE 12 is refined into CE [161,162,163,164] * CE 13 is refined into CE [165] * CE 14 is refined into CE [166,167,168] * CE 15 is refined into CE [169,170,171,172,173] * CE 16 is refined into CE [174,175,176] ### Cost equations --> "Loop" of start/5 * CEs [133,174] --> Loop 64 * CEs [157,158,170] --> Loop 65 * CEs [88,89,90] --> Loop 66 * CEs [91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,139,141,142,162] --> Loop 67 * CEs [127,128,129,130,131,132,134,135,136,137,138,140,143,144,145,146,147,148,149,150,151,152,153,154,155,156,159,160,161,163,164,165,166,167,168,169,171,172,173,175,176] --> Loop 68 ### Ranking functions of CR start(V,V1,V6,V14,V19) #### Partial ranking functions of CR start(V,V1,V6,V14,V19) Computing Bounds ===================================== #### Cost of chains of f2(V,V1,V6,Out): * Chain [29]: 3 with precondition: [V=0,V1=1,Out=1,V6>=0] * Chain [28]: 2 with precondition: [V1=1,Out=2,V>=0,V6>=0] * Chain [27]: 0 with precondition: [Out=0,V>=0,V1>=0,V6>=0] * Chain [26,28]: 5 with precondition: [V=0,V1=1,V6=1,Out=2] * Chain [26,27]: 3 with precondition: [V=0,V1=1,Out=0,V6>=0] #### Cost of chains of ge(V,V1,Out): * Chain [[30],33]: 1*it(30)+1 Such that:it(30) =< V with precondition: [Out=1,V>=1,V1>=V+1] * Chain [[30],32]: 1*it(30)+1 Such that:it(30) =< V1 with precondition: [Out=2,V1>=1,V>=V1] * Chain [[30],31]: 1*it(30)+0 Such that:it(30) =< V1 with precondition: [Out=0,V>=1,V1>=1] * Chain [33]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [32]: 1 with precondition: [V1=0,Out=2,V>=0] * Chain [31]: 0 with precondition: [Out=0,V>=0,V1>=0] #### Cost of chains of p(V,Out): * Chain [[34],36]: 1*it(34)+1 Such that:it(34) =< Out with precondition: [Out>=1,V>=Out+1] * Chain [[34],35]: 1*it(34)+1 Such that:it(34) =< Out with precondition: [V=Out+1,V>=2] * Chain [36]: 1 with precondition: [Out=0,V>=0] * Chain [35]: 1 with precondition: [V=Out+1,V>=1] #### Cost of chains of inc(V,Out): * Chain [[37],38]: 1*it(37)+1 Such that:it(37) =< Out with precondition: [V+1=Out,V>=1] * Chain [38]: 1 with precondition: [V+1=Out,V>=0] #### Cost of chains of isZero(V,Out): * Chain [[39],41]: 1*it(39)+1 Such that:it(39) =< V with precondition: [Out=1,V>=2] * Chain [[39],40]: 1*it(39)+0 Such that:it(39) =< V with precondition: [Out=0,V>=2] * Chain [42]: 1 with precondition: [V=0,Out=2] * Chain [41]: 1 with precondition: [V=1,Out=1] * Chain [40]: 0 with precondition: [Out=0,V>=0] #### Cost of chains of plus(V,V1,Out): * Chain [[43],49]: 7*it(43)+4*s(5)+3*s(22)+2*s(23)+1*s(24)+5 Such that:aux(8) =< V+V1 aux(2) =< V+V1+1 aux(10) =< V it(43) =< aux(10) s(5) =< aux(2) aux(7) =< aux(10)-1 s(25) =< it(43)*aux(8) s(26) =< it(43)*aux(10) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [Out=0,V>=2,V1>=0] * Chain [[43],46]: 5*it(43)+3*s(22)+2*s(23)+1*s(24)+1*s(27)+3 Such that:aux(11) =< V aux(12) =< V+V1 it(43) =< aux(11) s(27) =< aux(12) aux(7) =< aux(11)-1 s(25) =< it(43)*aux(12) s(26) =< it(43)*aux(11) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [Out=0,V>=2,V1>=0] * Chain [[43],45,49]: 5*it(43)+4*s(5)+3*s(22)+2*s(23)+1*s(24)+2*s(28)+10 Such that:aux(2) =< V+V1+1 aux(14) =< V aux(15) =< V+V1 it(43) =< aux(14) s(5) =< aux(2) s(28) =< aux(15) aux(7) =< aux(14)-1 s(25) =< it(43)*aux(15) s(26) =< it(43)*aux(14) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [Out=0,V>=2,V1>=0] * Chain [[43],45,48]: 5*it(43)+3*s(22)+2*s(23)+1*s(24)+3*s(28)+1*s(31)+10 Such that:aux(8) =< V+V1 aux(16) =< Out s(31) =< Out+1 aux(17) =< V it(43) =< aux(17) s(28) =< aux(16) aux(7) =< aux(17)-1 s(25) =< it(43)*aux(8) s(26) =< it(43)*aux(17) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [V1>=0,Out>=V1+2,V+V1>=Out] * Chain [[43],45,47]: 5*it(43)+3*s(22)+2*s(23)+1*s(24)+3*s(28)+1*s(33)+10 Such that:s(33) =< V+V1+1 aux(19) =< V aux(20) =< V+V1 it(43) =< aux(19) s(28) =< aux(20) aux(7) =< aux(19)-1 s(25) =< it(43)*aux(20) s(26) =< it(43)*aux(19) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [V>=2,V1>=0,Out>=1,V+V1>=Out] * Chain [[43],44,49]: 6*it(43)+4*s(5)+3*s(22)+2*s(23)+1*s(24)+1*s(36)+10 Such that:aux(8) =< V+V1 s(36) =< V+V1+1 aux(2) =< V+V1+2 aux(21) =< V it(43) =< aux(21) s(5) =< aux(2) aux(7) =< aux(21)-1 s(25) =< it(43)*aux(8) s(26) =< it(43)*aux(21) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [Out=0,V>=3,V1>=0] * Chain [[43],44,48]: 6*it(43)+3*s(22)+2*s(23)+1*s(24)+1*s(31)+2*s(32)+10 Such that:aux(8) =< V+V1 aux(22) =< Out s(31) =< Out+1 aux(23) =< V it(43) =< aux(23) s(32) =< aux(22) aux(7) =< aux(23)-1 s(25) =< it(43)*aux(8) s(26) =< it(43)*aux(23) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [V1>=0,Out>=V1+2,V+V1>=Out+1] * Chain [[43],44,47]: 6*it(43)+3*s(22)+2*s(23)+1*s(24)+1*s(33)+2*s(34)+10 Such that:aux(8) =< V+V1 aux(24) =< V+V1+1 s(33) =< V+V1+2 aux(25) =< V it(43) =< aux(25) s(34) =< aux(24) aux(7) =< aux(25)-1 s(25) =< it(43)*aux(8) s(26) =< it(43)*aux(25) s(24) =< it(43)*aux(7) s(22) =< s(26) s(23) =< s(25) with precondition: [V>=3,V1>=0,Out>=1,V+V1>=Out+1] * Chain [49]: 4*s(5)+2*s(6)+5 Such that:aux(1) =< V aux(2) =< V1+1 s(6) =< aux(1) s(5) =< aux(2) with precondition: [Out=0,V>=0,V1>=0] * Chain [48]: 1*s(31)+1*s(32)+5 Such that:s(32) =< V1 s(31) =< V1+1 with precondition: [V=0,V1=Out,V1>=0] * Chain [47]: 1*s(33)+1*s(34)+5 Such that:s(34) =< V1 s(33) =< V1+1 with precondition: [V=0,Out>=1,V1>=Out] * Chain [46]: 1*s(27)+3 Such that:s(27) =< V1+1 with precondition: [V=1,Out=0,V1>=0] * Chain [45,49]: 4*s(5)+2*s(28)+10 Such that:aux(13) =< V1+1 aux(2) =< V1+2 s(5) =< aux(2) s(28) =< aux(13) with precondition: [V=1,Out=0,V1>=0] * Chain [45,48]: 3*s(28)+1*s(31)+10 Such that:s(31) =< Out+1 aux(16) =< Out s(28) =< aux(16) with precondition: [V=1,Out=V1+1,Out>=1] * Chain [45,47]: 3*s(28)+1*s(33)+10 Such that:s(33) =< V1+2 aux(18) =< V1+1 s(28) =< aux(18) with precondition: [V=1,Out>=1,V1+1>=Out] * Chain [44,49]: 4*s(5)+1*s(35)+1*s(36)+10 Such that:s(35) =< V s(36) =< V1+1 aux(2) =< V1+2 s(5) =< aux(2) with precondition: [Out=0,V>=2,V1>=0] * Chain [44,48]: 1*s(31)+2*s(32)+1*s(35)+10 Such that:s(35) =< V s(31) =< Out+1 aux(22) =< Out s(32) =< aux(22) with precondition: [Out=V1+1,V>=2,Out>=1] * Chain [44,47]: 1*s(33)+2*s(34)+1*s(35)+10 Such that:s(35) =< V s(33) =< V1+2 aux(24) =< V1+1 s(34) =< aux(24) with precondition: [V>=2,Out>=1,V1+1>=Out] #### Cost of chains of timesIter(V,V1,V6,V14,Out): * Chain [[50,51,52,53,54],63]: 42*it(50)+18*it(53)+3*s(156)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+2 Such that:aux(95) =< -2*V+2*V1+V6 aux(93) =< -2*V+2*V1+V6-V14+1 aux(89) =< -V+V1+V6 aux(114) =< -V+V1+V6-V14 aux(87) =< -V+V1+V6-V14+1 aux(51) =< V6+1 aux(129) =< V6-V14 aux(101) =< V6-V14+1 aux(39) =< V6+V14 aux(131) =< -V+V1 aux(132) =< V1 aux(133) =< V14 s(156) =< aux(132) it(50) =< aux(131) it(53) =< aux(131) aux(59) =< aux(51)-1 aux(122) =< aux(51)-2 aux(117) =< aux(89) aux(116) =< aux(89)-1 aux(79) =< aux(51) aux(50) =< aux(132)+1 aux(96) =< aux(95)+1 aux(52) =< aux(51)+1 aux(90) =< aux(89)+1 aux(61) =< aux(132) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(89) s(292) =< it(50)*aux(51) s(275) =< it(50)*aux(132) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(114) aux(47) =< aux(100)+aux(40)+aux(101) aux(41) =< aux(100)+aux(40)+aux(101) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(87) s(321) =< aux(86)+aux(85)+aux(87) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(133)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(133) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [Out=0,V>=1,V6>=0,V14>=0,V1>=V+1] * Chain [[50,51,52,53,54],60]: 42*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(331)+3 Such that:aux(95) =< -2*V+2*V1+V6 aux(93) =< -2*V+2*V1+V6-V14+1 aux(89) =< -V+V1+V6 aux(114) =< -V+V1+V6-V14 aux(87) =< -V+V1+V6-V14+1 aux(51) =< V6+1 aux(129) =< V6-V14 aux(101) =< V6-V14+1 aux(39) =< V6+V14 aux(130) =< V14 aux(72) =< V14-Out aux(134) =< -V+V1 aux(135) =< V1 s(331) =< aux(135) it(50) =< aux(134) it(53) =< aux(134) aux(59) =< aux(51)-1 aux(122) =< aux(51)-2 aux(117) =< aux(89) aux(116) =< aux(89)-1 aux(79) =< aux(51) aux(50) =< aux(135)+1 aux(96) =< aux(95)+1 aux(52) =< aux(51)+1 aux(90) =< aux(89)+1 aux(61) =< aux(135) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(89) s(292) =< it(50)*aux(51) s(275) =< it(50)*aux(135) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(114) aux(47) =< aux(100)+aux(40)+aux(101) aux(41) =< aux(100)+aux(40)+aux(101) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(87) s(321) =< aux(86)+aux(85)+aux(87) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(130)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(130) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [V>=1,V6>=0,V14>=0,Out>=0,V1>=V+1] * Chain [63]: 2*s(156)+1*s(157)+2 Such that:s(157) =< V aux(36) =< V1 s(156) =< aux(36) with precondition: [Out=0,V>=0,V1>=0,V6>=0,V14>=0] * Chain [62]: 2 with precondition: [V1=0,Out=0,V>=0,V6>=0,V14>=0] * Chain [61]: 3 with precondition: [V1=0,V14=Out,V>=0,V6>=0,V14>=0] * Chain [60]: 1*s(331)+3 Such that:s(331) =< V1 with precondition: [V14=Out,V1>=1,V6>=0,V14>=0,V>=V1] * Chain [59,[50,51,52,53,54],63]: 45*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(332)+1*s(333)+1*s(334)+11 Such that:aux(89) =< V1+V6 aux(93) =< 2*V1 aux(95) =< 2*V1+V6 aux(39) =< 2*V6 aux(136) =< 1 aux(137) =< V1 aux(138) =< V6 aux(139) =< V6+1 s(332) =< aux(136) s(333) =< aux(138) s(334) =< aux(139) it(50) =< aux(137) it(53) =< aux(137) aux(59) =< aux(139)-1 aux(122) =< aux(139)-2 aux(117) =< aux(89) aux(116) =< aux(89)-1 aux(79) =< aux(139) aux(50) =< aux(137)+1 aux(96) =< aux(95)+1 aux(52) =< aux(139)+1 aux(90) =< aux(89)+1 aux(61) =< aux(137) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(89) s(292) =< it(50)*aux(139) s(275) =< it(50)*aux(137) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118) s(329) =< aux(113)+aux(112)+aux(137) aux(47) =< aux(100)+aux(40)+aux(136) aux(41) =< aux(100)+aux(40)+aux(136) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(137) s(321) =< aux(86)+aux(85)+aux(137) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(138)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(138) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [V=0,V14=0,Out=0,V1>=2,V6>=0] * Chain [59,[50,51,52,53,54],60]: 43*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(332)+1*s(333)+1*s(334)+12 Such that:aux(89) =< V1+V6 aux(93) =< 2*V1 aux(95) =< 2*V1+V6 aux(72) =< V6-Out aux(39) =< 2*V6 aux(140) =< 1 aux(141) =< V1 aux(142) =< V6 aux(143) =< V6+1 s(332) =< aux(140) s(333) =< aux(142) s(334) =< aux(143) it(50) =< aux(141) it(53) =< aux(141) aux(59) =< aux(143)-1 aux(122) =< aux(143)-2 aux(117) =< aux(89) aux(116) =< aux(89)-1 aux(79) =< aux(143) aux(50) =< aux(141)+1 aux(96) =< aux(95)+1 aux(52) =< aux(143)+1 aux(90) =< aux(89)+1 aux(61) =< aux(141) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(89) s(292) =< it(50)*aux(143) s(275) =< it(50)*aux(141) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118) s(329) =< aux(113)+aux(112)+aux(141) aux(47) =< aux(100)+aux(40)+aux(140) aux(41) =< aux(100)+aux(40)+aux(140) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(141) s(321) =< aux(86)+aux(85)+aux(141) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(142)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(142) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [V=0,V14=0,V1>=2,V6>=0,Out>=0] * Chain [59,63]: 2*s(156)+2*s(157)+1*s(333)+1*s(334)+11 Such that:aux(36) =< V1 s(333) =< V6 s(334) =< V6+1 aux(144) =< 1 s(157) =< aux(144) s(156) =< aux(36) with precondition: [V=0,V14=0,Out=0,V1>=1,V6>=0] * Chain [59,60]: 2*s(331)+1*s(333)+1*s(334)+12 Such that:s(333) =< Out s(334) =< Out+1 aux(145) =< 1 s(331) =< aux(145) with precondition: [V=0,V1=1,V14=0,V6=Out,V6>=0] * Chain [58,[50,51,52,53,54],63]: 45*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(335)+1*s(336)+1*s(337)+11 Such that:s(335) =< 1 aux(95) =< 2*V1+V6 aux(93) =< 2*V1+2*V6 s(336) =< V6 aux(129) =< 2*V6 aux(101) =< 2*V6+1 aux(146) =< V1 aux(147) =< V1+V6 aux(148) =< V1+2*V6 aux(149) =< V6+1 s(337) =< aux(149) it(50) =< aux(146) it(53) =< aux(146) aux(59) =< aux(149)-1 aux(122) =< aux(149)-2 aux(117) =< aux(147) aux(116) =< aux(147)-1 aux(79) =< aux(149) aux(50) =< aux(146)+1 aux(96) =< aux(95)+1 aux(52) =< aux(149)+1 aux(90) =< aux(147)+1 aux(61) =< aux(146) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(147) s(292) =< it(50)*aux(149) s(275) =< it(50)*aux(146) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(148) aux(47) =< aux(100)+aux(40)+aux(101) aux(41) =< aux(100)+aux(40)+aux(101) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(147) s(321) =< aux(86)+aux(85)+aux(147) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(147)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(148)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(147) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [V=0,V14=0,Out=0,V1>=2,V6>=1] * Chain [58,[50,51,52,53,54],60]: 43*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(335)+1*s(336)+1*s(337)+12 Such that:s(335) =< 1 aux(95) =< 2*V1+V6 aux(93) =< 2*V1+2*V6 s(336) =< V6 aux(72) =< V6-Out aux(129) =< 2*V6 aux(101) =< 2*V6+1 aux(150) =< V1 aux(151) =< V1+V6 aux(152) =< V1+2*V6 aux(153) =< V6+1 s(337) =< aux(153) it(50) =< aux(150) it(53) =< aux(150) aux(59) =< aux(153)-1 aux(122) =< aux(153)-2 aux(117) =< aux(151) aux(116) =< aux(151)-1 aux(79) =< aux(153) aux(50) =< aux(150)+1 aux(96) =< aux(95)+1 aux(52) =< aux(153)+1 aux(90) =< aux(151)+1 aux(61) =< aux(150) aux(91) =< it(50)*aux(95) aux(85) =< it(50)*aux(151) s(292) =< it(50)*aux(153) s(275) =< it(50)*aux(150) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(152) aux(47) =< aux(100)+aux(40)+aux(101) aux(41) =< aux(100)+aux(40)+aux(101) aux(42) =< aux(92)+aux(91)+aux(93) s(318) =< aux(92)+aux(91)+aux(93) s(328) =< aux(92)+aux(91)+aux(93) it(53) =< aux(86)+aux(85)+aux(151) s(321) =< aux(86)+aux(85)+aux(151) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(151)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(152)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(151) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) with precondition: [V=0,V14=0,V1>=2,V6>=1,Out>=0] * Chain [58,63]: 2*s(156)+2*s(157)+1*s(336)+1*s(337)+11 Such that:aux(36) =< V1 s(336) =< V6 s(337) =< V6+1 aux(154) =< 1 s(157) =< aux(154) s(156) =< aux(36) with precondition: [V=0,V14=0,Out=0,V1>=1,V6>=1] * Chain [58,60]: 2*s(331)+1*s(336)+1*s(337)+12 Such that:s(336) =< V6 s(337) =< V6+1 aux(155) =< 1 s(331) =< aux(155) with precondition: [V=0,V1=1,V14=0,Out>=1,V6>=Out] * Chain [57,[50,51,52,53,54],63]: 45*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(338)+1*s(340)+4*s(342)+3*s(343)+16 Such that:s(338) =< 1 aux(39) =< 2*V1+2*V6 aux(129) =< V6 s(340) =< V6+2 aux(156) =< V1 aux(157) =< V1+V6 aux(158) =< 2*V1+V6 aux(159) =< V6+1 s(342) =< aux(158) it(50) =< aux(156) it(53) =< aux(156) aux(59) =< aux(159)-1 aux(122) =< aux(159)-2 aux(117) =< aux(157) aux(116) =< aux(157)-1 aux(79) =< aux(159) aux(50) =< aux(156)+1 aux(96) =< aux(158)+1 aux(52) =< aux(159)+1 aux(90) =< aux(157)+1 aux(61) =< aux(156) aux(91) =< it(50)*aux(158) aux(85) =< it(50)*aux(157) s(292) =< it(50)*aux(159) s(275) =< it(50)*aux(156) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(157) aux(47) =< aux(100)+aux(40)+aux(159) aux(41) =< aux(100)+aux(40)+aux(159) aux(42) =< aux(92)+aux(91)+aux(158) s(318) =< aux(92)+aux(91)+aux(158) s(328) =< aux(92)+aux(91)+aux(158) it(53) =< aux(86)+aux(85)+aux(157) s(321) =< aux(86)+aux(85)+aux(157) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(158)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(158) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(343) =< aux(159) with precondition: [V=0,V14=1,Out=0,V1>=2,V6>=0] * Chain [57,[50,51,52,53,54],60]: 43*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(338)+1*s(340)+4*s(342)+3*s(343)+17 Such that:s(338) =< 1 aux(39) =< 2*V1+2*V6 aux(129) =< V6 s(340) =< V6+2 aux(72) =< V6-Out+1 aux(160) =< V1 aux(161) =< V1+V6 aux(162) =< 2*V1+V6 aux(163) =< V6+1 s(342) =< aux(162) it(50) =< aux(160) it(53) =< aux(160) aux(59) =< aux(163)-1 aux(122) =< aux(163)-2 aux(117) =< aux(161) aux(116) =< aux(161)-1 aux(79) =< aux(163) aux(50) =< aux(160)+1 aux(96) =< aux(162)+1 aux(52) =< aux(163)+1 aux(90) =< aux(161)+1 aux(61) =< aux(160) aux(91) =< it(50)*aux(162) aux(85) =< it(50)*aux(161) s(292) =< it(50)*aux(163) s(275) =< it(50)*aux(160) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(129) s(329) =< aux(113)+aux(112)+aux(161) aux(47) =< aux(100)+aux(40)+aux(163) aux(41) =< aux(100)+aux(40)+aux(163) aux(42) =< aux(92)+aux(91)+aux(162) s(318) =< aux(92)+aux(91)+aux(162) s(328) =< aux(92)+aux(91)+aux(162) it(53) =< aux(86)+aux(85)+aux(161) s(321) =< aux(86)+aux(85)+aux(161) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(162)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(162) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(343) =< aux(163) with precondition: [V=0,V14=1,V1>=2,V6>=0,Out>=0] * Chain [57,63]: 2*s(156)+2*s(157)+2*s(340)+6*s(343)+16 Such that:aux(36) =< V1 aux(164) =< 1 aux(165) =< V6+1 aux(166) =< V6+2 s(157) =< aux(164) s(340) =< aux(166) s(156) =< aux(36) s(343) =< aux(165) with precondition: [V=0,V14=1,Out=0,V1>=1,V6>=0] * Chain [57,60]: 2*s(331)+1*s(340)+1*s(342)+3*s(343)+3*s(344)+17 Such that:s(339) =< V6+1 s(340) =< V6+2 s(341) =< Out s(342) =< Out+1 aux(167) =< 1 s(331) =< aux(167) s(343) =< s(339) s(344) =< s(341) with precondition: [V=0,V1=1,V14=1,Out>=1,V6+1>=Out] * Chain [56,[50,51,52,53,54],63]: 45*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(345)+26*s(352)+9*s(353)+8*s(354)+8*s(355)+3*s(356)+4*s(360)+12*s(361)+8*s(362)+4*s(363)+16 Such that:s(345) =< 1 s(351) =< V6+2 s(348) =< V6+V14 s(349) =< V6+V14+1 s(346) =< V6+V14+2 s(347) =< V14 aux(168) =< V1 aux(169) =< V1+V6 aux(170) =< 2*V1+V6 aux(171) =< V6 aux(172) =< V6+1 it(50) =< aux(168) it(53) =< aux(168) aux(59) =< aux(172)-1 aux(122) =< aux(172)-2 aux(117) =< aux(169) aux(116) =< aux(169)-1 aux(79) =< aux(172) aux(50) =< aux(168)+1 aux(96) =< aux(170)+1 aux(52) =< aux(172)+1 aux(90) =< aux(169)+1 aux(61) =< aux(168) aux(91) =< it(50)*aux(170) aux(85) =< it(50)*aux(169) s(292) =< it(50)*aux(172) s(275) =< it(50)*aux(168) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(171) s(329) =< aux(113)+aux(112)+aux(169) aux(47) =< aux(100)+aux(40)+aux(172) aux(41) =< aux(100)+aux(40)+aux(172) aux(42) =< aux(92)+aux(91)+aux(170) s(318) =< aux(92)+aux(91)+aux(170) s(328) =< aux(92)+aux(91)+aux(170) it(53) =< aux(86)+aux(85)+aux(169) s(321) =< aux(86)+aux(85)+aux(169) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(171)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(352) =< s(347) s(353) =< s(349) s(354) =< aux(172) s(355) =< s(351) s(356) =< s(348) s(357) =< s(347)-1 s(358) =< s(352)*s(348) s(359) =< s(352)*s(347) s(360) =< s(352)*s(357) s(361) =< s(359) s(362) =< s(358) s(363) =< s(346) with precondition: [V=0,Out=0,V1>=2,V6>=0,V14>=0] * Chain [56,[50,51,52,53,54],60]: 43*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(345)+26*s(352)+9*s(353)+8*s(354)+8*s(355)+3*s(356)+4*s(360)+12*s(361)+8*s(362)+4*s(363)+17 Such that:s(345) =< 1 s(351) =< V6+2 s(348) =< V6+V14 s(349) =< V6+V14+1 s(346) =< V6+V14+2 s(347) =< V14 aux(72) =< -Out aux(173) =< V1 aux(174) =< V1+V6 aux(175) =< 2*V1+V6 aux(176) =< V6 aux(177) =< V6+1 it(50) =< aux(173) it(53) =< aux(173) aux(59) =< aux(177)-1 aux(122) =< aux(177)-2 aux(117) =< aux(174) aux(116) =< aux(174)-1 aux(79) =< aux(177) aux(50) =< aux(173)+1 aux(96) =< aux(175)+1 aux(52) =< aux(177)+1 aux(90) =< aux(174)+1 aux(61) =< aux(173) aux(91) =< it(50)*aux(175) aux(85) =< it(50)*aux(174) s(292) =< it(50)*aux(177) s(275) =< it(50)*aux(173) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(176) s(329) =< aux(113)+aux(112)+aux(174) aux(47) =< aux(100)+aux(40)+aux(177) aux(41) =< aux(100)+aux(40)+aux(177) aux(42) =< aux(92)+aux(91)+aux(175) s(318) =< aux(92)+aux(91)+aux(175) s(328) =< aux(92)+aux(91)+aux(175) it(53) =< aux(86)+aux(85)+aux(174) s(321) =< aux(86)+aux(85)+aux(174) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(176)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(352) =< s(347) s(353) =< s(349) s(354) =< aux(177) s(355) =< s(351) s(356) =< s(348) s(357) =< s(347)-1 s(358) =< s(352)*s(348) s(359) =< s(352)*s(347) s(360) =< s(352)*s(357) s(361) =< s(359) s(362) =< s(358) s(363) =< s(346) with precondition: [V=0,V1>=2,V6>=0,V14>=0,Out>=0] * Chain [56,63]: 2*s(156)+2*s(157)+26*s(352)+9*s(353)+8*s(354)+8*s(355)+3*s(356)+4*s(360)+12*s(361)+8*s(362)+4*s(363)+16 Such that:aux(36) =< V1 s(350) =< V6+1 s(351) =< V6+2 s(348) =< V6+V14 s(349) =< V6+V14+1 s(346) =< V6+V14+2 s(347) =< V14 aux(178) =< 1 s(157) =< aux(178) s(156) =< aux(36) s(352) =< s(347) s(353) =< s(349) s(354) =< s(350) s(355) =< s(351) s(356) =< s(348) s(357) =< s(347)-1 s(358) =< s(352)*s(348) s(359) =< s(352)*s(347) s(360) =< s(352)*s(357) s(361) =< s(359) s(362) =< s(358) s(363) =< s(346) with precondition: [V=0,Out=0,V1>=1,V6>=0,V14>=0] * Chain [56,60]: 2*s(331)+26*s(352)+9*s(353)+8*s(354)+8*s(355)+3*s(356)+4*s(360)+12*s(361)+8*s(362)+4*s(363)+17 Such that:s(350) =< V6+1 s(351) =< V6+2 s(348) =< V6+V14 s(349) =< V6+V14+1 s(346) =< V6+V14+2 s(347) =< V14 aux(179) =< 1 s(331) =< aux(179) s(352) =< s(347) s(353) =< s(349) s(354) =< s(350) s(355) =< s(351) s(356) =< s(348) s(357) =< s(347)-1 s(358) =< s(352)*s(348) s(359) =< s(352)*s(347) s(360) =< s(352)*s(357) s(361) =< s(359) s(362) =< s(358) s(363) =< s(346) with precondition: [V=0,V1=1,Out=0,V6>=0,V14>=0] * Chain [55,[50,51,52,53,54],63]: 45*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(364)+1*s(365)+1*s(367)+24*s(373)+6*s(374)+2*s(376)+10*s(377)+4*s(381)+12*s(382)+8*s(383)+16 Such that:s(364) =< 1 s(367) =< V6+2 s(365) =< V6+V14+2 aux(39) =< 2*V6+V14 s(368) =< V14 aux(180) =< V1 aux(181) =< V1+V6 aux(182) =< 2*V1+V6 aux(183) =< V6 aux(184) =< V6+1 aux(185) =< V6+V14 aux(186) =< V6+V14+1 it(50) =< aux(180) it(53) =< aux(180) aux(59) =< aux(184)-1 aux(122) =< aux(184)-2 aux(117) =< aux(181) aux(116) =< aux(181)-1 aux(79) =< aux(184) aux(50) =< aux(180)+1 aux(96) =< aux(182)+1 aux(52) =< aux(184)+1 aux(90) =< aux(181)+1 aux(61) =< aux(180) aux(91) =< it(50)*aux(182) aux(85) =< it(50)*aux(181) s(292) =< it(50)*aux(184) s(275) =< it(50)*aux(180) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(183) s(329) =< aux(113)+aux(112)+aux(181) aux(47) =< aux(100)+aux(40)+aux(183) aux(41) =< aux(100)+aux(40)+aux(183) aux(42) =< aux(92)+aux(91)+aux(182) s(318) =< aux(92)+aux(91)+aux(182) s(328) =< aux(92)+aux(91)+aux(182) it(53) =< aux(86)+aux(85)+aux(181) s(321) =< aux(86)+aux(85)+aux(181) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(185)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(185) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(373) =< s(368) s(374) =< aux(186) s(376) =< aux(184) s(377) =< aux(185) s(378) =< s(368)-1 s(379) =< s(373)*aux(185) s(380) =< s(373)*s(368) s(381) =< s(373)*s(378) s(382) =< s(380) s(383) =< s(379) with precondition: [V=0,Out=0,V1>=2,V6>=0,V14>=2] * Chain [55,[50,51,52,53,54],60]: 43*it(50)+18*it(53)+1*s(275)+3*s(276)+1*s(277)+2*s(278)+24*s(279)+15*s(280)+2*s(282)+13*s(283)+4*s(284)+12*s(285)+8*s(286)+2*s(296)+26*s(298)+11*s(300)+8*s(301)+4*s(303)+12*s(304)+8*s(305)+4*s(306)+1*s(318)+3*s(320)+4*s(323)+1*s(324)+1*s(325)+1*s(328)+1*s(329)+1*s(364)+1*s(365)+1*s(367)+24*s(373)+6*s(374)+2*s(376)+10*s(377)+4*s(381)+12*s(382)+8*s(383)+17 Such that:s(364) =< 1 s(367) =< V6+2 s(365) =< V6+V14+2 aux(72) =< V6+V14-Out aux(39) =< 2*V6+V14 s(368) =< V14 aux(187) =< V1 aux(188) =< V1+V6 aux(189) =< 2*V1+V6 aux(190) =< V6 aux(191) =< V6+1 aux(192) =< V6+V14 aux(193) =< V6+V14+1 it(50) =< aux(187) it(53) =< aux(187) aux(59) =< aux(191)-1 aux(122) =< aux(191)-2 aux(117) =< aux(188) aux(116) =< aux(188)-1 aux(79) =< aux(191) aux(50) =< aux(187)+1 aux(96) =< aux(189)+1 aux(52) =< aux(191)+1 aux(90) =< aux(188)+1 aux(61) =< aux(187) aux(91) =< it(50)*aux(189) aux(85) =< it(50)*aux(188) s(292) =< it(50)*aux(191) s(275) =< it(50)*aux(187) aux(40) =< it(50)*aux(59) aux(118) =< it(50)*aux(122) aux(113) =< it(50)*aux(117) aux(112) =< it(50)*aux(116) aux(41) =< it(50)*aux(59) aux(100) =< it(50)*aux(79) aux(92) =< it(50)*aux(96) s(318) =< it(50)*aux(52) aux(86) =< it(50)*aux(90) s(321) =< it(50)*aux(79) s(278) =< it(50)*aux(52) s(276) =< it(50)*aux(50) s(296) =< it(50)*aux(61) s(311) =< it(50)*aux(52) aux(43) =< aux(40)+aux(118)+aux(190) s(329) =< aux(113)+aux(112)+aux(188) aux(47) =< aux(100)+aux(40)+aux(190) aux(41) =< aux(100)+aux(40)+aux(190) aux(42) =< aux(92)+aux(91)+aux(189) s(318) =< aux(92)+aux(91)+aux(189) s(328) =< aux(92)+aux(91)+aux(189) it(53) =< aux(86)+aux(85)+aux(188) s(321) =< aux(86)+aux(85)+aux(188) aux(43) =< it(53)*aux(59) s(329) =< it(53)*aux(79) s(326) =< it(53)*aux(50) aux(65) =< it(53)*aux(59) s(325) =< it(53)*aux(79) s(324) =< it(53)*aux(59) s(188) =< aux(192)+aux(40)+aux(41)+aux(47)+aux(47) s(185) =< aux(39)+aux(40)+aux(41)+aux(42)+aux(43) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(192) aux(55) =< s(185)+2 aux(54) =< s(185)+1 aux(53) =< s(185) aux(56) =< s(188) s(314) =< aux(43)+aux(65)+aux(40)+aux(40)+aux(72) s(307) =< it(50)*aux(55) s(293) =< it(50)*aux(54) s(288) =< it(50)*aux(53) s(314) =< it(50)*aux(56) s(295) =< it(50)*aux(56) s(277) =< it(50)*aux(55) s(323) =< s(326) s(300) =< aux(100) s(320) =< s(321) s(298) =< s(314) s(280) =< s(293) s(301) =< s(311) s(283) =< s(288) s(236) =< aux(56)-1 s(308) =< s(298)*aux(53) s(309) =< s(298)*aux(56) s(303) =< s(298)*s(236) s(304) =< s(309) s(305) =< s(308) s(306) =< s(307) s(279) =< s(295) s(282) =< s(292) s(196) =< s(188)-1 s(289) =< s(279)*s(185) s(290) =< s(279)*s(188) s(284) =< s(279)*s(196) s(285) =< s(290) s(286) =< s(289) s(373) =< s(368) s(374) =< aux(193) s(376) =< aux(191) s(377) =< aux(192) s(378) =< s(368)-1 s(379) =< s(373)*aux(192) s(380) =< s(373)*s(368) s(381) =< s(373)*s(378) s(382) =< s(380) s(383) =< s(379) with precondition: [V=0,V1>=2,V6>=0,V14>=2,Out>=0] * Chain [55,63]: 2*s(156)+2*s(157)+1*s(365)+1*s(367)+24*s(373)+6*s(374)+2*s(376)+10*s(377)+4*s(381)+12*s(382)+8*s(383)+16 Such that:aux(36) =< V1 s(366) =< V6+1 s(367) =< V6+2 s(365) =< V6+V14+2 s(368) =< V14 aux(194) =< 1 aux(195) =< V6+V14 aux(196) =< V6+V14+1 s(157) =< aux(194) s(156) =< aux(36) s(373) =< s(368) s(374) =< aux(196) s(376) =< s(366) s(377) =< aux(195) s(378) =< s(368)-1 s(379) =< s(373)*aux(195) s(380) =< s(373)*s(368) s(381) =< s(373)*s(378) s(382) =< s(380) s(383) =< s(379) with precondition: [V=0,Out=0,V1>=1,V6>=0,V14>=2] * Chain [55,60]: 2*s(331)+1*s(365)+1*s(367)+24*s(373)+3*s(374)+3*s(375)+2*s(376)+7*s(377)+4*s(381)+12*s(382)+8*s(383)+3*s(384)+17 Such that:s(366) =< V6+1 s(367) =< V6+2 s(369) =< V6+V14 s(370) =< V6+V14+1 s(365) =< V6+V14+2 s(368) =< V14 s(371) =< Out s(372) =< Out+1 aux(197) =< 1 s(331) =< aux(197) s(373) =< s(368) s(374) =< s(370) s(375) =< s(372) s(376) =< s(366) s(377) =< s(371) s(378) =< s(368)-1 s(379) =< s(373)*s(369) s(380) =< s(373)*s(368) s(381) =< s(373)*s(378) s(382) =< s(380) s(383) =< s(379) s(384) =< s(369) with precondition: [V=0,V1=1,V6>=0,V14>=2,Out>=1,V6+V14>=Out] #### Cost of chains of start(V,V1,V6,V14,V19): * Chain [68]: 509*s(1361)+110*s(1362)+463*s(1371)+15*s(1372)+63*s(1374)+13*s(1375)+8*s(1379)+24*s(1380)+16*s(1381)+5*s(1382)+48*s(1424)+108*s(1428)+9*s(1442)+4*s(1450)+18*s(1453)+27*s(1454)+18*s(1455)+4*s(1458)+4*s(1461)+6*s(1464)+6*s(1465)+2*s(1477)+24*s(1478)+99*s(1479)+18*s(1480)+52*s(1481)+30*s(1482)+72*s(1483)+26*s(1484)+8*s(1488)+24*s(1489)+16*s(1490)+8*s(1491)+48*s(1492)+18*s(1493)+8*s(1497)+24*s(1498)+16*s(1499)+2*s(1523)+26*s(1524)+30*s(1525)+26*s(1526)+4*s(1530)+12*s(1531)+8*s(1532)+8*s(1533)+48*s(1534)+8*s(1538)+24*s(1539)+8*s(1540)+18*s(1542)+1*s(1558)+1*s(1566)+1*s(1569)+1*s(1572)+1*s(1573)+1*s(1585)+4*s(1586)+3*s(1588)+26*s(1589)+15*s(1590)+13*s(1592)+4*s(1596)+12*s(1597)+8*s(1598)+4*s(1599)+8*s(1607)+2*s(1645)+2*s(1653)+2*s(1656)+2*s(1672)+26*s(1676)+30*s(1677)+26*s(1679)+4*s(1683)+12*s(1684)+8*s(1685)+8*s(1686)+48*s(1687)+8*s(1692)+24*s(1693)+16*s(1694)+36*s(1695)+2*s(1697)+2*s(1700)+2*s(1703)+2*s(1706)+2*s(1707)+2*s(1719)+8*s(1720)+6*s(1721)+52*s(1722)+30*s(1723)+26*s(1724)+8*s(1728)+24*s(1729)+16*s(1730)+8*s(1731)+48*s(1732)+8*s(1736)+24*s(1737)+16*s(1738)+26*s(1860)+4*s(1866)+12*s(1867)+8*s(1868)+24*s(1870)+4*s(1874)+12*s(1875)+8*s(1876)+26*s(1896)+4*s(1902)+12*s(1903)+8*s(1904)+8*s(1957)+66*s(1958)+42*s(1966)+20*s(1996)+144*s(1998)+10*s(2012)+6*s(2020)+20*s(2023)+30*s(2024)+20*s(2025)+6*s(2028)+6*s(2031)+8*s(2034)+8*s(2035)+2*s(2047)+32*s(2048)+110*s(2049)+24*s(2050)+52*s(2051)+30*s(2052)+80*s(2053)+26*s(2054)+8*s(2058)+24*s(2059)+16*s(2060)+8*s(2061)+48*s(2062)+20*s(2063)+8*s(2067)+24*s(2068)+16*s(2069)+200*s(2070)+60*s(2071)+52*s(2073)+32*s(2077)+96*s(2078)+64*s(2079)+2*s(2093)+52*s(2094)+30*s(2095)+26*s(2096)+8*s(2100)+24*s(2101)+16*s(2102)+8*s(2103)+48*s(2104)+8*s(2108)+24*s(2109)+16*s(2110)+84*s(2111)+36*s(2112)+2*s(2120)+2*s(2128)+4*s(2131)+6*s(2132)+4*s(2133)+2*s(2136)+2*s(2139)+2*s(2142)+2*s(2143)+2*s(2155)+8*s(2156)+22*s(2157)+6*s(2158)+52*s(2159)+30*s(2160)+16*s(2161)+26*s(2162)+8*s(2166)+24*s(2167)+16*s(2168)+8*s(2169)+48*s(2170)+4*s(2171)+8*s(2175)+24*s(2176)+16*s(2177)+2*s(2237)+2*s(2245)+2*s(2248)+2*s(2264)+26*s(2268)+30*s(2269)+26*s(2271)+4*s(2275)+12*s(2276)+8*s(2277)+8*s(2278)+48*s(2279)+8*s(2284)+24*s(2285)+16*s(2286)+36*s(2287)+2*s(2289)+2*s(2292)+2*s(2295)+2*s(2298)+2*s(2299)+2*s(2311)+8*s(2312)+6*s(2313)+52*s(2314)+30*s(2315)+26*s(2316)+8*s(2320)+24*s(2321)+16*s(2322)+8*s(2323)+48*s(2324)+8*s(2328)+24*s(2329)+16*s(2330)+26*s(2488)+4*s(2494)+12*s(2495)+8*s(2496)+8*s(2559)+2*s(2610)+26*s(2614)+30*s(2615)+26*s(2617)+4*s(2621)+12*s(2622)+8*s(2623)+8*s(2624)+48*s(2625)+8*s(2630)+24*s(2631)+16*s(2632)+26*s(2698)+4*s(2705)+12*s(2706)+8*s(2707)+1*s(2808)+18 Such that:s(2808) =< V+1 s(1404) =< 2*V+V1+1 aux(255) =< 1 aux(256) =< -2*V+2*V1+V6 aux(257) =< -2*V+2*V1+V6-V14+1 aux(258) =< -V+V1 aux(259) =< -V+V1+V6 aux(260) =< -V+V1+V6-V14 aux(261) =< -V+V1+V6-V14+1 aux(262) =< V aux(263) =< V+V1 aux(264) =< V+V1+1 aux(265) =< V+V1+2 aux(266) =< V+2*V1 aux(267) =< 2*V aux(268) =< 2*V+V1 aux(269) =< 2*V+2*V1 aux(270) =< V1 aux(271) =< V1+1 aux(272) =< V1+2 aux(273) =< V1+V6 aux(274) =< V1+2*V6 aux(275) =< 2*V1 aux(276) =< 2*V1+1 aux(277) =< 2*V1+V6 aux(278) =< 2*V1+2*V6 aux(279) =< V6 aux(280) =< V6+1 aux(281) =< V6+2 aux(282) =< V6-V14 aux(283) =< V6-V14+1 aux(284) =< V6+V14 aux(285) =< V6+V14+1 aux(286) =< V6+V14+2 aux(287) =< 2*V6 aux(288) =< 2*V6+1 aux(289) =< 2*V6+V14 aux(290) =< V14 s(1424) =< aux(255) s(1371) =< aux(262) s(1382) =< aux(265) s(1361) =< aux(270) s(1362) =< aux(271) s(1374) =< aux(272) s(1957) =< aux(279) s(1958) =< aux(280) s(1966) =< aux(281) s(1996) =< aux(286) s(1428) =< aux(262) s(1429) =< aux(271)-1 s(1430) =< aux(271)-2 s(1431) =< aux(263) s(1432) =< aux(263)-1 s(1433) =< aux(271) s(1434) =< aux(262)+1 s(1435) =< aux(268)+1 s(1436) =< aux(271)+1 s(1437) =< aux(263)+1 s(1438) =< aux(262) s(1439) =< s(1371)*aux(268) s(1377) =< s(1371)*aux(263) s(1441) =< s(1371)*aux(271) s(1442) =< s(1371)*aux(262) s(1443) =< s(1371)*s(1429) s(1444) =< s(1371)*s(1430) s(1445) =< s(1371)*s(1431) s(1446) =< s(1371)*s(1432) s(1447) =< s(1371)*s(1429) s(1448) =< s(1371)*s(1433) s(1449) =< s(1371)*s(1435) s(1450) =< s(1371)*s(1436) s(1451) =< s(1371)*s(1437) s(1452) =< s(1371)*s(1433) s(1453) =< s(1371)*s(1436) s(1454) =< s(1371)*s(1434) s(1455) =< s(1371)*s(1438) s(1456) =< s(1371)*s(1436) s(1457) =< s(1443)+s(1444)+aux(270) s(1458) =< s(1445)+s(1446)+aux(263) s(1459) =< s(1448)+s(1443)+aux(270) s(1447) =< s(1448)+s(1443)+aux(270) s(1460) =< s(1449)+s(1439)+aux(268) s(1450) =< s(1449)+s(1439)+aux(268) s(1461) =< s(1449)+s(1439)+aux(268) s(1428) =< s(1451)+s(1377)+aux(263) s(1452) =< s(1451)+s(1377)+aux(263) s(1457) =< s(1428)*s(1429) s(1458) =< s(1428)*s(1433) s(1462) =< s(1428)*s(1434) s(1463) =< s(1428)*s(1429) s(1464) =< s(1428)*s(1433) s(1465) =< s(1428)*s(1429) s(1466) =< aux(270)+s(1443)+s(1447)+s(1459)+s(1459) s(1467) =< aux(275)+s(1443)+s(1447)+s(1460)+s(1457) s(1468) =< s(1457)+s(1463)+s(1443)+s(1443)+aux(270) s(1469) =< s(1467)+2 s(1470) =< s(1467)+1 s(1471) =< s(1467) s(1472) =< s(1466) s(1473) =< s(1371)*s(1469) s(1474) =< s(1371)*s(1470) s(1475) =< s(1371)*s(1471) s(1468) =< s(1371)*s(1472) s(1476) =< s(1371)*s(1472) s(1477) =< s(1371)*s(1469) s(1478) =< s(1462) s(1479) =< s(1448) s(1480) =< s(1452) s(1481) =< s(1468) s(1482) =< s(1474) s(1483) =< s(1456) s(1484) =< s(1475) s(1485) =< s(1472)-1 s(1486) =< s(1481)*s(1471) s(1487) =< s(1481)*s(1472) s(1488) =< s(1481)*s(1485) s(1489) =< s(1487) s(1490) =< s(1486) s(1491) =< s(1473) s(1492) =< s(1476) s(1493) =< s(1441) s(1494) =< s(1466)-1 s(1495) =< s(1492)*s(1467) s(1496) =< s(1492)*s(1466) s(1497) =< s(1492)*s(1494) s(1498) =< s(1496) s(1499) =< s(1495) s(1510) =< s(1371)*s(1429) s(1511) =< s(1448)+s(1443)+aux(271) s(1510) =< s(1448)+s(1443)+aux(271) s(1512) =< s(1443)+s(1510)+s(1511)+s(1511) s(1513) =< aux(270)+s(1443)+s(1510)+s(1460)+s(1457) s(1514) =< s(1457)+s(1463)+s(1443)+s(1443) s(1515) =< s(1513)+2 s(1516) =< s(1513)+1 s(1517) =< s(1513) s(1518) =< s(1512) s(1519) =< s(1371)*s(1515) s(1520) =< s(1371)*s(1516) s(1521) =< s(1371)*s(1517) s(1514) =< s(1371)*s(1518) s(1522) =< s(1371)*s(1518) s(1523) =< s(1371)*s(1515) s(1524) =< s(1514) s(1525) =< s(1520) s(1526) =< s(1521) s(1527) =< s(1518)-1 s(1528) =< s(1524)*s(1517) s(1529) =< s(1524)*s(1518) s(1530) =< s(1524)*s(1527) s(1531) =< s(1529) s(1532) =< s(1528) s(1533) =< s(1519) s(1534) =< s(1522) s(1535) =< s(1512)-1 s(1536) =< s(1534)*s(1513) s(1537) =< s(1534)*s(1512) s(1538) =< s(1534)*s(1535) s(1539) =< s(1537) s(1540) =< s(1536) s(1542) =< aux(262) s(1558) =< s(1371)*s(1436) s(1560) =< s(1371)*s(1433) s(1565) =< s(1443)+s(1444)+aux(270) s(1566) =< s(1445)+s(1446)+aux(263) s(1568) =< s(1449)+s(1439)+s(1404) s(1558) =< s(1449)+s(1439)+s(1404) s(1569) =< s(1449)+s(1439)+s(1404) s(1542) =< s(1451)+s(1377)+aux(264) s(1560) =< s(1451)+s(1377)+aux(264) s(1565) =< s(1542)*s(1429) s(1566) =< s(1542)*s(1433) s(1570) =< s(1542)*s(1434) s(1571) =< s(1542)*s(1429) s(1572) =< s(1542)*s(1433) s(1573) =< s(1542)*s(1429) s(1575) =< aux(270)+s(1443)+s(1510)+s(1568)+s(1565) s(1576) =< s(1565)+s(1571)+s(1443)+s(1443) s(1577) =< s(1575)+2 s(1578) =< s(1575)+1 s(1579) =< s(1575) s(1581) =< s(1371)*s(1577) s(1582) =< s(1371)*s(1578) s(1583) =< s(1371)*s(1579) s(1576) =< s(1371)*s(1518) s(1585) =< s(1371)*s(1577) s(1586) =< s(1570) s(1588) =< s(1560) s(1589) =< s(1576) s(1590) =< s(1582) s(1592) =< s(1583) s(1594) =< s(1589)*s(1579) s(1595) =< s(1589)*s(1518) s(1596) =< s(1589)*s(1527) s(1597) =< s(1595) s(1598) =< s(1594) s(1599) =< s(1581) s(1603) =< s(1534)*s(1575) s(1607) =< s(1603) s(1642) =< s(1371)*s(1429) s(1645) =< s(1371)*s(1436) s(1652) =< s(1443)+s(1444)+aux(275) s(1653) =< s(1445)+s(1446)+aux(266) s(1654) =< s(1448)+s(1443)+aux(276) s(1642) =< s(1448)+s(1443)+aux(276) s(1655) =< s(1449)+s(1439)+aux(269) s(1645) =< s(1449)+s(1439)+aux(269) s(1656) =< s(1449)+s(1439)+aux(269) s(1652) =< s(1428)*s(1429) s(1653) =< s(1428)*s(1433) s(1661) =< aux(263)+s(1443)+s(1642)+s(1654)+s(1654) s(1662) =< aux(266)+s(1443)+s(1642)+s(1655)+s(1652) s(1663) =< s(1652)+s(1463)+s(1443)+s(1443)+aux(263) s(1664) =< s(1662)+2 s(1665) =< s(1662)+1 s(1666) =< s(1662) s(1667) =< s(1661) s(1668) =< s(1371)*s(1664) s(1669) =< s(1371)*s(1665) s(1670) =< s(1371)*s(1666) s(1663) =< s(1371)*s(1667) s(1671) =< s(1371)*s(1667) s(1672) =< s(1371)*s(1664) s(1676) =< s(1663) s(1677) =< s(1669) s(1679) =< s(1670) s(1680) =< s(1667)-1 s(1681) =< s(1676)*s(1666) s(1682) =< s(1676)*s(1667) s(1683) =< s(1676)*s(1680) s(1684) =< s(1682) s(1685) =< s(1681) s(1686) =< s(1668) s(1687) =< s(1671) s(1689) =< s(1661)-1 s(1690) =< s(1687)*s(1662) s(1691) =< s(1687)*s(1661) s(1692) =< s(1687)*s(1689) s(1693) =< s(1691) s(1694) =< s(1690) s(1695) =< aux(262) s(1696) =< s(1371)*s(1429) s(1697) =< s(1371)*s(1436) s(1698) =< s(1371)*s(1433) s(1699) =< s(1443)+s(1444) s(1700) =< s(1445)+s(1446)+aux(262) s(1701) =< s(1448)+s(1443)+aux(255) s(1696) =< s(1448)+s(1443)+aux(255) s(1702) =< s(1449)+s(1439)+aux(267) s(1697) =< s(1449)+s(1439)+aux(267) s(1703) =< s(1449)+s(1439)+aux(267) s(1695) =< s(1451)+s(1377)+aux(262) s(1698) =< s(1451)+s(1377)+aux(262) s(1699) =< s(1695)*s(1429) s(1700) =< s(1695)*s(1433) s(1704) =< s(1695)*s(1434) s(1705) =< s(1695)*s(1429) s(1706) =< s(1695)*s(1433) s(1707) =< s(1695)*s(1429) s(1708) =< aux(270)+s(1443)+s(1696)+s(1701)+s(1701) s(1709) =< aux(275)+s(1443)+s(1696)+s(1702)+s(1699) s(1710) =< s(1699)+s(1705)+s(1443)+s(1443)+aux(270) s(1711) =< s(1709)+2 s(1712) =< s(1709)+1 s(1713) =< s(1709) s(1714) =< s(1708) s(1715) =< s(1371)*s(1711) s(1716) =< s(1371)*s(1712) s(1717) =< s(1371)*s(1713) s(1710) =< s(1371)*s(1714) s(1718) =< s(1371)*s(1714) s(1719) =< s(1371)*s(1711) s(1720) =< s(1704) s(1721) =< s(1698) s(1722) =< s(1710) s(1723) =< s(1716) s(1724) =< s(1717) s(1725) =< s(1714)-1 s(1726) =< s(1722)*s(1713) s(1727) =< s(1722)*s(1714) s(1728) =< s(1722)*s(1725) s(1729) =< s(1727) s(1730) =< s(1726) s(1731) =< s(1715) s(1732) =< s(1718) s(1733) =< s(1708)-1 s(1734) =< s(1732)*s(1709) s(1735) =< s(1732)*s(1708) s(1736) =< s(1732)*s(1733) s(1737) =< s(1735) s(1738) =< s(1734) s(1848) =< s(1443)+s(1510)+s(1511)+s(1511) s(1850) =< s(1457)+s(1463)+s(1443)+s(1443) s(1854) =< s(1848) s(1850) =< s(1371)*s(1854) s(1858) =< s(1371)*s(1854) s(1860) =< s(1850) s(1863) =< s(1854)-1 s(1864) =< s(1860)*s(1517) s(1865) =< s(1860)*s(1854) s(1866) =< s(1860)*s(1863) s(1867) =< s(1865) s(1868) =< s(1864) s(1870) =< s(1858) s(1871) =< s(1848)-1 s(1872) =< s(1870)*s(1513) s(1873) =< s(1870)*s(1848) s(1874) =< s(1870)*s(1871) s(1875) =< s(1873) s(1876) =< s(1872) s(1886) =< s(1652)+s(1463)+s(1443)+s(1443)+aux(263) s(1886) =< s(1652)+s(1463)+s(1443)+s(1443)+aux(270) s(1886) =< s(1371)*s(1667) s(1896) =< s(1886) s(1900) =< s(1896)*s(1666) s(1901) =< s(1896)*s(1667) s(1902) =< s(1896)*s(1680) s(1903) =< s(1901) s(1904) =< s(1900) s(1998) =< aux(270) s(1999) =< aux(280)-1 s(2000) =< aux(280)-2 s(2001) =< aux(273) s(2002) =< aux(273)-1 s(2003) =< aux(280) s(2004) =< aux(270)+1 s(2005) =< aux(277)+1 s(2006) =< aux(280)+1 s(2007) =< aux(273)+1 s(2008) =< aux(270) s(2009) =< s(1361)*aux(277) s(2010) =< s(1361)*aux(273) s(2011) =< s(1361)*aux(280) s(2012) =< s(1361)*aux(270) s(2013) =< s(1361)*s(1999) s(2014) =< s(1361)*s(2000) s(2015) =< s(1361)*s(2001) s(2016) =< s(1361)*s(2002) s(2017) =< s(1361)*s(1999) s(2018) =< s(1361)*s(2003) s(2019) =< s(1361)*s(2005) s(2020) =< s(1361)*s(2006) s(2021) =< s(1361)*s(2007) s(2022) =< s(1361)*s(2003) s(2023) =< s(1361)*s(2006) s(2024) =< s(1361)*s(2004) s(2025) =< s(1361)*s(2008) s(2026) =< s(1361)*s(2006) s(2027) =< s(2013)+s(2014)+aux(279) s(2028) =< s(2015)+s(2016)+aux(273) s(2029) =< s(2018)+s(2013)+aux(279) s(2017) =< s(2018)+s(2013)+aux(279) s(2030) =< s(2019)+s(2009)+aux(277) s(2020) =< s(2019)+s(2009)+aux(277) s(2031) =< s(2019)+s(2009)+aux(277) s(1998) =< s(2021)+s(2010)+aux(273) s(2022) =< s(2021)+s(2010)+aux(273) s(2027) =< s(1998)*s(1999) s(2028) =< s(1998)*s(2003) s(2032) =< s(1998)*s(2004) s(2033) =< s(1998)*s(1999) s(2034) =< s(1998)*s(2003) s(2035) =< s(1998)*s(1999) s(2036) =< aux(284)+s(2013)+s(2017)+s(2029)+s(2029) s(2037) =< aux(289)+s(2013)+s(2017)+s(2030)+s(2027) s(2038) =< s(2027)+s(2033)+s(2013)+s(2013)+aux(284) s(2039) =< s(2037)+2 s(2040) =< s(2037)+1 s(2041) =< s(2037) s(2042) =< s(2036) s(2043) =< s(1361)*s(2039) s(2044) =< s(1361)*s(2040) s(2045) =< s(1361)*s(2041) s(2038) =< s(1361)*s(2042) s(2046) =< s(1361)*s(2042) s(2047) =< s(1361)*s(2039) s(2048) =< s(2032) s(2049) =< s(2018) s(2050) =< s(2022) s(2051) =< s(2038) s(2052) =< s(2044) s(2053) =< s(2026) s(2054) =< s(2045) s(2055) =< s(2042)-1 s(2056) =< s(2051)*s(2041) s(2057) =< s(2051)*s(2042) s(2058) =< s(2051)*s(2055) s(2059) =< s(2057) s(2060) =< s(2056) s(2061) =< s(2043) s(2062) =< s(2046) s(2063) =< s(2011) s(2064) =< s(2036)-1 s(2065) =< s(2062)*s(2037) s(2066) =< s(2062)*s(2036) s(2067) =< s(2062)*s(2064) s(2068) =< s(2066) s(2069) =< s(2065) s(2070) =< aux(290) s(2071) =< aux(285) s(2073) =< aux(284) s(2074) =< aux(290)-1 s(2075) =< s(2070)*aux(284) s(2076) =< s(2070)*aux(290) s(2077) =< s(2070)*s(2074) s(2078) =< s(2076) s(2079) =< s(2075) s(2080) =< s(1361)*s(1999) s(2081) =< s(2018)+s(2013)+aux(280) s(2080) =< s(2018)+s(2013)+aux(280) s(2082) =< s(2013)+s(2080)+s(2081)+s(2081) s(2083) =< aux(279)+s(2013)+s(2080)+s(2030)+s(2027) s(2084) =< s(2027)+s(2033)+s(2013)+s(2013) s(2085) =< s(2083)+2 s(2086) =< s(2083)+1 s(2087) =< s(2083) s(2088) =< s(2082) s(2089) =< s(1361)*s(2085) s(2090) =< s(1361)*s(2086) s(2091) =< s(1361)*s(2087) s(2084) =< s(1361)*s(2088) s(2092) =< s(1361)*s(2088) s(2093) =< s(1361)*s(2085) s(2094) =< s(2084) s(2095) =< s(2090) s(2096) =< s(2091) s(2097) =< s(2088)-1 s(2098) =< s(2094)*s(2087) s(2099) =< s(2094)*s(2088) s(2100) =< s(2094)*s(2097) s(2101) =< s(2099) s(2102) =< s(2098) s(2103) =< s(2089) s(2104) =< s(2092) s(2105) =< s(2082)-1 s(2106) =< s(2104)*s(2083) s(2107) =< s(2104)*s(2082) s(2108) =< s(2104)*s(2105) s(2109) =< s(2107) s(2110) =< s(2106) s(2111) =< aux(258) s(2112) =< aux(258) s(2113) =< aux(259) s(2114) =< aux(259)-1 s(2115) =< aux(256)+1 s(2116) =< aux(259)+1 s(2117) =< s(2111)*aux(256) s(2118) =< s(2111)*aux(259) s(2119) =< s(2111)*aux(280) s(2120) =< s(2111)*aux(270) s(2121) =< s(2111)*s(1999) s(2122) =< s(2111)*s(2000) s(2123) =< s(2111)*s(2113) s(2124) =< s(2111)*s(2114) s(2125) =< s(2111)*s(1999) s(2126) =< s(2111)*s(2003) s(2127) =< s(2111)*s(2115) s(2128) =< s(2111)*s(2006) s(2129) =< s(2111)*s(2116) s(2130) =< s(2111)*s(2003) s(2131) =< s(2111)*s(2006) s(2132) =< s(2111)*s(2004) s(2133) =< s(2111)*s(2008) s(2134) =< s(2111)*s(2006) s(2135) =< s(2121)+s(2122)+aux(282) s(2136) =< s(2123)+s(2124)+aux(260) s(2137) =< s(2126)+s(2121)+aux(283) s(2125) =< s(2126)+s(2121)+aux(283) s(2138) =< s(2127)+s(2117)+aux(257) s(2128) =< s(2127)+s(2117)+aux(257) s(2139) =< s(2127)+s(2117)+aux(257) s(2112) =< s(2129)+s(2118)+aux(261) s(2130) =< s(2129)+s(2118)+aux(261) s(2135) =< s(2112)*s(1999) s(2136) =< s(2112)*s(2003) s(2140) =< s(2112)*s(2004) s(2141) =< s(2112)*s(1999) s(2142) =< s(2112)*s(2003) s(2143) =< s(2112)*s(1999) s(2144) =< aux(290)+s(2121)+s(2125)+s(2137)+s(2137) s(2145) =< aux(284)+s(2121)+s(2125)+s(2138)+s(2135) s(2146) =< s(2135)+s(2141)+s(2121)+s(2121)+aux(290) s(2147) =< s(2145)+2 s(2148) =< s(2145)+1 s(2149) =< s(2145) s(2150) =< s(2144) s(2151) =< s(2111)*s(2147) s(2152) =< s(2111)*s(2148) s(2153) =< s(2111)*s(2149) s(2146) =< s(2111)*s(2150) s(2154) =< s(2111)*s(2150) s(2155) =< s(2111)*s(2147) s(2156) =< s(2140) s(2157) =< s(2126) s(2158) =< s(2130) s(2159) =< s(2146) s(2160) =< s(2152) s(2161) =< s(2134) s(2162) =< s(2153) s(2163) =< s(2150)-1 s(2164) =< s(2159)*s(2149) s(2165) =< s(2159)*s(2150) s(2166) =< s(2159)*s(2163) s(2167) =< s(2165) s(2168) =< s(2164) s(2169) =< s(2151) s(2170) =< s(2154) s(2171) =< s(2119) s(2172) =< s(2144)-1 s(2173) =< s(2170)*s(2145) s(2174) =< s(2170)*s(2144) s(2175) =< s(2170)*s(2172) s(2176) =< s(2174) s(2177) =< s(2173) s(2234) =< s(1361)*s(1999) s(2237) =< s(1361)*s(2006) s(2244) =< s(2013)+s(2014)+aux(287) s(2245) =< s(2015)+s(2016)+aux(274) s(2246) =< s(2018)+s(2013)+aux(288) s(2234) =< s(2018)+s(2013)+aux(288) s(2247) =< s(2019)+s(2009)+aux(278) s(2237) =< s(2019)+s(2009)+aux(278) s(2248) =< s(2019)+s(2009)+aux(278) s(2244) =< s(1998)*s(1999) s(2245) =< s(1998)*s(2003) s(2253) =< aux(273)+s(2013)+s(2234)+s(2246)+s(2246) s(2254) =< aux(274)+s(2013)+s(2234)+s(2247)+s(2244) s(2255) =< s(2244)+s(2033)+s(2013)+s(2013)+aux(273) s(2256) =< s(2254)+2 s(2257) =< s(2254)+1 s(2258) =< s(2254) s(2259) =< s(2253) s(2260) =< s(1361)*s(2256) s(2261) =< s(1361)*s(2257) s(2262) =< s(1361)*s(2258) s(2255) =< s(1361)*s(2259) s(2263) =< s(1361)*s(2259) s(2264) =< s(1361)*s(2256) s(2268) =< s(2255) s(2269) =< s(2261) s(2271) =< s(2262) s(2272) =< s(2259)-1 s(2273) =< s(2268)*s(2258) s(2274) =< s(2268)*s(2259) s(2275) =< s(2268)*s(2272) s(2276) =< s(2274) s(2277) =< s(2273) s(2278) =< s(2260) s(2279) =< s(2263) s(2281) =< s(2253)-1 s(2282) =< s(2279)*s(2254) s(2283) =< s(2279)*s(2253) s(2284) =< s(2279)*s(2281) s(2285) =< s(2283) s(2286) =< s(2282) s(2287) =< aux(270) s(2288) =< s(1361)*s(1999) s(2289) =< s(1361)*s(2006) s(2290) =< s(1361)*s(2003) s(2291) =< s(2013)+s(2014) s(2292) =< s(2015)+s(2016)+aux(270) s(2293) =< s(2018)+s(2013)+aux(255) s(2288) =< s(2018)+s(2013)+aux(255) s(2294) =< s(2019)+s(2009)+aux(275) s(2289) =< s(2019)+s(2009)+aux(275) s(2295) =< s(2019)+s(2009)+aux(275) s(2287) =< s(2021)+s(2010)+aux(270) s(2290) =< s(2021)+s(2010)+aux(270) s(2291) =< s(2287)*s(1999) s(2292) =< s(2287)*s(2003) s(2296) =< s(2287)*s(2004) s(2297) =< s(2287)*s(1999) s(2298) =< s(2287)*s(2003) s(2299) =< s(2287)*s(1999) s(2300) =< aux(279)+s(2013)+s(2288)+s(2293)+s(2293) s(2301) =< aux(287)+s(2013)+s(2288)+s(2294)+s(2291) s(2302) =< s(2291)+s(2297)+s(2013)+s(2013)+aux(279) s(2303) =< s(2301)+2 s(2304) =< s(2301)+1 s(2305) =< s(2301) s(2306) =< s(2300) s(2307) =< s(1361)*s(2303) s(2308) =< s(1361)*s(2304) s(2309) =< s(1361)*s(2305) s(2302) =< s(1361)*s(2306) s(2310) =< s(1361)*s(2306) s(2311) =< s(1361)*s(2303) s(2312) =< s(2296) s(2313) =< s(2290) s(2314) =< s(2302) s(2315) =< s(2308) s(2316) =< s(2309) s(2317) =< s(2306)-1 s(2318) =< s(2314)*s(2305) s(2319) =< s(2314)*s(2306) s(2320) =< s(2314)*s(2317) s(2321) =< s(2319) s(2322) =< s(2318) s(2323) =< s(2307) s(2324) =< s(2310) s(2325) =< s(2300)-1 s(2326) =< s(2324)*s(2301) s(2327) =< s(2324)*s(2300) s(2328) =< s(2324)*s(2325) s(2329) =< s(2327) s(2330) =< s(2326) s(2478) =< s(2244)+s(2033)+s(2013)+s(2013)+aux(273) s(2478) =< s(2244)+s(2033)+s(2013)+s(2013)+aux(279) s(2478) =< s(1361)*s(2259) s(2488) =< s(2478) s(2492) =< s(2488)*s(2258) s(2493) =< s(2488)*s(2259) s(2494) =< s(2488)*s(2272) s(2495) =< s(2493) s(2496) =< s(2492) s(2559) =< aux(277) s(2599) =< aux(277)+s(2013)+s(2080)+s(2081)+s(2081) s(2600) =< aux(278)+s(2013)+s(2080)+s(2030)+s(2027) s(2601) =< s(2027)+s(2033)+s(2013)+s(2013)+aux(277) s(2602) =< s(2600)+2 s(2603) =< s(2600)+1 s(2604) =< s(2600) s(2605) =< s(2599) s(2606) =< s(1361)*s(2602) s(2607) =< s(1361)*s(2603) s(2608) =< s(1361)*s(2604) s(2601) =< s(1361)*s(2605) s(2609) =< s(1361)*s(2605) s(2610) =< s(1361)*s(2602) s(2614) =< s(2601) s(2615) =< s(2607) s(2617) =< s(2608) s(2618) =< s(2605)-1 s(2619) =< s(2614)*s(2604) s(2620) =< s(2614)*s(2605) s(2621) =< s(2614)*s(2618) s(2622) =< s(2620) s(2623) =< s(2619) s(2624) =< s(2606) s(2625) =< s(2609) s(2627) =< s(2599)-1 s(2628) =< s(2625)*s(2600) s(2629) =< s(2625)*s(2599) s(2630) =< s(2625)*s(2627) s(2631) =< s(2629) s(2632) =< s(2628) s(2685) =< s(2027)+s(2033)+s(2013)+s(2013)+aux(277) s(2685) =< s(2027)+s(2033)+s(2013)+s(2013)+aux(280) s(2685) =< s(1361)*s(2605) s(2698) =< s(2685) s(2703) =< s(2698)*s(2604) s(2704) =< s(2698)*s(2605) s(2705) =< s(2698)*s(2618) s(2706) =< s(2704) s(2707) =< s(2703) s(1372) =< aux(264) s(1375) =< aux(263) s(1376) =< aux(262)-1 s(1378) =< s(1371)*aux(262) s(1379) =< s(1371)*s(1376) s(1380) =< s(1378) s(1381) =< s(1377) with precondition: [V>=0] * Chain [67]: 38*s(2814)+291*s(2815)+392*s(2816)+46*s(2838)+198*s(2839)+67*s(2840)+512*s(2841)+180*s(2842)+10*s(2856)+10*s(2864)+20*s(2867)+30*s(2868)+20*s(2869)+10*s(2872)+10*s(2875)+10*s(2878)+10*s(2879)+2*s(2891)+40*s(2892)+110*s(2893)+30*s(2894)+26*s(2895)+30*s(2896)+80*s(2897)+26*s(2898)+4*s(2902)+12*s(2903)+8*s(2904)+8*s(2905)+24*s(2906)+20*s(2907)+4*s(2911)+12*s(2912)+8*s(2913)+136*s(2915)+29*s(2917)+40*s(2921)+120*s(2922)+40*s(2923)+5*s(2937)+130*s(2938)+75*s(2939)+65*s(2940)+20*s(2944)+60*s(2945)+40*s(2946)+20*s(2947)+120*s(2948)+20*s(2952)+60*s(2953)+40*s(2954)+420*s(2955)+36*s(2956)+10*s(2964)+2*s(2972)+20*s(2975)+30*s(2976)+20*s(2977)+2*s(2980)+2*s(2983)+2*s(2986)+2*s(2987)+2*s(2999)+8*s(3000)+110*s(3001)+6*s(3002)+52*s(3003)+30*s(3004)+80*s(3005)+26*s(3006)+8*s(3010)+24*s(3011)+16*s(3012)+8*s(3013)+48*s(3014)+20*s(3015)+8*s(3019)+24*s(3020)+16*s(3021)+52*s(3203)+8*s(3210)+24*s(3211)+8*s(3212)+48*s(3214)+8*s(3219)+24*s(3220)+8*s(3221)+40*s(3231)+126*s(3264)+7*s(3280)+7*s(3288)+7*s(3291)+7*s(3294)+7*s(3295)+1*s(3307)+28*s(3308)+21*s(3310)+26*s(3311)+15*s(3312)+13*s(3314)+4*s(3318)+12*s(3319)+8*s(3320)+4*s(3321)+24*s(3322)+4*s(3327)+12*s(3328)+8*s(3329)+18*s(3358)+1*s(3380)+1*s(3388)+1*s(3391)+1*s(3394)+1*s(3395)+1*s(3407)+4*s(3408)+3*s(3410)+26*s(3411)+15*s(3412)+13*s(3414)+4*s(3418)+12*s(3419)+8*s(3420)+4*s(3421)+24*s(3422)+4*s(3427)+12*s(3428)+8*s(3429)+250*s(3437)+75*s(3438)+191*s(3441)+40*s(3445)+120*s(3446)+80*s(3447)+25*s(3448)+1*s(3523)+26*s(3527)+15*s(3528)+13*s(3530)+4*s(3534)+12*s(3535)+8*s(3536)+4*s(3537)+24*s(3538)+4*s(3543)+12*s(3544)+8*s(3545)+2*s(3631)+52*s(3635)+30*s(3636)+26*s(3638)+8*s(3642)+24*s(3643)+16*s(3644)+8*s(3645)+48*s(3646)+8*s(3651)+24*s(3652)+16*s(3653)+14*s(3848)+1*s(3899)+15*s(3904)+13*s(3906)+8*s(3912)+4*s(3913)+8*s(3921)+20*s(3929)+60*s(3930)+40*s(3931)+1*s(4007)+26*s(4011)+15*s(4012)+13*s(4014)+4*s(4018)+12*s(4019)+8*s(4020)+4*s(4021)+24*s(4022)+4*s(4027)+12*s(4028)+8*s(4029)+1*s(4056)+3*s(4058)+1*s(4123)+26*s(4127)+15*s(4128)+13*s(4130)+4*s(4134)+12*s(4135)+8*s(4136)+4*s(4137)+24*s(4138)+4*s(4143)+12*s(4144)+8*s(4145)+14*s(4190)+1*s(4241)+26*s(4245)+15*s(4246)+13*s(4248)+4*s(4252)+12*s(4253)+8*s(4254)+4*s(4255)+24*s(4256)+4*s(4261)+12*s(4262)+8*s(4263)+39*s(4265)+29*s(4267)+20*s(4271)+60*s(4272)+40*s(4273)+2*s(4349)+52*s(4353)+30*s(4354)+26*s(4356)+8*s(4360)+24*s(4361)+16*s(4362)+8*s(4363)+48*s(4364)+8*s(4369)+24*s(4370)+16*s(4371)+53*s(4545)+34*s(4557)+106*s(4572)+56*s(4580)+16*s(4587)+48*s(4588)+32*s(4589)+10*s(4590)+2*s(4667)+29 Such that:s(3344) =< -2*V1+2*V6+2*V14 s(4056) =< -V1+V6+V14+1 aux(371) =< V1+2 s(3844) =< 2*V14+3 s(4185) =< 2*V14+V19+1 s(4186) =< 2*V14+V19+2 s(3834) =< 3*V14+1 s(4176) =< 3*V14+V19 aux(372) =< 1 aux(373) =< -2*V1+2*V6 aux(374) =< -2*V1+2*V6+V14 aux(375) =< -V1+V6 aux(376) =< -V1+V6+V14 aux(377) =< -V1+V6+2*V14 aux(378) =< V1 aux(379) =< V1+1 aux(380) =< V1+V6 aux(381) =< V1+V6+1 aux(382) =< V6 aux(383) =< V6+1 aux(384) =< V6+2 aux(385) =< V6+V14 aux(386) =< 2*V6+V14 aux(387) =< V14 aux(388) =< V14+1 aux(389) =< V14+2 aux(390) =< V14+V19 aux(391) =< V14+V19+1 aux(392) =< V14+V19+2 aux(393) =< 2*V14 aux(394) =< 2*V14+1 aux(395) =< 2*V14+2 aux(396) =< 2*V14+V19 aux(397) =< 3*V14 aux(398) =< V19 s(2838) =< aux(372) s(4572) =< aux(378) s(2814) =< aux(379) s(4590) =< aux(381) s(2841) =< aux(382) s(4545) =< aux(383) s(4557) =< aux(384) s(2815) =< aux(387) s(2816) =< aux(388) s(2839) =< aux(389) s(3448) =< aux(392) s(2955) =< aux(375) s(2956) =< aux(375) s(2843) =< aux(388)-1 s(2844) =< aux(388)-2 s(2957) =< aux(376) s(2958) =< aux(376)-1 s(2847) =< aux(388) s(2848) =< aux(382)+1 s(2959) =< aux(374)+1 s(2850) =< aux(388)+1 s(2960) =< aux(376)+1 s(2852) =< aux(382) s(2961) =< s(2955)*aux(374) s(2962) =< s(2955)*aux(376) s(2963) =< s(2955)*aux(388) s(2964) =< s(2955)*aux(382) s(2965) =< s(2955)*s(2843) s(2966) =< s(2955)*s(2844) s(2967) =< s(2955)*s(2957) s(2968) =< s(2955)*s(2958) s(2969) =< s(2955)*s(2843) s(2970) =< s(2955)*s(2847) s(2971) =< s(2955)*s(2959) s(2972) =< s(2955)*s(2850) s(2973) =< s(2955)*s(2960) s(2974) =< s(2955)*s(2847) s(2975) =< s(2955)*s(2850) s(2976) =< s(2955)*s(2848) s(2977) =< s(2955)*s(2852) s(2978) =< s(2955)*s(2850) s(2979) =< s(2965)+s(2966) s(2980) =< s(2967)+s(2968)+aux(375) s(2981) =< s(2970)+s(2965)+aux(372) s(2969) =< s(2970)+s(2965)+aux(372) s(2982) =< s(2971)+s(2961)+aux(373) s(2972) =< s(2971)+s(2961)+aux(373) s(2983) =< s(2971)+s(2961)+aux(373) s(2956) =< s(2973)+s(2962)+aux(375) s(2974) =< s(2973)+s(2962)+aux(375) s(2979) =< s(2956)*s(2843) s(2980) =< s(2956)*s(2847) s(2984) =< s(2956)*s(2848) s(2985) =< s(2956)*s(2843) s(2986) =< s(2956)*s(2847) s(2987) =< s(2956)*s(2843) s(2988) =< aux(387)+s(2965)+s(2969)+s(2981)+s(2981) s(2989) =< aux(393)+s(2965)+s(2969)+s(2982)+s(2979) s(2990) =< s(2979)+s(2985)+s(2965)+s(2965)+aux(387) s(2991) =< s(2989)+2 s(2992) =< s(2989)+1 s(2993) =< s(2989) s(2994) =< s(2988) s(2995) =< s(2955)*s(2991) s(2996) =< s(2955)*s(2992) s(2997) =< s(2955)*s(2993) s(2990) =< s(2955)*s(2994) s(2998) =< s(2955)*s(2994) s(2999) =< s(2955)*s(2991) s(3000) =< s(2984) s(3001) =< s(2970) s(3002) =< s(2974) s(3003) =< s(2990) s(3004) =< s(2996) s(3005) =< s(2978) s(3006) =< s(2997) s(3007) =< s(2994)-1 s(3008) =< s(3003)*s(2993) s(3009) =< s(3003)*s(2994) s(3010) =< s(3003)*s(3007) s(3011) =< s(3009) s(3012) =< s(3008) s(3013) =< s(2995) s(3014) =< s(2998) s(3015) =< s(2963) s(3016) =< s(2988)-1 s(3017) =< s(3014)*s(2989) s(3018) =< s(3014)*s(2988) s(3019) =< s(3014)*s(3016) s(3020) =< s(3018) s(3021) =< s(3017) s(2840) =< aux(395) s(2842) =< aux(382) s(2845) =< aux(385) s(2846) =< aux(385)-1 s(2849) =< aux(386)+1 s(2851) =< aux(385)+1 s(2853) =< s(2841)*aux(386) s(2854) =< s(2841)*aux(385) s(2855) =< s(2841)*aux(388) s(2856) =< s(2841)*aux(382) s(2857) =< s(2841)*s(2843) s(2858) =< s(2841)*s(2844) s(2859) =< s(2841)*s(2845) s(2860) =< s(2841)*s(2846) s(2861) =< s(2841)*s(2843) s(2862) =< s(2841)*s(2847) s(2863) =< s(2841)*s(2849) s(2864) =< s(2841)*s(2850) s(2865) =< s(2841)*s(2851) s(2866) =< s(2841)*s(2847) s(2867) =< s(2841)*s(2850) s(2868) =< s(2841)*s(2848) s(2869) =< s(2841)*s(2852) s(2870) =< s(2841)*s(2850) s(2871) =< s(2857)+s(2858)+aux(387) s(2872) =< s(2859)+s(2860)+aux(385) s(2873) =< s(2862)+s(2857)+aux(387) s(2861) =< s(2862)+s(2857)+aux(387) s(2874) =< s(2863)+s(2853)+aux(386) s(2864) =< s(2863)+s(2853)+aux(386) s(2875) =< s(2863)+s(2853)+aux(386) s(2842) =< s(2865)+s(2854)+aux(385) s(2866) =< s(2865)+s(2854)+aux(385) s(2871) =< s(2842)*s(2843) s(2872) =< s(2842)*s(2847) s(2876) =< s(2842)*s(2848) s(2877) =< s(2842)*s(2843) s(2878) =< s(2842)*s(2847) s(2879) =< s(2842)*s(2843) s(3188) =< aux(394)+s(2857)+s(2861)+s(2873)+s(2873) s(2881) =< aux(397)+s(2857)+s(2861)+s(2874)+s(2871) s(3190) =< s(2871)+s(2877)+s(2857)+s(2857)+aux(394) s(2883) =< s(2881)+2 s(2884) =< s(2881)+1 s(2885) =< s(2881) s(3194) =< s(3188) s(2887) =< s(2841)*s(2883) s(2888) =< s(2841)*s(2884) s(2889) =< s(2841)*s(2885) s(3190) =< s(2841)*s(3194) s(3198) =< s(2841)*s(3194) s(2891) =< s(2841)*s(2883) s(2892) =< s(2876) s(2893) =< s(2862) s(2894) =< s(2866) s(3203) =< s(3190) s(2896) =< s(2888) s(2897) =< s(2870) s(2898) =< s(2889) s(3207) =< s(3194)-1 s(3208) =< s(3203)*s(2885) s(3209) =< s(3203)*s(3194) s(3210) =< s(3203)*s(3207) s(3211) =< s(3209) s(3212) =< s(3208) s(2905) =< s(2887) s(3214) =< s(3198) s(2907) =< s(2855) s(3216) =< s(3188)-1 s(3217) =< s(3214)*s(2881) s(3218) =< s(3214)*s(3188) s(3219) =< s(3214)*s(3216) s(3220) =< s(3218) s(3221) =< s(3217) s(2915) =< aux(394) s(2918) =< aux(387)-1 s(3227) =< s(2815)*aux(394) s(2920) =< s(2815)*aux(387) s(2921) =< s(2815)*s(2918) s(2922) =< s(2920) s(3231) =< s(3227) s(2924) =< s(2841)*s(2843) s(2925) =< s(2862)+s(2857)+aux(388) s(2924) =< s(2862)+s(2857)+aux(388) s(2926) =< s(2857)+s(2924)+s(2925)+s(2925) s(2927) =< aux(387)+s(2857)+s(2924)+s(2874)+s(2871) s(2928) =< s(2871)+s(2877)+s(2857)+s(2857) s(2929) =< s(2927)+2 s(2930) =< s(2927)+1 s(2931) =< s(2927) s(2932) =< s(2926) s(2933) =< s(2841)*s(2929) s(2934) =< s(2841)*s(2930) s(2935) =< s(2841)*s(2931) s(2928) =< s(2841)*s(2932) s(2936) =< s(2841)*s(2932) s(2937) =< s(2841)*s(2929) s(2938) =< s(2928) s(2939) =< s(2934) s(2940) =< s(2935) s(2941) =< s(2932)-1 s(2942) =< s(2938)*s(2931) s(2943) =< s(2938)*s(2932) s(2944) =< s(2938)*s(2941) s(2945) =< s(2943) s(2946) =< s(2942) s(2947) =< s(2933) s(2948) =< s(2936) s(2949) =< s(2926)-1 s(2950) =< s(2948)*s(2927) s(2951) =< s(2948)*s(2926) s(2952) =< s(2948)*s(2949) s(2953) =< s(2951) s(2954) =< s(2950) s(3264) =< aux(375) s(3277) =< s(2955)*s(2843) s(3280) =< s(2955)*s(2850) s(3282) =< s(2955)*s(2847) s(3287) =< s(2965)+s(2966)+aux(393) s(3288) =< s(2967)+s(2968)+aux(376) s(3289) =< s(2970)+s(2965)+aux(394) s(3277) =< s(2970)+s(2965)+aux(394) s(3290) =< s(2971)+s(2961)+aux(374) s(3280) =< s(2971)+s(2961)+aux(374) s(3291) =< s(2971)+s(2961)+aux(374) s(3264) =< s(2973)+s(2962)+aux(376) s(3282) =< s(2973)+s(2962)+aux(376) s(3287) =< s(3264)*s(2843) s(3288) =< s(3264)*s(2847) s(3292) =< s(3264)*s(2848) s(3293) =< s(3264)*s(2843) s(3294) =< s(3264)*s(2847) s(3295) =< s(3264)*s(2843) s(3296) =< aux(387)+s(2965)+s(3277)+s(3289)+s(3289) s(3297) =< aux(394)+s(2965)+s(3277)+s(3290)+s(3287) s(3298) =< s(3287)+s(3293)+s(2965)+s(2965)+aux(387) s(3299) =< s(3297)+2 s(3300) =< s(3297)+1 s(3301) =< s(3297) s(3302) =< s(3296) s(3303) =< s(2955)*s(3299) s(3304) =< s(2955)*s(3300) s(3305) =< s(2955)*s(3301) s(3298) =< s(2955)*s(3302) s(3306) =< s(2955)*s(3302) s(3307) =< s(2955)*s(3299) s(3308) =< s(3292) s(3310) =< s(3282) s(3311) =< s(3298) s(3312) =< s(3304) s(3314) =< s(3305) s(3315) =< s(3302)-1 s(3316) =< s(3311)*s(3301) s(3317) =< s(3311)*s(3302) s(3318) =< s(3311)*s(3315) s(3319) =< s(3317) s(3320) =< s(3316) s(3321) =< s(3303) s(3322) =< s(3306) s(3324) =< s(3296)-1 s(3325) =< s(3322)*s(3297) s(3326) =< s(3322)*s(3296) s(3327) =< s(3322)*s(3324) s(3328) =< s(3326) s(3329) =< s(3325) s(3512) =< aux(387)+s(2857)+s(2861)+s(2873)+s(2873) s(3513) =< aux(393)+s(2857)+s(2861)+s(2874)+s(2871) s(3514) =< s(2871)+s(2877)+s(2857)+s(2857)+aux(387) s(3515) =< s(3513)+2 s(3516) =< s(3513)+1 s(3517) =< s(3513) s(3518) =< s(3512) s(3519) =< s(2841)*s(3515) s(3520) =< s(2841)*s(3516) s(3521) =< s(2841)*s(3517) s(3514) =< s(2841)*s(3518) s(3522) =< s(2841)*s(3518) s(3523) =< s(2841)*s(3515) s(3527) =< s(3514) s(3528) =< s(3520) s(3530) =< s(3521) s(3531) =< s(3518)-1 s(3532) =< s(3527)*s(3517) s(3533) =< s(3527)*s(3518) s(3534) =< s(3527)*s(3531) s(3535) =< s(3533) s(3536) =< s(3532) s(3537) =< s(3519) s(3538) =< s(3522) s(3540) =< s(3512)-1 s(3541) =< s(3538)*s(3513) s(3542) =< s(3538)*s(3512) s(3543) =< s(3538)*s(3540) s(3544) =< s(3542) s(3545) =< s(3541) s(3601) =< s(2955)*s(2843) s(3611) =< s(2965)+s(2966)+aux(387) s(3613) =< s(2970)+s(2965)+aux(388) s(3601) =< s(2970)+s(2965)+aux(388) s(3611) =< s(3264)*s(2843) s(3620) =< s(2965)+s(3601)+s(3613)+s(3613) s(3621) =< aux(387)+s(2965)+s(3601)+s(3290)+s(3611) s(3622) =< s(3611)+s(3293)+s(2965)+s(2965) s(3623) =< s(3621)+2 s(3624) =< s(3621)+1 s(3625) =< s(3621) s(3626) =< s(3620) s(3627) =< s(2955)*s(3623) s(3628) =< s(2955)*s(3624) s(3629) =< s(2955)*s(3625) s(3622) =< s(2955)*s(3626) s(3630) =< s(2955)*s(3626) s(3631) =< s(2955)*s(3623) s(3635) =< s(3622) s(3636) =< s(3628) s(3638) =< s(3629) s(3639) =< s(3626)-1 s(3640) =< s(3635)*s(3625) s(3641) =< s(3635)*s(3626) s(3642) =< s(3635)*s(3639) s(3643) =< s(3641) s(3644) =< s(3640) s(3645) =< s(3627) s(3646) =< s(3630) s(3648) =< s(3620)-1 s(3649) =< s(3646)*s(3621) s(3650) =< s(3646)*s(3620) s(3651) =< s(3646)*s(3648) s(3652) =< s(3650) s(3653) =< s(3649) s(3437) =< aux(398) s(3438) =< aux(391) s(3441) =< aux(390) s(3442) =< aux(398)-1 s(3443) =< s(3437)*aux(390) s(3444) =< s(3437)*aux(398) s(3445) =< s(3437)*s(3442) s(3446) =< s(3444) s(3447) =< s(3443) s(3848) =< s(3844) s(3889) =< s(3834)+s(2857)+s(2861)+s(2874)+s(2871) s(3891) =< s(3889)+2 s(3892) =< s(3889)+1 s(3893) =< s(3889) s(3895) =< s(2841)*s(3891) s(3896) =< s(2841)*s(3892) s(3897) =< s(2841)*s(3893) s(3899) =< s(2841)*s(3891) s(3904) =< s(3896) s(3906) =< s(3897) s(3908) =< s(3203)*s(3893) s(3912) =< s(3908) s(3913) =< s(3895) s(3917) =< s(3214)*s(3889) s(3921) =< s(3917) s(3927) =< s(2816)*aux(394) s(3928) =< s(2816)*aux(388) s(3929) =< s(2816)*s(2843) s(3930) =< s(3928) s(3931) =< s(3927) s(3996) =< aux(388)+s(2965)+s(3601)+s(3613)+s(3613) s(3997) =< aux(394)+s(2965)+s(3601)+s(3290)+s(3611) s(3998) =< s(3611)+s(3293)+s(2965)+s(2965)+aux(388) s(3999) =< s(3997)+2 s(4000) =< s(3997)+1 s(4001) =< s(3997) s(4002) =< s(3996) s(4003) =< s(2955)*s(3999) s(4004) =< s(2955)*s(4000) s(4005) =< s(2955)*s(4001) s(3998) =< s(2955)*s(4002) s(4006) =< s(2955)*s(4002) s(4007) =< s(2955)*s(3999) s(4011) =< s(3998) s(4012) =< s(4004) s(4014) =< s(4005) s(4015) =< s(4002)-1 s(4016) =< s(4011)*s(4001) s(4017) =< s(4011)*s(4002) s(4018) =< s(4011)*s(4015) s(4019) =< s(4017) s(4020) =< s(4016) s(4021) =< s(4003) s(4022) =< s(4006) s(4024) =< s(3996)-1 s(4025) =< s(4022)*s(3997) s(4026) =< s(4022)*s(3996) s(4027) =< s(4022)*s(4024) s(4028) =< s(4026) s(4029) =< s(4025) s(4190) =< s(4186) s(4230) =< aux(396)+s(2857)+s(2861)+s(2873)+s(2873) s(4231) =< s(4176)+s(2857)+s(2861)+s(2874)+s(2871) s(4232) =< s(2871)+s(2877)+s(2857)+s(2857)+aux(396) s(4233) =< s(4231)+2 s(4234) =< s(4231)+1 s(4235) =< s(4231) s(4236) =< s(4230) s(4237) =< s(2841)*s(4233) s(4238) =< s(2841)*s(4234) s(4239) =< s(2841)*s(4235) s(4232) =< s(2841)*s(4236) s(4240) =< s(2841)*s(4236) s(4241) =< s(2841)*s(4233) s(4245) =< s(4232) s(4246) =< s(4238) s(4248) =< s(4239) s(4249) =< s(4236)-1 s(4250) =< s(4245)*s(4235) s(4251) =< s(4245)*s(4236) s(4252) =< s(4245)*s(4249) s(4253) =< s(4251) s(4254) =< s(4250) s(4255) =< s(4237) s(4256) =< s(4240) s(4258) =< s(4230)-1 s(4259) =< s(4256)*s(4231) s(4260) =< s(4256)*s(4230) s(4261) =< s(4256)*s(4258) s(4262) =< s(4260) s(4263) =< s(4259) s(4265) =< s(4185) s(4267) =< aux(396) s(4268) =< aux(390)-1 s(4269) =< s(3441)*aux(396) s(4270) =< s(3441)*aux(390) s(4271) =< s(3441)*s(4268) s(4272) =< s(4270) s(4273) =< s(4269) s(4319) =< s(2955)*s(2843) s(4331) =< s(2970)+s(2965)+aux(387) s(4319) =< s(2970)+s(2965)+aux(387) s(4338) =< aux(390)+s(2965)+s(4319)+s(4331)+s(4331) s(4339) =< aux(396)+s(2965)+s(4319)+s(3290)+s(3611) s(4340) =< s(3611)+s(3293)+s(2965)+s(2965)+aux(390) s(4341) =< s(4339)+2 s(4342) =< s(4339)+1 s(4343) =< s(4339) s(4344) =< s(4338) s(4345) =< s(2955)*s(4341) s(4346) =< s(2955)*s(4342) s(4347) =< s(2955)*s(4343) s(4340) =< s(2955)*s(4344) s(4348) =< s(2955)*s(4344) s(4349) =< s(2955)*s(4341) s(4353) =< s(4340) s(4354) =< s(4346) s(4356) =< s(4347) s(4357) =< s(4344)-1 s(4358) =< s(4353)*s(4343) s(4359) =< s(4353)*s(4344) s(4360) =< s(4353)*s(4357) s(4361) =< s(4359) s(4362) =< s(4358) s(4363) =< s(4345) s(4364) =< s(4348) s(4366) =< s(4338)-1 s(4367) =< s(4364)*s(4339) s(4368) =< s(4364)*s(4338) s(4369) =< s(4364)*s(4366) s(4370) =< s(4368) s(4371) =< s(4367) s(2880) =< aux(393)+s(2857)+s(2861)+s(2873)+s(2873) s(2882) =< s(2871)+s(2877)+s(2857)+s(2857)+aux(393) s(2886) =< s(2880) s(2882) =< s(2841)*s(2886) s(2890) =< s(2841)*s(2886) s(2895) =< s(2882) s(2899) =< s(2886)-1 s(2900) =< s(2895)*s(2885) s(2901) =< s(2895)*s(2886) s(2902) =< s(2895)*s(2899) s(2903) =< s(2901) s(2904) =< s(2900) s(2906) =< s(2890) s(2908) =< s(2880)-1 s(2909) =< s(2906)*s(2881) s(2910) =< s(2906)*s(2880) s(2911) =< s(2906)*s(2908) s(2912) =< s(2910) s(2913) =< s(2909) s(2917) =< aux(393) s(2919) =< s(2815)*aux(393) s(2923) =< s(2919) s(3358) =< aux(375) s(3380) =< s(2955)*s(2850) s(3382) =< s(2955)*s(2847) s(3387) =< s(2965)+s(2966)+aux(393) s(3388) =< s(2967)+s(2968)+aux(377) s(3390) =< s(2971)+s(2961)+s(3344) s(3380) =< s(2971)+s(2961)+s(3344) s(3391) =< s(2971)+s(2961)+s(3344) s(3358) =< s(2973)+s(2962)+aux(377) s(3382) =< s(2973)+s(2962)+aux(377) s(3387) =< s(3358)*s(2843) s(3388) =< s(3358)*s(2847) s(3392) =< s(3358)*s(2848) s(3393) =< s(3358)*s(2843) s(3394) =< s(3358)*s(2847) s(3395) =< s(3358)*s(2843) s(3396) =< aux(374)+s(2965)+s(3277)+s(3289)+s(3289) s(3397) =< aux(394)+s(2965)+s(3277)+s(3390)+s(3387) s(3398) =< s(3387)+s(3393)+s(2965)+s(2965)+aux(374) s(3399) =< s(3397)+2 s(3400) =< s(3397)+1 s(3401) =< s(3397) s(3402) =< s(3396) s(3398) =< s(3387)+s(3393)+s(2965)+s(2965)+aux(387) s(3403) =< s(2955)*s(3399) s(3404) =< s(2955)*s(3400) s(3405) =< s(2955)*s(3401) s(3398) =< s(2955)*s(3402) s(3406) =< s(2955)*s(3402) s(3407) =< s(2955)*s(3399) s(3408) =< s(3392) s(3410) =< s(3382) s(3411) =< s(3398) s(3412) =< s(3404) s(3414) =< s(3405) s(3415) =< s(3402)-1 s(3416) =< s(3411)*s(3401) s(3417) =< s(3411)*s(3402) s(3418) =< s(3411)*s(3415) s(3419) =< s(3417) s(3420) =< s(3416) s(3421) =< s(3403) s(3422) =< s(3406) s(3424) =< s(3396)-1 s(3425) =< s(3422)*s(3397) s(3426) =< s(3422)*s(3396) s(3427) =< s(3422)*s(3424) s(3428) =< s(3426) s(3429) =< s(3425) s(4112) =< aux(376)+s(2965)+s(3601)+s(3613)+s(3613) s(4113) =< aux(377)+s(2965)+s(3601)+s(3290)+s(3611) s(4114) =< s(3611)+s(3293)+s(2965)+s(2965)+aux(376) s(4115) =< s(4113)+2 s(4116) =< s(4113)+1 s(4117) =< s(4113) s(4118) =< s(4112) s(4114) =< s(3611)+s(3293)+s(2965)+s(2965)+aux(388) s(4119) =< s(2955)*s(4115) s(4120) =< s(2955)*s(4116) s(4121) =< s(2955)*s(4117) s(4114) =< s(2955)*s(4118) s(4122) =< s(2955)*s(4118) s(4123) =< s(2955)*s(4115) s(4127) =< s(4114) s(4128) =< s(4120) s(4130) =< s(4121) s(4131) =< s(4118)-1 s(4132) =< s(4127)*s(4117) s(4133) =< s(4127)*s(4118) s(4134) =< s(4127)*s(4131) s(4135) =< s(4133) s(4136) =< s(4132) s(4137) =< s(4119) s(4138) =< s(4122) s(4140) =< s(4112)-1 s(4141) =< s(4138)*s(4113) s(4142) =< s(4138)*s(4112) s(4143) =< s(4138)*s(4140) s(4144) =< s(4142) s(4145) =< s(4141) s(4058) =< aux(376) s(4667) =< aux(371) s(4580) =< aux(380) s(4584) =< aux(378)-1 s(4585) =< s(4572)*aux(380) s(4586) =< s(4572)*aux(378) s(4587) =< s(4572)*s(4584) s(4588) =< s(4586) s(4589) =< s(4585) with precondition: [V=1] * Chain [66]: 2*s(4680)+2 Such that:aux(399) =< V6 s(4680) =< aux(399) with precondition: [V=2,V1>=0,V6>=0] * Chain [65]: 3 with precondition: [V1=0,V>=0] * Chain [64]: 6 with precondition: [V1=1,V>=0,V6>=0] Closed-form bounds of start(V,V1,V6,V14,V19): ------------------------------------- * Chain [68] with precondition: [V>=0] - Upper bound: 1231*V+66+443*V*V+288*V*V*V*nat(nat(V1+1)+ -2)*nat(nat(V1+1)+ -1)+144*V*V*V*nat(nat(V1+1)+ -2)*nat(V1+1)+288*V*V*V*nat(nat(V1+1)+ -1)+2720*V*V*V*nat(nat(V1+1)+ -1)*nat(nat(V1+1)+ -1)+2288*V*V*V*nat(nat(V1+1)+ -1)*nat(V1+1)+576*V*V*V*nat(nat(V1+1)+ -1)*nat(2*V+V1)+144*V*V*V*nat(V1+1)+464*V*V*V*nat(V1+1)*nat(V1+1)+288*V*V*V*nat(V1+1)*nat(2*V+V1)+64*V*V*nat(V1)+64*V*V*nat(V1)*nat(nat(V1+1)+ -2)+1280*V*V*nat(V1)*nat(nat(V1+1)+ -1)+544*V*V*nat(V1)*nat(V1+1)+128*V*V*nat(V1)*nat(2*V+V1)+401*V*V*nat(nat(V1+1)+ -2)+72*V*V*nat(nat(V1+1)+ -2)*nat(nat(V1+1)+ -2)+968*V*V*nat(nat(V1+1)+ -2)*nat(nat(V1+1)+ -1)+16*V*V*nat(nat(V1+1)+ -2)*nat(V+V1)+280*V*V*nat(nat(V1+1)+ -2)*nat(V1+1)+144*V*V*nat(nat(V1+1)+ -2)*nat(2*V+V1)+32*V*V*nat(nat(V1+1)+ -2)*nat(2*V1+1)+32*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1)*3)*nat(nat(V1+1)+ -1)+16*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1)*3)*nat(V1+1)+32*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)*nat(nat(V1+1)+ -1)+16*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)*nat(V1+1)+48*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1+1)*2)*nat(nat(V1+1)+ -1)+24*V*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1+1)*2)*nat(V1+1)+2619*V*V*nat(nat(V1+1)+ -1)+2720*V*V*nat(nat(V1+1)+ -1)*nat(nat(V1+1)+ -1)+64*V*V*nat(nat(V1+1)+ -1)*(2*V)+192*V*V*nat(nat(V1+1)+ -1)*nat(2*V1)+240*V*V*nat(nat(V1+1)+ -1)*nat(V+V1)+64*V*V*nat(nat(V1+1)+ -1)*nat(V+2*V1)+1648*V*V*nat(nat(V1+1)+ -1)*nat(V1+1)+704*V*V*nat(nat(V1+1)+ -1)*nat(2*V+V1)+64*V*V*nat(nat(V1+1)+ -1)*nat(2*V+2*V1)+480*V*V*nat(nat(V1+1)+ -1)*nat(2*V1+1)+32*V*V*nat(nat(V1+1)+ -1)*nat(2*V+V1+1)+32*V*V*(2*V)*nat(V1+1)+96*V*V*nat(2*V1)*nat(V1+1)+16*V*V*nat(V+V1)+96*V*V*nat(V+V1)*nat(V1+1)+32*V*V*nat(V+V1)*nat(2*V+V1)+32*V*V*nat(V+2*V1)*nat(V1+1)+720*V*V*nat(V1+1)+288*V*V*nat(V1+1)*nat(V1+1)+160*V*V*nat(V1+1)*nat(2*V+V1)+32*V*V*nat(V1+1)*nat(2*V+2*V1)+192*V*V*nat(V1+1)*nat(2*V1+1)+16*V*V*nat(V1+1)*nat(2*V+V1+1)+658*V*V*nat(2*V+V1)+64*V*V*nat(2*V+V1)*nat(2*V1+1)+32*V*V*nat(2*V1+1)+648*V*nat(V1)+296*V*nat(V1)*nat(V1)+240*V*nat(V1)*nat(nat(V1+1)+ -2)+24*V*nat(V1)*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1)*3)+1352*V*nat(V1)*nat(nat(V1+1)+ -1)+16*V*nat(V1)*(2*V)+64*V*nat(V1)*nat(2*V1)+328*V*nat(V1)*nat(V1+1)+192*V*nat(V1)*nat(2*V+V1)+290*V*nat(nat(V1+1)+ -2)+8*V*nat(nat(V1+1)+ -2)*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1)*3)+8*V*nat(nat(V1+1)+ -2)*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)+12*V*nat(nat(V1+1)+ -2)*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1+1)*2)+16*V*nat(nat(V1+1)+ -2)*(2*V)+64*V*nat(nat(V1+1)+ -2)*nat(2*V1)+40*V*nat(nat(V1+1)+ -2)*nat(V+V1)+16*V*nat(nat(V1+1)+ -2)*nat(V+2*V1)+72*V*nat(nat(V1+1)+ -2)*nat(V1+1)+32*V*nat(nat(V1+1)+ -2)*nat(2*V+V1)+16*V*nat(nat(V1+1)+ -2)*nat(2*V+2*V1)+48*V*nat(nat(V1+1)+ -2)*nat(2*V1+1)+8*V*nat(nat(V1+1)+ -2)*nat(2*V+V1+1)+8*V*nat(V-1)+32*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1)*3)*nat(nat(V1+1)+ -1)+32*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)*nat(nat(V1+1)+ -1)+8*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)*nat(V+V1)+16*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V+V1)+nat(2*V1+1)*2)*nat(2*V1+1)+48*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1+1)*2)*nat(nat(V1+1)+ -1)+24*V*nat(4*V*nat(nat(V1+1)+ -1)+ -1+2*V*nat(V1+1)+nat(V1+1)*2)*nat(V1+1)+9*V*nat(nat(V+V1)+ -1)+1169*V*nat(nat(V1+1)+ -1)+64*V*nat(nat(V1+1)+ -1)*(2*V)+336*V*nat(nat(V1+1)+ -1)*nat(2*V1)+240*V*nat(nat(V1+1)+ -1)*nat(V+V1)+64*V*nat(nat(V1+1)+ -1)*nat(V+2*V1)+288*V*nat(nat(V1+1)+ -1)*nat(V1+1)+128*V*nat(nat(V1+1)+ -1)*nat(2*V+V1)+64*V*nat(nat(V1+1)+ -1)*nat(2*V+2*V1)+192*V*nat(nat(V1+1)+ -1)*nat(2*V1+1)+32*V*nat(nat(V1+1)+ -1)*nat(2*V+V1+1)+98*V*(2*V)+246*V*nat(2*V1)+16*V*nat(2*V1)*nat(V+V1)+48*V*nat(2*V1)*nat(V1+1)+32*V*nat(2*V1)*nat(2*V+V1)+32*V*nat(2*V1)*nat(2*V1+1)+89*V*nat(V+V1)+24*V*nat(V+V1)*nat(V+V1)+16*V*nat(V+V1)*nat(V+2*V1)+48*V*nat(V+V1)*nat(V1+1)+32*V*nat(V+V1)*nat(2*V+V1)+16*V*nat(V+V1)*nat(2*V+2*V1)+96*V*nat(V+V1)*nat(2*V1+1)+66*V*nat(V+2*V1)+32*V*nat(V+2*V1)*nat(2*V1+1)+396*V*nat(V1+1)+144*V*nat(V1+1)*nat(V1+1)+32*V*nat(V1+1)*nat(2*V+V1)+16*V*nat(V1+1)*nat(2*V+V1+1)+150*V*nat(2*V+V1)+66*V*nat(2*V+2*V1)+32*V*nat(2*V+2*V1)*nat(2*V1+1)+96*V*nat(2*V1+1)+96*V*nat(2*V1+1)*nat(2*V1+1)+33*V*nat(2*V+V1+1)+nat(V1)*1629+nat(V1)*718*nat(V1)+nat(V1)*320*nat(V1)*nat(V1)*nat(nat(V6+1)+ -2)*nat(nat(V6+1)+ -1)+nat(V1)*160*nat(V1)*nat(V1)*nat(nat(V6+1)+ -2)*nat(V6+1)+nat(V1)*320*nat(V1)*nat(V1)*nat(nat(V6+1)+ -1)+nat(V1)*3008*nat(V1)*nat(V1)*nat(nat(V6+1)+ -1)*nat(nat(V6+1)+ -1)+nat(V1)*2528*nat(V1)*nat(V1)*nat(nat(V6+1)+ -1)*nat(V6+1)+nat(V1)*640*nat(V1)*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V1+V6)+nat(V1)*160*nat(V1)*nat(V1)*nat(V6+1)+nat(V1)*512*nat(V1)*nat(V1)*nat(V6+1)*nat(V6+1)+nat(V1)*320*nat(V1)*nat(V1)*nat(V6+1)*nat(2*V1+V6)+nat(V1)*48*nat(V1)*nat(V6)+nat(V1)*48*nat(V1)*nat(V6)*nat(nat(V6+1)+ -2)+nat(V1)*1040*nat(V1)*nat(V6)*nat(nat(V6+1)+ -1)+nat(V1)*448*nat(V1)*nat(V6)*nat(V6+1)+nat(V1)*96*nat(V1)*nat(V6)*nat(2*V1+V6)+nat(V1)*442*nat(V1)*nat(nat(V6+1)+ -2)+nat(V1)*80*nat(V1)*nat(nat(V6+1)+ -2)*nat(nat(V6+1)+ -2)+nat(V1)*1072*nat(V1)*nat(nat(V6+1)+ -2)*nat(nat(V6+1)+ -1)+nat(V1)*16*nat(V1)*nat(nat(V6+1)+ -2)*nat(V1+V6)+nat(V1)*16*nat(V1)*nat(nat(V6+1)+ -2)*nat(V6+V14)+nat(V1)*320*nat(V1)*nat(nat(V6+1)+ -2)*nat(V6+1)+nat(V1)*176*nat(V1)*nat(nat(V6+1)+ -2)*nat(2*V1+V6)+nat(V1)*32*nat(V1)*nat(nat(V6+1)+ -2)*nat(2*V6+1)+nat(V1)*32*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6)*2+nat(V6+V14))*nat(nat(V6+1)+ -1)+nat(V1)*16*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6)*2+nat(V6+V14))*nat(V6+1)+nat(V1)*32*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V1+V6)+nat(2*V6+1)*2)*nat(nat(V6+1)+ -1)+nat(V1)*16*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V1+V6)+nat(2*V6+1)*2)*nat(V6+1)+nat(V1)*32*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2)*nat(nat(V6+1)+ -1)+nat(V1)*16*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2)*nat(V6+1)+nat(V1)*32*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2+nat(2*V1+V6))*nat(nat(V6+1)+ -1)+nat(V1)*16*nat(V1)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2+nat(2*V1+V6))*nat(V6+1)+nat(V1)*2846*nat(V1)*nat(nat(V6+1)+ -1)+nat(V1)*3008*nat(V1)*nat(nat(V6+1)+ -1)*nat(nat(V6+1)+ -1)+nat(V1)*64*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V1)+nat(V1)*128*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V6)+nat(V1)*240*nat(V1)*nat(nat(V6+1)+ -1)*nat(V1+V6)+nat(V1)*64*nat(V1)*nat(nat(V6+1)+ -1)*nat(V1+2*V6)+nat(V1)*240*nat(V1)*nat(nat(V6+1)+ -1)*nat(V6+V14)+nat(V1)*1984*nat(V1)*nat(nat(V6+1)+ -1)*nat(V6+1)+nat(V1)*1072*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V1+V6)+nat(V1)*128*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V1+2*V6)+nat(V1)*64*nat(V1)*nat(nat(V6+1)+ -1)*nat(2*V6+V14)+nat(V1)*480*nat(V1)*nat(nat(V6+1)+ 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-1)+nat(V1)*16*nat(V6)*nat(2*V1)+nat(V1)*16*nat(V6)*nat(2*V6)+nat(V1)*112*nat(V6)*nat(V6+V14)+nat(V1)*304*nat(V6)*nat(V6+1)+nat(V1)*176*nat(V6)*nat(2*V1+V6)+nat(V1)*32*nat(V6)*nat(2*V6+V14)+nat(V1)*316*nat(nat(V6+1)+ -2)+nat(V1)*8*nat(nat(V6+1)+ -2)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6)*2+nat(V6+V14))+nat(V1)*8*nat(nat(V6+1)+ -2)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V1+V6)+nat(2*V6+1)*2)+nat(V1)*8*nat(nat(V6+1)+ -2)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2)+nat(V1)*8*nat(nat(V6+1)+ -2)*nat(nat(V1)*4*nat(nat(V6+1)+ -1)+ -1+nat(V1)*2*nat(V6+1)+nat(V6+1)*2+nat(2*V1+V6))+nat(V1)*16*nat(nat(V6+1)+ -2)*nat(2*V1)+nat(V1)*48*nat(nat(V6+1)+ -2)*nat(2*V6)+nat(V1)*40*nat(nat(V6+1)+ -2)*nat(V1+V6)+nat(V1)*16*nat(nat(V6+1)+ -2)*nat(V1+2*V6)+nat(V1)*40*nat(nat(V6+1)+ -2)*nat(V6+V14)+nat(V1)*96*nat(nat(V6+1)+ -2)*nat(V6+1)+nat(V1)*88*nat(nat(V6+1)+ -2)*nat(2*V1+V6)+nat(V1)*32*nat(nat(V6+1)+ 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-1)*454*nat(-V+V1)*nat(-V+V1)+nat(nat(V6+1)+ -1)*64*nat(-V+V1)*nat(-V+V1)*nat(-V+V1)+nat(nat(V6+1)+ -1)*128*nat(-V+V1)*nat(-V+V1)*nat(-V+V1)*nat(-2*V+2*V1+V6)+nat(nat(V6+1)+ -1)*128*nat(-V+V1)*nat(-V+V1)*nat(-2*V+2*V1+V6)+nat(nat(V6+1)+ -1)*480*nat(-V+V1)*nat(-V+V1)*nat(V6-V14+1)+nat(nat(V6+1)+ -1)*64*nat(-V+V1)*nat(-V+V1)*nat(-2*V+2*V1+V6-V14+1)+nat(nat(V6+1)+ -1)*64*nat(-V+V1)*nat(-V+V1)*nat(V6-V14)+nat(nat(V6+1)+ -1)*192*nat(-V+V1)*nat(V6-V14+1)+nat(nat(V6+1)+ -1)*64*nat(-V+V1)*nat(-2*V+2*V1+V6-V14+1)+nat(nat(V6+1)+ -1)*208*nat(-V+V1)*nat(V6-V14)+nat(nat(-V+V1+V6)+ 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- Complexity: n^5 * Chain [67] with precondition: [V=1] - Upper bound: nat(V1)*106+75+nat(V1)*48*nat(V1)+nat(V1)*16*nat(nat(V1)+ -1)+nat(V1)*32*nat(V1+V6)+nat(V6)*1132+nat(V6)*430*nat(V6)+nat(V6)*320*nat(V6)*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -1)+nat(V6)*160*nat(V6)*nat(V6)*nat(nat(V14+1)+ -2)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)+nat(V6)*2880*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(nat(V14+1)+ -1)+nat(V6)*2400*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(V14+1)+nat(V6)*640*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V6+V14)+nat(V6)*160*nat(V6)*nat(V6)*nat(V14+1)+nat(V6)*480*nat(V6)*nat(V6)*nat(V14+1)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V6)*nat(V14+1)*nat(2*V6+V14)+nat(V6)*88*nat(V6)*nat(V14)+nat(V6)*88*nat(V6)*nat(V14)*nat(nat(V14+1)+ -2)+nat(V6)*1800*nat(V6)*nat(V14)*nat(nat(V14+1)+ -1)+nat(V6)*768*nat(V6)*nat(V14)*nat(V14+1)+nat(V6)*176*nat(V6)*nat(V14)*nat(2*V6+V14)+nat(V6)*410*nat(V6)*nat(nat(V14+1)+ -2)+nat(V6)*80*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -2)+nat(V6)*1040*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14)+nat(V6)*320*nat(V6)*nat(nat(V14+1)+ -2)*nat(V14+1)+nat(V6)*160*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V6+V14)+nat(V6)*8*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14+V19)+nat(V6)*16*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(V14+1)+nat(V6)*32*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(nat(V14+1)+ -1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)*nat(V14+1)+nat(V6)*80*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(nat(V14+1)+ -1)+nat(V6)*40*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(V14+1)+nat(V6)*2270*nat(V6)*nat(nat(V14+1)+ -1)+nat(V6)*2880*nat(V6)*nat(nat(V14+1)+ -1)*nat(nat(V14+1)+ -1)+nat(V6)*152*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14)+nat(V6)*64*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14)+nat(V6)*2160*nat(V6)*nat(nat(V14+1)+ -1)*nat(V14+1)+nat(V6)*960*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V6+V14)+nat(V6)*120*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14+V19)+nat(V6)*240*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14+1)+nat(V6)*32*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14+V19)+nat(V6)*32*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14+1)+nat(V6)*8*nat(V6)*nat(2*V14)+nat(V6)*64*nat(V6)*nat(2*V14)*nat(V14+1)+nat(V6)*16*nat(V6)*nat(2*V14)*nat(2*V6+V14)+nat(V6)*32*nat(V6)*nat(3*V14)*nat(V14+1)+nat(V6)*560*nat(V6)*nat(V14+1)+nat(V6)*480*nat(V6)*nat(V14+1)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V14+1)*nat(2*V6+V14)+nat(V6)*48*nat(V6)*nat(V14+1)*nat(2*V14+V19)+nat(V6)*96*nat(V6)*nat(V14+1)*nat(2*V14+1)+nat(V6)*16*nat(V6)*nat(V14+1)*nat(3*V14+V19)+nat(V6)*16*nat(V6)*nat(V14+1)*nat(3*V14+1)+nat(V6)*660*nat(V6)*nat(2*V6+V14)+nat(V6)*16*nat(V6)*nat(2*V6+V14)*nat(2*V14+V19)+nat(V6)*32*nat(V6)*nat(2*V6+V14)*nat(2*V14+1)+nat(V6)*8*nat(V6)*nat(2*V14+V19)+nat(V6)*16*nat(V6)*nat(2*V14+1)+nat(V6)*847*nat(V14)+nat(V6)*388*nat(V14)*nat(V14)+nat(V6)*340*nat(V14)*nat(nat(V14+1)+ -2)+nat(V6)*8*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))+nat(V6)*8*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))+nat(V6)*16*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))+nat(V6)*12*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)+nat(V6)*1800*nat(V14)*nat(nat(V14+1)+ -1)+nat(V6)*80*nat(V14)*nat(2*V14)+nat(V6)*32*nat(V14)*nat(3*V14)+nat(V6)*424*nat(V14)*nat(V14+1)+nat(V6)*264*nat(V14)*nat(2*V6+V14)+nat(V6)*56*nat(V14)*nat(2*V14+V19)+nat(V6)*112*nat(V14)*nat(2*V14+1)+nat(V6)*16*nat(V14)*nat(3*V14+V19)+nat(V6)*16*nat(V14)*nat(3*V14+1)+nat(V6)*260*nat(nat(V14+1)+ -2)+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))+nat(V6)*8*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)+nat(V6)*20*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)+nat(V6)*28*nat(nat(V14+1)+ -2)*nat(2*V14)+nat(V6)*16*nat(nat(V14+1)+ -2)*nat(3*V14)+nat(V6)*120*nat(nat(V14+1)+ -2)*nat(V14+1)+nat(V6)*80*nat(nat(V14+1)+ -2)*nat(2*V6+V14)+nat(V6)*20*nat(nat(V14+1)+ -2)*nat(2*V14+V19)+nat(V6)*40*nat(nat(V14+1)+ -2)*nat(2*V14+1)+nat(V6)*8*nat(nat(V14+1)+ -2)*nat(3*V14+V19)+nat(V6)*8*nat(nat(V14+1)+ -2)*nat(3*V14+1)+nat(V6)*16*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(nat(V14+1)+ -1)+nat(V6)*4*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(2*V14)+nat(V6)*16*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(nat(V14+1)+ -1)+nat(V6)*4*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(2*V14+V19)+nat(V6)*32*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(2*V14+1)+nat(V6)*16*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)*nat(nat(V14+1)+ -1)+nat(V6)*80*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(nat(V14+1)+ -1)+nat(V6)*40*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(V14+1)+nat(V6)*10*nat(nat(V6+V14)+ -1)+nat(V6)*1050*nat(nat(V14+1)+ -1)+nat(V6)*152*nat(nat(V14+1)+ -1)*nat(2*V14)+nat(V6)*64*nat(nat(V14+1)+ -1)*nat(3*V14)+nat(V6)*480*nat(nat(V14+1)+ -1)*nat(V14+1)+nat(V6)*320*nat(nat(V14+1)+ -1)*nat(2*V6+V14)+nat(V6)*120*nat(nat(V14+1)+ -1)*nat(2*V14+V19)+nat(V6)*240*nat(nat(V14+1)+ -1)*nat(2*V14+1)+nat(V6)*32*nat(nat(V14+1)+ -1)*nat(3*V14+V19)+nat(V6)*32*nat(nat(V14+1)+ -1)*nat(3*V14+1)+nat(V6)*65*nat(2*V14)+nat(V6)*12*nat(2*V14)*nat(2*V14)+nat(V6)*8*nat(2*V14)*nat(3*V14)+nat(V6)*24*nat(2*V14)*nat(V14+1)+nat(V6)*24*nat(2*V14)*nat(2*V6+V14)+nat(V6)*66*nat(3*V14)+nat(V6)*8*nat(3*V14)*nat(2*V14+1)+nat(V6)*10*nat(V6+V14)+nat(V6)*520*nat(V14+1)+nat(V6)*240*nat(V14+1)*nat(V14+1)+nat(V6)*80*nat(V14+1)*nat(2*V6+V14)+nat(V6)*24*nat(V14+1)*nat(2*V14+V19)+nat(V6)*48*nat(V14+1)*nat(2*V14+1)+nat(V6)*100*nat(-V1+V6)+nat(V6)*350*nat(2*V6+V14)+nat(V6)*24*nat(2*V6+V14)*nat(2*V14+V19)+nat(V6)*48*nat(2*V6+V14)*nat(2*V14+1)+nat(V6)*32*nat(2*V14+V19)+nat(V6)*12*nat(2*V14+V19)*nat(2*V14+V19)+nat(V6)*8*nat(2*V14+V19)*nat(3*V14+V19)+nat(V6)*64*nat(2*V14+1)+nat(V6)*24*nat(2*V14+1)*nat(2*V14+1)+nat(V6)*8*nat(2*V14+1)*nat(3*V14+1)+nat(V6)*33*nat(3*V14+V19)+nat(V6)*33*nat(3*V14+1)+nat(V14)*867+nat(V14)*572*nat(V14)+nat(V14)*172*nat(V14)*nat(-V1+V6)+nat(V14)*228*nat(nat(V14+1)+ -2)*nat(-V1+V6)+nat(V14)*56*nat(nat(V14+1)+ 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-1+nat(V14+1)*2+nat(V14+1)*2*nat(-V1+V6))+nat(V14)*4*nat(nat(nat(V14+1)+ -1)*4*nat(-V1+V6)+ -1+nat(V14+1)*2+nat(V14+1)*2*nat(-V1+V6)+nat(-V1+V6+V14))+nat(V14)*4*nat(nat(nat(V14+1)+ -1)*4*nat(-V1+V6)+ -1+nat(V14+1)*3+nat(V14+1)*2*nat(-V1+V6))+nat(V14)*1304*nat(nat(V14+1)+ -1)*nat(-V1+V6)+nat(V14)*1160*nat(nat(V14+1)+ 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-1)*32*nat(-V1+V6)*nat(-2*V1+2*V6+2*V14)+nat(nat(-V1+V6+V14)+ -1)*10*nat(-V1+V6)+nat(2*V14)*107+nat(2*V14)*28*nat(2*V14)+nat(2*V14)*8*nat(3*V14)+nat(2*V14)*48*nat(V14+1)*nat(-V1+V6)+nat(2*V14)*64*nat(V14+1)*nat(-V1+V6)*nat(-V1+V6)+nat(2*V14)*180*nat(-V1+V6)+nat(2*V14)*32*nat(-V1+V6)*nat(2*V14+1)+nat(2*V14)*40*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(2*V14)*8*nat(2*V6+V14)+nat(2*V14)*64*nat(2*V14+1)+nat(2*V14)*28*nat(-2*V1+2*V6+V14)+nat(2*V14)*8*nat(-2*V1+2*V6+2*V14)+nat(3*V14)*8*nat(2*V14+1)+nat(V1+V6)*56+nat(V1+1)*38+nat(V1+2)*2+nat(V6+V14)*10+nat(V6+1)*53+nat(V6+2)*34+nat(V14+V19)*243+nat(V14+V19)*84*nat(V14+V19)+nat(V14+V19)*24*nat(V14+V19)*nat(-V1+V6)+nat(V14+V19)*48*nat(V14+1)*nat(-V1+V6)+nat(V14+V19)*96*nat(V14+1)*nat(-V1+V6)*nat(-V1+V6)+nat(V14+V19)*64*nat(-V1+V6)+nat(V14+V19)*16*nat(-V1+V6)*nat(-V1+V6)+nat(V14+V19)*32*nat(-V1+V6)*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(V14+V19)*16*nat(-V1+V6)*nat(2*V14+V19)+nat(V14+V19)*48*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(V14+V19)*56*nat(2*V14+V19)+nat(V14+V19)*16*nat(-2*V1+2*V6+V14)+nat(V14+1)*418+nat(V14+1)*96*nat(V14+1)+nat(V14+1)*276*nat(V14+1)*nat(-V1+V6)+nat(V14+1)*432*nat(V14+1)*nat(-V1+V6)*nat(-V1+V6)+nat(V14+1)*512*nat(V14+1)*nat(-V1+V6)*nat(-V1+V6)*nat(-V1+V6)+nat(V14+1)*504*nat(-V1+V6)+nat(V14+1)*792*nat(-V1+V6)*nat(-V1+V6)+nat(V14+1)*160*nat(-V1+V6)*nat(-V1+V6)*nat(-V1+V6)+nat(V14+1)*320*nat(-V1+V6)*nat(-V1+V6)*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(V14+1)*32*nat(-V1+V6)*nat(-V1+V6)*nat(-2*V1+2*V6)+nat(V14+1)*32*nat(-V1+V6)*nat(-V1+V6)*nat(2*V14+V19)+nat(V14+1)*240*nat(-V1+V6)*nat(-V1+V6)*nat(2*V14+1)+nat(V14+1)*48*nat(-V1+V6)*nat(-V1+V6)*nat(-V1+V6+V14)+nat(V14+1)*16*nat(-V1+V6)*nat(-V1+V6)*nat(-V1+V6+2*V14)+nat(V14+1)*304*nat(-V1+V6)*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(V14+1)*16*nat(-V1+V6)*nat(-V1+V6)*nat(-2*V1+2*V6+2*V14)+nat(V14+1)*24*nat(-V1+V6)*nat(2*V14+1)+nat(V14+1)*72*nat(-V1+V6)*nat(-V1+V6+V14)+nat(V14+1)*16*nat(-V1+V6)*nat(-V1+V6+2*V14)+nat(V14+1)*112*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(V14+1)*48*nat(2*V14+1)+nat(V14+1)*24*nat(-V1+V6+V14)+nat(V14+1)*8*nat(-2*V1+2*V6+V14)+nat(V14+2)*198+nat(-V1+V6)*1250+nat(-V1+V6)*362*nat(-V1+V6)+nat(-V1+V6)*32*nat(-V1+V6)*nat(2*V14+1)+nat(-V1+V6)*64*nat(-V1+V6)*nat(2*V14+1)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*8*nat(-V1+V6)*nat(-V1+V6+V14)+nat(-V1+V6)*16*nat(-V1+V6)*nat(-V1+V6+V14)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*732*nat(-V1+V6)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*16*nat(-V1+V6)*nat(-2*V1+2*V6+V14)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*98*nat(-2*V1+2*V6)+nat(-V1+V6)*66*nat(2*V14+V19)+nat(-V1+V6)*195*nat(2*V14+1)+nat(-V1+V6)*128*nat(2*V14+1)*nat(2*V14+1)+nat(-V1+V6)*72*nat(2*V14+1)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*16*nat(2*V14+1)*nat(-2*V1+2*V6+2*V14)+nat(-V1+V6)*42*nat(-V1+V6+V14)+nat(-V1+V6)*12*nat(-V1+V6+V14)*nat(-V1+V6+V14)+nat(-V1+V6)*8*nat(-V1+V6+V14)*nat(-V1+V6+2*V14)+nat(-V1+V6)*24*nat(-V1+V6+V14)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*33*nat(-V1+V6+2*V14)+nat(-V1+V6)*283*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*28*nat(-2*V1+2*V6+V14)*nat(-2*V1+2*V6+V14)+nat(-V1+V6)*8*nat(-2*V1+2*V6+V14)*nat(-2*V1+2*V6+2*V14)+nat(-V1+V6)*33*nat(-2*V1+2*V6+2*V14)+nat(-2*V1+2*V6)*2+nat(2*V6+V14)*10+nat(2*V6+V14)*8*nat(2*V14+V19)+nat(2*V6+V14)*16*nat(2*V14+1)+nat(2*V14+V19)*55+nat(2*V14+V19)*12*nat(2*V14+V19)+nat(2*V14+V19)*8*nat(3*V14+V19)+nat(2*V14+1)*188+nat(2*V14+1)*24*nat(2*V14+1)+nat(2*V14+1)*8*nat(3*V14+1)+nat(2*V14+1)*32*nat(-2*V1+2*V6+V14)+nat(2*V14+2)*67+nat(2*V14+3)*14+nat(V1+V6+1)*10+nat(V14+V19+1)*75+nat(V14+V19+2)*25+nat(-V1+V6+V14)*36+nat(-V1+V6+V14)*12*nat(-V1+V6+V14)+nat(-V1+V6+V14)*8*nat(-V1+V6+2*V14)+nat(-V1+V6+V14)*8*nat(-2*V1+2*V6+V14)+nat(-V1+V6+2*V14)+nat(-2*V1+2*V6+V14)*33+nat(-2*V1+2*V6+V14)*12*nat(-2*V1+2*V6+V14)+nat(-2*V1+2*V6+V14)*8*nat(-2*V1+2*V6+2*V14)+nat(-2*V1+2*V6+2*V14)+nat(2*V14+V19+1)*39+nat(2*V14+V19+2)*14+nat(-V1+V6+V14+1) - Complexity: n^5 * Chain [66] with precondition: [V=2,V1>=0,V6>=0] - Upper bound: 2*V6+2 - Complexity: n * Chain [65] with precondition: [V1=0,V>=0] - Upper bound: 3 - Complexity: constant * Chain [64] with precondition: [V1=1,V>=0,V6>=0] - Upper bound: 6 - Complexity: constant ### Maximum cost of start(V,V1,V6,V14,V19): max([4,nat(V1)*106+64+nat(V1)*48*nat(V1)+nat(V1)*32*nat(V1+V6)+nat(V6)*270+nat(V6)*144*nat(V6)+nat(V6)*10*nat(V6+V14)+nat(V6)*16*nat(2*V6+V14)+nat(V14)*252+nat(V14)*120*nat(V14)+nat(V14)*32*nat(nat(V14)+ -1)+nat(V1+V6)*56+nat(V1+1)*38+nat(V1+2)*2+nat(V6+V14)*10+nat(V6+1)*53+nat(V6+2)*34+max([nat(V1)*16*nat(nat(V1)+ -1)+9+nat(V6)*860+nat(V6)*286*nat(V6)+nat(V6)*320*nat(V6)*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -1)+nat(V6)*160*nat(V6)*nat(V6)*nat(nat(V14+1)+ -2)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)+nat(V6)*2880*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(nat(V14+1)+ -1)+nat(V6)*2400*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(V14+1)+nat(V6)*640*nat(V6)*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V6+V14)+nat(V6)*160*nat(V6)*nat(V6)*nat(V14+1)+nat(V6)*480*nat(V6)*nat(V6)*nat(V14+1)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V6)*nat(V14+1)*nat(2*V6+V14)+nat(V6)*88*nat(V6)*nat(V14)+nat(V6)*88*nat(V6)*nat(V14)*nat(nat(V14+1)+ -2)+nat(V6)*1800*nat(V6)*nat(V14)*nat(nat(V14+1)+ -1)+nat(V6)*768*nat(V6)*nat(V14)*nat(V14+1)+nat(V6)*176*nat(V6)*nat(V14)*nat(2*V6+V14)+nat(V6)*410*nat(V6)*nat(nat(V14+1)+ -2)+nat(V6)*80*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -2)+nat(V6)*1040*nat(V6)*nat(nat(V14+1)+ -2)*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14)+nat(V6)*320*nat(V6)*nat(nat(V14+1)+ -2)*nat(V14+1)+nat(V6)*160*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V6+V14)+nat(V6)*8*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14+V19)+nat(V6)*16*nat(V6)*nat(nat(V14+1)+ -2)*nat(2*V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))*nat(V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))*nat(V14+1)+nat(V6)*32*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(nat(V14+1)+ -1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))*nat(V14+1)+nat(V6)*16*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)*nat(nat(V14+1)+ -1)+nat(V6)*8*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)*nat(V14+1)+nat(V6)*80*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(nat(V14+1)+ -1)+nat(V6)*40*nat(V6)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14+1)*2)*nat(V14+1)+nat(V6)*2270*nat(V6)*nat(nat(V14+1)+ -1)+nat(V6)*2880*nat(V6)*nat(nat(V14+1)+ -1)*nat(nat(V14+1)+ -1)+nat(V6)*152*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14)+nat(V6)*64*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14)+nat(V6)*2160*nat(V6)*nat(nat(V14+1)+ -1)*nat(V14+1)+nat(V6)*960*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V6+V14)+nat(V6)*120*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14+V19)+nat(V6)*240*nat(V6)*nat(nat(V14+1)+ -1)*nat(2*V14+1)+nat(V6)*32*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14+V19)+nat(V6)*32*nat(V6)*nat(nat(V14+1)+ -1)*nat(3*V14+1)+nat(V6)*8*nat(V6)*nat(2*V14)+nat(V6)*64*nat(V6)*nat(2*V14)*nat(V14+1)+nat(V6)*16*nat(V6)*nat(2*V14)*nat(2*V6+V14)+nat(V6)*32*nat(V6)*nat(3*V14)*nat(V14+1)+nat(V6)*560*nat(V6)*nat(V14+1)+nat(V6)*480*nat(V6)*nat(V14+1)*nat(V14+1)+nat(V6)*320*nat(V6)*nat(V14+1)*nat(2*V6+V14)+nat(V6)*48*nat(V6)*nat(V14+1)*nat(2*V14+V19)+nat(V6)*96*nat(V6)*nat(V14+1)*nat(2*V14+1)+nat(V6)*16*nat(V6)*nat(V14+1)*nat(3*V14+V19)+nat(V6)*16*nat(V6)*nat(V14+1)*nat(3*V14+1)+nat(V6)*660*nat(V6)*nat(2*V6+V14)+nat(V6)*16*nat(V6)*nat(2*V6+V14)*nat(2*V14+V19)+nat(V6)*32*nat(V6)*nat(2*V6+V14)*nat(2*V14+1)+nat(V6)*8*nat(V6)*nat(2*V14+V19)+nat(V6)*16*nat(V6)*nat(2*V14+1)+nat(V6)*847*nat(V14)+nat(V6)*388*nat(V14)*nat(V14)+nat(V6)*340*nat(V14)*nat(nat(V14+1)+ -2)+nat(V6)*8*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))+nat(V6)*8*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))+nat(V6)*16*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))+nat(V6)*12*nat(V14)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*3)+nat(V6)*1800*nat(V14)*nat(nat(V14+1)+ -1)+nat(V6)*80*nat(V14)*nat(2*V14)+nat(V6)*32*nat(V14)*nat(3*V14)+nat(V6)*424*nat(V14)*nat(V14+1)+nat(V6)*264*nat(V14)*nat(2*V6+V14)+nat(V6)*56*nat(V14)*nat(2*V14+V19)+nat(V6)*112*nat(V14)*nat(2*V14+1)+nat(V6)*16*nat(V14)*nat(3*V14+V19)+nat(V6)*16*nat(V14)*nat(3*V14+1)+nat(V6)*260*nat(nat(V14+1)+ -2)+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14))+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+V19))+nat(V6)*8*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ -1+nat(V6)*2*nat(V14+1)+nat(V14)*2+nat(2*V14+1))+nat(V6)*4*nat(nat(V14+1)+ -2)*nat(nat(V6)*4*nat(nat(V14+1)+ -1)+ 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Asymptotic class: n^5 * Total analysis performed in 44348 ms. ---------------------------------------- (10) BOUNDS(1, n^5) ---------------------------------------- (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (12) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (13) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence isZero(s(s(x))) ->^+ isZero(s(x)) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [x / s(x)]. The result substitution is [ ]. ---------------------------------------- (14) Complex Obligation (BEST) ---------------------------------------- (15) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (16) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (17) BOUNDS(n^1, INF) ---------------------------------------- (18) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c S is empty. Rewrite Strategy: INNERMOST