1115.54/291.62 WORST_CASE(Omega(n^1), O(n^2)) 1115.54/291.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1115.54/291.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.54/291.63 1115.54/291.63 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.54/291.63 1115.54/291.63 (0) CpxTRS 1115.54/291.63 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (2) CpxWeightedTrs 1115.54/291.63 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (4) CpxTypedWeightedTrs 1115.54/291.63 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1115.54/291.63 (6) CpxTypedWeightedCompleteTrs 1115.54/291.63 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1115.54/291.63 (8) CpxRNTS 1115.54/291.63 (9) CompleteCoflocoProof [FINISHED, 5268 ms] 1115.54/291.63 (10) BOUNDS(1, n^2) 1115.54/291.63 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (12) CpxTRS 1115.54/291.63 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (14) typed CpxTrs 1115.54/291.63 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1115.54/291.63 (16) typed CpxTrs 1115.54/291.63 (17) RewriteLemmaProof [LOWER BOUND(ID), 269 ms] 1115.54/291.63 (18) BEST 1115.54/291.63 (19) proven lower bound 1115.54/291.63 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.54/291.63 (21) BOUNDS(n^1, INF) 1115.54/291.63 (22) typed CpxTrs 1115.54/291.63 (23) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 1115.54/291.63 (24) typed CpxTrs 1115.54/291.63 (25) RewriteLemmaProof [LOWER BOUND(ID), 23 ms] 1115.54/291.63 (26) typed CpxTrs 1115.54/291.63 1115.54/291.63 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (0) 1115.54/291.63 Obligation: 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.54/291.63 1115.54/291.63 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.63 quot(0, s(y)) -> 0 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.63 le(0, y) -> true 1115.54/291.63 le(s(x), 0) -> false 1115.54/291.63 le(s(x), s(y)) -> le(x, y) 1115.54/291.63 inc(s(x)) -> s(inc(x)) 1115.54/291.63 inc(0) -> s(0) 1115.54/291.63 log(x) -> logIter(x, 0) 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) 1115.54/291.63 if(false, b, x, y) -> logZeroError 1115.54/291.63 if(true, false, x, s(y)) -> y 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) 1115.54/291.63 1115.54/291.63 S is empty. 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1115.54/291.63 Transformed relative TRS to weighted TRS 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (2) 1115.54/291.63 Obligation: 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1115.54/291.63 1115.54/291.63 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x [1] 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) [1] 1115.54/291.63 quot(0, s(y)) -> 0 [1] 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 1115.54/291.63 le(0, y) -> true [1] 1115.54/291.63 le(s(x), 0) -> false [1] 1115.54/291.63 le(s(x), s(y)) -> le(x, y) [1] 1115.54/291.63 inc(s(x)) -> s(inc(x)) [1] 1115.54/291.63 inc(0) -> s(0) [1] 1115.54/291.63 log(x) -> logIter(x, 0) [1] 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) [1] 1115.54/291.63 if(false, b, x, y) -> logZeroError [1] 1115.54/291.63 if(true, false, x, s(y)) -> y [1] 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) [1] 1115.54/291.63 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.54/291.63 Infered types. 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (4) 1115.54/291.63 Obligation: 1115.54/291.63 Runtime Complexity Weighted TRS with Types. 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x [1] 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) [1] 1115.54/291.63 quot(0, s(y)) -> 0 [1] 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 1115.54/291.63 le(0, y) -> true [1] 1115.54/291.63 le(s(x), 0) -> false [1] 1115.54/291.63 le(s(x), s(y)) -> le(x, y) [1] 1115.54/291.63 inc(s(x)) -> s(inc(x)) [1] 1115.54/291.63 inc(0) -> s(0) [1] 1115.54/291.63 log(x) -> logIter(x, 0) [1] 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) [1] 1115.54/291.63 if(false, b, x, y) -> logZeroError [1] 1115.54/291.63 if(true, false, x, s(y)) -> y [1] 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) [1] 1115.54/291.63 1115.54/291.63 The TRS has the following type information: 1115.54/291.63 minus :: 0:s:logZeroError -> 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 0 :: 0:s:logZeroError 1115.54/291.63 s :: 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 quot :: 0:s:logZeroError -> 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 le :: 0:s:logZeroError -> 0:s:logZeroError -> true:false 1115.54/291.63 true :: true:false 1115.54/291.63 false :: true:false 1115.54/291.63 inc :: 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 log :: 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 logIter :: 0:s:logZeroError -> 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 if :: true:false -> true:false -> 0:s:logZeroError -> 0:s:logZeroError -> 0:s:logZeroError 1115.54/291.63 logZeroError :: 0:s:logZeroError 1115.54/291.63 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (5) CompletionProof (UPPER BOUND(ID)) 1115.54/291.63 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 1115.54/291.63 1115.54/291.63 minus(v0, v1) -> null_minus [0] 1115.54/291.63 quot(v0, v1) -> null_quot [0] 1115.54/291.63 le(v0, v1) -> null_le [0] 1115.54/291.63 inc(v0) -> null_inc [0] 1115.54/291.63 if(v0, v1, v2, v3) -> null_if [0] 1115.54/291.63 1115.54/291.63 And the following fresh constants: null_minus, null_quot, null_le, null_inc, null_if 1115.54/291.63 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (6) 1115.54/291.63 Obligation: 1115.54/291.63 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 1115.54/291.63 1115.54/291.63 Runtime Complexity Weighted TRS with Types. 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x [1] 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) [1] 1115.54/291.63 quot(0, s(y)) -> 0 [1] 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 1115.54/291.63 le(0, y) -> true [1] 1115.54/291.63 le(s(x), 0) -> false [1] 1115.54/291.63 le(s(x), s(y)) -> le(x, y) [1] 1115.54/291.63 inc(s(x)) -> s(inc(x)) [1] 1115.54/291.63 inc(0) -> s(0) [1] 1115.54/291.63 log(x) -> logIter(x, 0) [1] 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) [1] 1115.54/291.63 if(false, b, x, y) -> logZeroError [1] 1115.54/291.63 if(true, false, x, s(y)) -> y [1] 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) [1] 1115.54/291.63 minus(v0, v1) -> null_minus [0] 1115.54/291.63 quot(v0, v1) -> null_quot [0] 1115.54/291.63 le(v0, v1) -> null_le [0] 1115.54/291.63 inc(v0) -> null_inc [0] 1115.54/291.63 if(v0, v1, v2, v3) -> null_if [0] 1115.54/291.63 1115.54/291.63 The TRS has the following type information: 1115.54/291.63 minus :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 0 :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 s :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 quot :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 le :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> true:false:null_le 1115.54/291.63 true :: true:false:null_le 1115.54/291.63 false :: true:false:null_le 1115.54/291.63 inc :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 log :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 logIter :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 if :: true:false:null_le -> true:false:null_le -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if -> 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 logZeroError :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 null_minus :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 null_quot :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 null_le :: true:false:null_le 1115.54/291.63 null_inc :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 null_if :: 0:s:logZeroError:null_minus:null_quot:null_inc:null_if 1115.54/291.63 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) 1115.54/291.63 Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. 1115.54/291.63 The constant constructors are abstracted as follows: 1115.54/291.63 1115.54/291.63 0 => 0 1115.54/291.63 true => 2 1115.54/291.63 false => 1 1115.54/291.63 logZeroError => 1 1115.54/291.63 null_minus => 0 1115.54/291.63 null_quot => 0 1115.54/291.63 null_le => 0 1115.54/291.63 null_inc => 0 1115.54/291.63 null_if => 0 1115.54/291.63 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (8) 1115.54/291.63 Obligation: 1115.54/291.63 Complexity RNTS consisting of the following rules: 1115.54/291.63 1115.54/291.63 if(z, z', z'', z1) -{ 1 }-> y :|: z = 2, x >= 0, y >= 0, z'' = x, z1 = 1 + y, z' = 1 1115.54/291.63 if(z, z', z'', z1) -{ 1 }-> logIter(x, y) :|: z = 2, z1 = y, z' = 2, x >= 0, y >= 0, z'' = x 1115.54/291.63 if(z, z', z'', z1) -{ 1 }-> 1 :|: b >= 0, z1 = y, z = 1, x >= 0, y >= 0, z' = b, z'' = x 1115.54/291.63 if(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 1115.54/291.63 inc(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 1115.54/291.63 inc(z) -{ 1 }-> 1 + inc(x) :|: x >= 0, z = 1 + x 1115.54/291.63 inc(z) -{ 1 }-> 1 + 0 :|: z = 0 1115.54/291.63 le(z, z') -{ 1 }-> le(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1115.54/291.63 le(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y 1115.54/291.63 le(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 1115.54/291.63 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1115.54/291.63 log(z) -{ 1 }-> logIter(x, 0) :|: x >= 0, z = x 1115.54/291.63 logIter(z, z') -{ 1 }-> if(le(1 + 0, x), le(1 + (1 + 0), x), quot(x, 1 + (1 + 0)), inc(y)) :|: x >= 0, y >= 0, z = x, z' = y 1115.54/291.63 minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 1115.54/291.63 minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1115.54/291.63 minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1115.54/291.63 quot(z, z') -{ 1 }-> 0 :|: z' = 1 + y, y >= 0, z = 0 1115.54/291.63 quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1115.54/291.63 quot(z, z') -{ 1 }-> 1 + quot(minus(x, y), 1 + y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1115.54/291.63 1115.54/291.63 Only complete derivations are relevant for the runtime complexity. 1115.54/291.63 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (9) CompleteCoflocoProof (FINISHED) 1115.54/291.63 Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: 1115.54/291.63 1115.54/291.63 eq(start(V1, V, V16, V20),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[quot(V1, V, Out)],[V1 >= 0,V >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[le(V1, V, Out)],[V1 >= 0,V >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[inc(V1, Out)],[V1 >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[log(V1, Out)],[V1 >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[logIter(V1, V, Out)],[V1 >= 0,V >= 0]). 1115.54/291.63 eq(start(V1, V, V16, V20),0,[if(V1, V, V16, V20, Out)],[V1 >= 0,V >= 0,V16 >= 0,V20 >= 0]). 1115.54/291.63 eq(minus(V1, V, Out),1,[],[Out = V2,V2 >= 0,V1 = V2,V = 0]). 1115.54/291.63 eq(minus(V1, V, Out),1,[minus(V3, V4, Ret)],[Out = Ret,V = 1 + V4,V3 >= 0,V4 >= 0,V1 = 1 + V3]). 1115.54/291.63 eq(quot(V1, V, Out),1,[],[Out = 0,V = 1 + V5,V5 >= 0,V1 = 0]). 1115.54/291.63 eq(quot(V1, V, Out),1,[minus(V7, V6, Ret10),quot(Ret10, 1 + V6, Ret1)],[Out = 1 + Ret1,V = 1 + V6,V7 >= 0,V6 >= 0,V1 = 1 + V7]). 1115.54/291.63 eq(le(V1, V, Out),1,[],[Out = 2,V8 >= 0,V1 = 0,V = V8]). 1115.54/291.63 eq(le(V1, V, Out),1,[],[Out = 1,V9 >= 0,V1 = 1 + V9,V = 0]). 1115.54/291.63 eq(le(V1, V, Out),1,[le(V11, V10, Ret2)],[Out = Ret2,V = 1 + V10,V11 >= 0,V10 >= 0,V1 = 1 + V11]). 1115.54/291.63 eq(inc(V1, Out),1,[inc(V12, Ret11)],[Out = 1 + Ret11,V12 >= 0,V1 = 1 + V12]). 1115.54/291.63 eq(inc(V1, Out),1,[],[Out = 1,V1 = 0]). 1115.54/291.63 eq(log(V1, Out),1,[logIter(V13, 0, Ret3)],[Out = Ret3,V13 >= 0,V1 = V13]). 1115.54/291.63 eq(logIter(V1, V, Out),1,[le(1 + 0, V15, Ret0),le(1 + (1 + 0), V15, Ret12),quot(V15, 1 + (1 + 0), Ret21),inc(V14, Ret31),if(Ret0, Ret12, Ret21, Ret31, Ret4)],[Out = Ret4,V15 >= 0,V14 >= 0,V1 = V15,V = V14]). 1115.54/291.63 eq(if(V1, V, V16, V20, Out),1,[],[Out = 1,V19 >= 0,V20 = V18,V1 = 1,V17 >= 0,V18 >= 0,V = V19,V16 = V17]). 1115.54/291.63 eq(if(V1, V, V16, V20, Out),1,[],[Out = V21,V1 = 2,V22 >= 0,V21 >= 0,V16 = V22,V20 = 1 + V21,V = 1]). 1115.54/291.63 eq(if(V1, V, V16, V20, Out),1,[logIter(V24, V23, Ret5)],[Out = Ret5,V1 = 2,V20 = V23,V = 2,V24 >= 0,V23 >= 0,V16 = V24]). 1115.54/291.63 eq(minus(V1, V, Out),0,[],[Out = 0,V26 >= 0,V25 >= 0,V1 = V26,V = V25]). 1115.54/291.63 eq(quot(V1, V, Out),0,[],[Out = 0,V28 >= 0,V27 >= 0,V1 = V28,V = V27]). 1115.54/291.63 eq(le(V1, V, Out),0,[],[Out = 0,V30 >= 0,V29 >= 0,V1 = V30,V = V29]). 1115.54/291.63 eq(inc(V1, Out),0,[],[Out = 0,V31 >= 0,V1 = V31]). 1115.54/291.63 eq(if(V1, V, V16, V20, Out),0,[],[Out = 0,V20 = V34,V32 >= 0,V16 = V35,V33 >= 0,V1 = V32,V = V33,V35 >= 0,V34 >= 0]). 1115.54/291.63 input_output_vars(minus(V1,V,Out),[V1,V],[Out]). 1115.54/291.63 input_output_vars(quot(V1,V,Out),[V1,V],[Out]). 1115.54/291.63 input_output_vars(le(V1,V,Out),[V1,V],[Out]). 1115.54/291.63 input_output_vars(inc(V1,Out),[V1],[Out]). 1115.54/291.63 input_output_vars(log(V1,Out),[V1],[Out]). 1115.54/291.63 input_output_vars(logIter(V1,V,Out),[V1,V],[Out]). 1115.54/291.63 input_output_vars(if(V1,V,V16,V20,Out),[V1,V,V16,V20],[Out]). 1115.54/291.63 1115.54/291.63 1115.54/291.63 CoFloCo proof output: 1115.54/291.63 Preprocessing Cost Relations 1115.54/291.63 ===================================== 1115.54/291.63 1115.54/291.63 #### Computed strongly connected components 1115.54/291.63 0. recursive : [inc/2] 1115.54/291.63 1. recursive : [le/3] 1115.54/291.63 2. recursive : [minus/3] 1115.54/291.63 3. recursive : [quot/3] 1115.54/291.63 4. recursive : [if/5,logIter/3] 1115.54/291.63 5. non_recursive : [log/2] 1115.54/291.63 6. non_recursive : [start/4] 1115.54/291.63 1115.54/291.63 #### Obtained direct recursion through partial evaluation 1115.54/291.63 0. SCC is partially evaluated into inc/2 1115.54/291.63 1. SCC is partially evaluated into le/3 1115.54/291.63 2. SCC is partially evaluated into minus/3 1115.54/291.63 3. SCC is partially evaluated into quot/3 1115.54/291.63 4. SCC is partially evaluated into logIter/3 1115.54/291.63 5. SCC is completely evaluated into other SCCs 1115.54/291.63 6. SCC is partially evaluated into start/4 1115.54/291.63 1115.54/291.63 Control-Flow Refinement of Cost Relations 1115.54/291.63 ===================================== 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations inc/2 1115.54/291.63 * CE 27 is refined into CE [28] 1115.54/291.63 * CE 26 is refined into CE [29] 1115.54/291.63 * CE 25 is refined into CE [30] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of inc/2 1115.54/291.63 * CEs [30] --> Loop 19 1115.54/291.63 * CEs [28] --> Loop 20 1115.54/291.63 * CEs [29] --> Loop 21 1115.54/291.63 1115.54/291.63 ### Ranking functions of CR inc(V1,Out) 1115.54/291.63 * RF of phase [19]: [V1] 1115.54/291.63 1115.54/291.63 #### Partial ranking functions of CR inc(V1,Out) 1115.54/291.63 * Partial RF of phase [19]: 1115.54/291.63 - RF of loop [19:1]: 1115.54/291.63 V1 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations le/3 1115.54/291.63 * CE 24 is refined into CE [31] 1115.54/291.63 * CE 22 is refined into CE [32] 1115.54/291.63 * CE 21 is refined into CE [33] 1115.54/291.63 * CE 23 is refined into CE [34] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of le/3 1115.54/291.63 * CEs [34] --> Loop 22 1115.54/291.63 * CEs [31] --> Loop 23 1115.54/291.63 * CEs [32] --> Loop 24 1115.54/291.63 * CEs [33] --> Loop 25 1115.54/291.63 1115.54/291.63 ### Ranking functions of CR le(V1,V,Out) 1115.54/291.63 * RF of phase [22]: [V,V1] 1115.54/291.63 1115.54/291.63 #### Partial ranking functions of CR le(V1,V,Out) 1115.54/291.63 * Partial RF of phase [22]: 1115.54/291.63 - RF of loop [22:1]: 1115.54/291.63 V 1115.54/291.63 V1 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations minus/3 1115.54/291.63 * CE 17 is refined into CE [35] 1115.54/291.63 * CE 15 is refined into CE [36] 1115.54/291.63 * CE 16 is refined into CE [37] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of minus/3 1115.54/291.63 * CEs [37] --> Loop 26 1115.54/291.63 * CEs [35] --> Loop 27 1115.54/291.63 * CEs [36] --> Loop 28 1115.54/291.63 1115.54/291.63 ### Ranking functions of CR minus(V1,V,Out) 1115.54/291.63 * RF of phase [26]: [V,V1] 1115.54/291.63 1115.54/291.63 #### Partial ranking functions of CR minus(V1,V,Out) 1115.54/291.63 * Partial RF of phase [26]: 1115.54/291.63 - RF of loop [26:1]: 1115.54/291.63 V 1115.54/291.63 V1 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations quot/3 1115.54/291.63 * CE 18 is refined into CE [38] 1115.54/291.63 * CE 20 is refined into CE [39] 1115.54/291.63 * CE 19 is refined into CE [40,41,42] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of quot/3 1115.54/291.63 * CEs [42] --> Loop 29 1115.54/291.63 * CEs [41] --> Loop 30 1115.54/291.63 * CEs [40] --> Loop 31 1115.54/291.63 * CEs [38,39] --> Loop 32 1115.54/291.63 1115.54/291.63 ### Ranking functions of CR quot(V1,V,Out) 1115.54/291.63 * RF of phase [29]: [V1-1,V1-V+1] 1115.54/291.63 * RF of phase [31]: [V1] 1115.54/291.63 1115.54/291.63 #### Partial ranking functions of CR quot(V1,V,Out) 1115.54/291.63 * Partial RF of phase [29]: 1115.54/291.63 - RF of loop [29:1]: 1115.54/291.63 V1-1 1115.54/291.63 V1-V+1 1115.54/291.63 * Partial RF of phase [31]: 1115.54/291.63 - RF of loop [31:1]: 1115.54/291.63 V1 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations logIter/3 1115.54/291.63 * CE 14 is refined into CE [43,44,45,46,47,48,49,50] 1115.54/291.63 * CE 11 is refined into CE [51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142] 1115.54/291.63 * CE 13 is refined into CE [143,144,145,146,147,148] 1115.54/291.63 * CE 12 is refined into CE [149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of logIter/3 1115.54/291.63 * CEs [164] --> Loop 33 1115.54/291.63 * CEs [163] --> Loop 34 1115.54/291.63 * CEs [162] --> Loop 35 1115.54/291.63 * CEs [156,160] --> Loop 36 1115.54/291.63 * CEs [155,159] --> Loop 37 1115.54/291.63 * CEs [154,158] --> Loop 38 1115.54/291.63 * CEs [152] --> Loop 39 1115.54/291.63 * CEs [151] --> Loop 40 1115.54/291.63 * CEs [150] --> Loop 41 1115.54/291.63 * CEs [161] --> Loop 42 1115.54/291.63 * CEs [153,157] --> Loop 43 1115.54/291.63 * CEs [149] --> Loop 44 1115.54/291.63 * CEs [63,67,71,75,87,91,95,99,103,107,111,115,127,131,135,139] --> Loop 45 1115.54/291.63 * CEs [145,148] --> Loop 46 1115.54/291.63 * CEs [144,147] --> Loop 47 1115.54/291.63 * CEs [79,80,81,82,83,84,85,86,119,120,121,122,123,124,125,126,143,146] --> Loop 48 1115.54/291.63 * CEs [43,44,45,46,47,48,49,50] --> Loop 49 1115.54/291.63 * CEs [51,52,53,54,55,56,57,58,59,60,61,62,64,65,66,68,69,70,72,73,74,76,77,78,88,89,90,92,93,94,96,97,98,100,101,102,104,105,106,108,109,110,112,113,114,116,117,118,128,129,130,132,133,134,136,137,138,140,141,142] --> Loop 50 1115.54/291.63 1115.54/291.63 ### Ranking functions of CR logIter(V1,V,Out) 1115.54/291.63 * RF of phase [33,34,35,36,37,38,42,43]: [V1-1] 1115.54/291.63 1115.54/291.63 #### Partial ranking functions of CR logIter(V1,V,Out) 1115.54/291.63 * Partial RF of phase [33,34,35,36,37,38,42,43]: 1115.54/291.63 - RF of loop [33:1,34:1,35:1,42:1]: 1115.54/291.63 V1-2 1115.54/291.63 - RF of loop [36:1,37:1,38:1,43:1]: 1115.54/291.63 V1-1 1115.54/291.63 - RF of loop [42:1,43:1]: 1115.54/291.63 -V+1 depends on loops [33:1,35:1,36:1,38:1] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Specialization of cost equations start/4 1115.54/291.63 * CE 2 is refined into CE [165,166,167,168,169,170,171] 1115.54/291.63 * CE 3 is refined into CE [172] 1115.54/291.63 * CE 1 is refined into CE [173] 1115.54/291.63 * CE 4 is refined into CE [174] 1115.54/291.63 * CE 5 is refined into CE [175,176,177] 1115.54/291.63 * CE 6 is refined into CE [178,179,180,181,182] 1115.54/291.63 * CE 7 is refined into CE [183,184,185,186,187] 1115.54/291.63 * CE 8 is refined into CE [188,189,190,191] 1115.54/291.63 * CE 9 is refined into CE [192,193,194,195,196] 1115.54/291.63 * CE 10 is refined into CE [197,198,199,200,201,202,203] 1115.54/291.63 1115.54/291.63 1115.54/291.63 ### Cost equations --> "Loop" of start/4 1115.54/291.63 * CEs [175,184,201] --> Loop 51 1115.54/291.63 * CEs [169] --> Loop 52 1115.54/291.63 * CEs [167,168] --> Loop 53 1115.54/291.63 * CEs [165,166,170,171] --> Loop 54 1115.54/291.63 * CEs [172,178] --> Loop 55 1115.54/291.63 * CEs [199,200] --> Loop 56 1115.54/291.63 * CEs [174] --> Loop 57 1115.54/291.63 * CEs [173,176,177,179,180,181,182,183,185,186,187,188,189,190,191,192,193,194,195,196,197,198,202,203] --> Loop 58 1115.54/291.64 1115.54/291.64 ### Ranking functions of CR start(V1,V,V16,V20) 1115.54/291.64 1115.54/291.64 #### Partial ranking functions of CR start(V1,V,V16,V20) 1115.54/291.64 1115.54/291.64 1115.54/291.64 Computing Bounds 1115.54/291.64 ===================================== 1115.54/291.64 1115.54/291.64 #### Cost of chains of inc(V1,Out): 1115.54/291.64 * Chain [[19],21]: 1*it(19)+1 1115.54/291.64 Such that:it(19) =< Out 1115.54/291.64 1115.54/291.64 with precondition: [V1+1=Out,V1>=1] 1115.54/291.64 1115.54/291.64 * Chain [[19],20]: 1*it(19)+0 1115.54/291.64 Such that:it(19) =< Out 1115.54/291.64 1115.54/291.64 with precondition: [Out>=1,V1>=Out] 1115.54/291.64 1115.54/291.64 * Chain [21]: 1 1115.54/291.64 with precondition: [V1=0,Out=1] 1115.54/291.64 1115.54/291.64 * Chain [20]: 0 1115.54/291.64 with precondition: [Out=0,V1>=0] 1115.54/291.64 1115.54/291.64 1115.54/291.64 #### Cost of chains of le(V1,V,Out): 1115.54/291.64 * Chain [[22],25]: 1*it(22)+1 1115.54/291.64 Such that:it(22) =< V1 1115.54/291.64 1115.54/291.64 with precondition: [Out=2,V1>=1,V>=V1] 1115.54/291.64 1115.54/291.64 * Chain [[22],24]: 1*it(22)+1 1115.54/291.64 Such that:it(22) =< V 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V>=1,V1>=V+1] 1115.54/291.64 1115.54/291.64 * Chain [[22],23]: 1*it(22)+0 1115.54/291.64 Such that:it(22) =< V 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=1,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [25]: 1 1115.54/291.64 with precondition: [V1=0,Out=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [24]: 1 1115.54/291.64 with precondition: [V=0,Out=1,V1>=1] 1115.54/291.64 1115.54/291.64 * Chain [23]: 0 1115.54/291.64 with precondition: [Out=0,V1>=0,V>=0] 1115.54/291.64 1115.54/291.64 1115.54/291.64 #### Cost of chains of minus(V1,V,Out): 1115.54/291.64 * Chain [[26],28]: 1*it(26)+1 1115.54/291.64 Such that:it(26) =< V 1115.54/291.64 1115.54/291.64 with precondition: [V1=Out+V,V>=1,V1>=V] 1115.54/291.64 1115.54/291.64 * Chain [[26],27]: 1*it(26)+0 1115.54/291.64 Such that:it(26) =< V 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=1,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [28]: 1 1115.54/291.64 with precondition: [V=0,V1=Out,V1>=0] 1115.54/291.64 1115.54/291.64 * Chain [27]: 0 1115.54/291.64 with precondition: [Out=0,V1>=0,V>=0] 1115.54/291.64 1115.54/291.64 1115.54/291.64 #### Cost of chains of quot(V1,V,Out): 1115.54/291.64 * Chain [[31],32]: 2*it(31)+1 1115.54/291.64 Such that:it(31) =< Out 1115.54/291.64 1115.54/291.64 with precondition: [V=1,Out>=1,V1>=Out] 1115.54/291.64 1115.54/291.64 * Chain [[31],30,32]: 2*it(31)+1*s(3)+2 1115.54/291.64 Such that:s(3) =< 1 1115.54/291.64 it(31) =< Out 1115.54/291.64 1115.54/291.64 with precondition: [V=1,Out>=2,V1>=Out] 1115.54/291.64 1115.54/291.64 * Chain [[29],32]: 2*it(29)+1*s(6)+1 1115.54/291.64 Such that:it(29) =< V1-V+1 1115.54/291.64 aux(3) =< V1 1115.54/291.64 it(29) =< aux(3) 1115.54/291.64 s(6) =< aux(3) 1115.54/291.64 1115.54/291.64 with precondition: [V>=2,Out>=1,V1+2>=2*Out+V] 1115.54/291.64 1115.54/291.64 * Chain [[29],30,32]: 2*it(29)+1*s(3)+1*s(6)+2 1115.54/291.64 Such that:it(29) =< V1-V+1 1115.54/291.64 s(3) =< V 1115.54/291.64 aux(4) =< V1 1115.54/291.64 it(29) =< aux(4) 1115.54/291.64 s(6) =< aux(4) 1115.54/291.64 1115.54/291.64 with precondition: [V>=2,Out>=2,V1+3>=2*Out+V] 1115.54/291.64 1115.54/291.64 * Chain [32]: 1 1115.54/291.64 with precondition: [Out=0,V1>=0,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [30,32]: 1*s(3)+2 1115.54/291.64 Such that:s(3) =< V 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=1,V>=1] 1115.54/291.64 1115.54/291.64 1115.54/291.64 #### Cost of chains of logIter(V1,V,Out): 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],50]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+19*s(10)+142*s(11)+48*s(34)+24*s(136)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+6 1115.54/291.64 Such that:aux(48) =< 1 1115.54/291.64 aux(49) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(52) =< 2*V1+2*V+2 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(125) =< V1 1115.54/291.64 aux(126) =< 2*V1 1115.54/291.64 aux(127) =< 2*V1+2*V 1115.54/291.64 aux(128) =< 3*V1 1115.54/291.64 s(136) =< aux(48) 1115.54/291.64 s(34) =< aux(49) 1115.54/291.64 s(11) =< aux(127) 1115.54/291.64 s(10) =< aux(52) 1115.54/291.64 aux(105) =< aux(125) 1115.54/291.64 it(33) =< aux(125) 1115.54/291.64 it(35) =< aux(125) 1115.54/291.64 it(37) =< aux(125) 1115.54/291.64 it(38) =< aux(125) 1115.54/291.64 it(42) =< aux(125) 1115.54/291.64 it(43) =< aux(125) 1115.54/291.64 s(409) =< aux(125) 1115.54/291.64 aux(110) =< aux(126) 1115.54/291.64 it(38) =< aux(126) 1115.54/291.64 it(42) =< aux(126) 1115.54/291.64 it(43) =< aux(126) 1115.54/291.64 aux(108) =< aux(127) 1115.54/291.64 aux(110) =< aux(127) 1115.54/291.64 it(38) =< aux(127) 1115.54/291.64 s(409) =< aux(126) 1115.54/291.64 aux(108) =< aux(128) 1115.54/291.64 aux(110) =< aux(128) 1115.54/291.64 it(35) =< aux(128) 1115.54/291.64 it(42) =< aux(128) 1115.54/291.64 s(409) =< aux(128) 1115.54/291.64 it(37) =< aux(128) 1115.54/291.64 it(38) =< aux(128) 1115.54/291.64 it(43) =< aux(128) 1115.54/291.64 aux(112) =< aux(125) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(127)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(127)+aux(111) 1115.54/291.64 s(365) =< aux(125)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(125) 1115.54/291.64 aux(105) =< aux(125)+aux(125)+aux(124) 1115.54/291.64 it(42) =< aux(125)+aux(125)+aux(124) 1115.54/291.64 s(409) =< aux(125)+aux(125)+aux(124) 1115.54/291.64 it(43) =< aux(125)+aux(125)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(126) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(128) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],48]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+11*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+36*s(410)+9*s(422)+7 1115.54/291.64 Such that:aux(147) =< 1 1115.54/291.64 aux(148) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(151) =< V1 1115.54/291.64 aux(152) =< 2*V1 1115.54/291.64 aux(153) =< 2*V1+2*V 1115.54/291.64 aux(154) =< 3*V1 1115.54/291.64 s(422) =< aux(148) 1115.54/291.64 s(380) =< aux(153) 1115.54/291.64 s(410) =< aux(147) 1115.54/291.64 aux(105) =< aux(151) 1115.54/291.64 it(33) =< aux(151) 1115.54/291.64 it(35) =< aux(151) 1115.54/291.64 it(37) =< aux(151) 1115.54/291.64 it(38) =< aux(151) 1115.54/291.64 it(42) =< aux(151) 1115.54/291.64 it(43) =< aux(151) 1115.54/291.64 s(409) =< aux(151) 1115.54/291.64 aux(110) =< aux(152) 1115.54/291.64 it(38) =< aux(152) 1115.54/291.64 it(42) =< aux(152) 1115.54/291.64 it(43) =< aux(152) 1115.54/291.64 aux(108) =< aux(153) 1115.54/291.64 aux(110) =< aux(153) 1115.54/291.64 it(38) =< aux(153) 1115.54/291.64 s(409) =< aux(152) 1115.54/291.64 aux(108) =< aux(154) 1115.54/291.64 aux(110) =< aux(154) 1115.54/291.64 it(35) =< aux(154) 1115.54/291.64 it(42) =< aux(154) 1115.54/291.64 s(409) =< aux(154) 1115.54/291.64 it(37) =< aux(154) 1115.54/291.64 it(38) =< aux(154) 1115.54/291.64 it(43) =< aux(154) 1115.54/291.64 aux(112) =< aux(151) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(153)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(153)+aux(111) 1115.54/291.64 s(365) =< aux(151)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(151) 1115.54/291.64 aux(105) =< aux(151)+aux(151)+aux(124) 1115.54/291.64 it(42) =< aux(151)+aux(151)+aux(124) 1115.54/291.64 s(409) =< aux(151)+aux(151)+aux(124) 1115.54/291.64 it(43) =< aux(151)+aux(151)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(152) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(154) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],47]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+4*s(463)+2*s(465)+1*s(468)+7 1115.54/291.64 Such that:aux(157) =< 1 1115.54/291.64 s(468) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(119) =< 2*V1+2*V 1115.54/291.64 aux(120) =< 2*V1+2*V-2*Out 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(82) =< 3*V1+4*V-4*Out 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(158) =< Out+1 1115.54/291.64 aux(159) =< V1 1115.54/291.64 aux(160) =< 2*V1 1115.54/291.64 aux(161) =< 3*V1 1115.54/291.64 s(465) =< aux(158) 1115.54/291.64 s(463) =< aux(157) 1115.54/291.64 aux(105) =< aux(159) 1115.54/291.64 it(33) =< aux(159) 1115.54/291.64 it(35) =< aux(159) 1115.54/291.64 it(37) =< aux(159) 1115.54/291.64 it(38) =< aux(159) 1115.54/291.64 it(42) =< aux(159) 1115.54/291.64 it(43) =< aux(159) 1115.54/291.64 s(409) =< aux(159) 1115.54/291.64 aux(110) =< aux(160) 1115.54/291.64 it(38) =< aux(160) 1115.54/291.64 it(42) =< aux(160) 1115.54/291.64 it(43) =< aux(160) 1115.54/291.64 aux(107) =< aux(119) 1115.54/291.64 aux(108) =< aux(119) 1115.54/291.64 aux(110) =< aux(119) 1115.54/291.64 it(38) =< aux(119) 1115.54/291.64 aux(107) =< aux(120) 1115.54/291.64 aux(108) =< aux(120) 1115.54/291.64 aux(110) =< aux(120) 1115.54/291.64 it(38) =< aux(120) 1115.54/291.64 s(409) =< aux(160) 1115.54/291.64 aux(108) =< aux(161) 1115.54/291.64 aux(110) =< aux(161) 1115.54/291.64 it(35) =< aux(161) 1115.54/291.64 it(42) =< aux(161) 1115.54/291.64 s(409) =< aux(161) 1115.54/291.64 it(37) =< aux(161) 1115.54/291.64 it(38) =< aux(161) 1115.54/291.64 it(43) =< aux(161) 1115.54/291.64 aux(112) =< aux(159) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(107)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(107)+aux(111) 1115.54/291.64 s(365) =< aux(159)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(159) 1115.54/291.64 aux(105) =< aux(159)+aux(159)+aux(124) 1115.54/291.64 it(42) =< aux(159)+aux(159)+aux(124) 1115.54/291.64 s(409) =< aux(159)+aux(159)+aux(124) 1115.54/291.64 it(43) =< aux(159)+aux(159)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(160) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(107) 1115.54/291.64 s(368) =< aux(161) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [V1>=2,V>=0,Out>=1,V+V1>=Out+1] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],46]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+5*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+4*s(470)+1*s(475)+6 1115.54/291.64 Such that:aux(164) =< 1 1115.54/291.64 s(475) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(82) =< 3*V1+4*V-4*Out 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(166) =< V1 1115.54/291.64 aux(167) =< 2*V1 1115.54/291.64 aux(168) =< 2*V1+2*V 1115.54/291.64 aux(169) =< 3*V1 1115.54/291.64 s(380) =< aux(168) 1115.54/291.64 s(470) =< aux(164) 1115.54/291.64 aux(105) =< aux(166) 1115.54/291.64 it(33) =< aux(166) 1115.54/291.64 it(35) =< aux(166) 1115.54/291.64 it(37) =< aux(166) 1115.54/291.64 it(38) =< aux(166) 1115.54/291.64 it(42) =< aux(166) 1115.54/291.64 it(43) =< aux(166) 1115.54/291.64 s(409) =< aux(166) 1115.54/291.64 aux(110) =< aux(167) 1115.54/291.64 it(38) =< aux(167) 1115.54/291.64 it(42) =< aux(167) 1115.54/291.64 it(43) =< aux(167) 1115.54/291.64 aux(108) =< aux(168) 1115.54/291.64 aux(110) =< aux(168) 1115.54/291.64 it(38) =< aux(168) 1115.54/291.64 s(409) =< aux(167) 1115.54/291.64 aux(108) =< aux(169) 1115.54/291.64 aux(110) =< aux(169) 1115.54/291.64 it(35) =< aux(169) 1115.54/291.64 it(42) =< aux(169) 1115.54/291.64 s(409) =< aux(169) 1115.54/291.64 it(37) =< aux(169) 1115.54/291.64 it(38) =< aux(169) 1115.54/291.64 it(43) =< aux(169) 1115.54/291.64 aux(112) =< aux(166) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(168)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(168)+aux(111) 1115.54/291.64 s(365) =< aux(166)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(166) 1115.54/291.64 aux(105) =< aux(166)+aux(166)+aux(124) 1115.54/291.64 it(42) =< aux(166)+aux(166)+aux(124) 1115.54/291.64 s(409) =< aux(166)+aux(166)+aux(124) 1115.54/291.64 it(43) =< aux(166)+aux(166)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(167) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(169) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [V1>=2,V>=0,Out>=0,V+V1>=Out+2] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],45]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+46*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+16*s(481)+8*s(509)+6 1115.54/291.64 Such that:aux(184) =< 1 1115.54/291.64 aux(185) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(187) =< V1 1115.54/291.64 aux(188) =< 2*V1 1115.54/291.64 aux(189) =< 2*V1+2*V 1115.54/291.64 aux(190) =< 3*V1 1115.54/291.64 s(509) =< aux(184) 1115.54/291.64 s(481) =< aux(185) 1115.54/291.64 s(368) =< aux(190) 1115.54/291.64 aux(105) =< aux(187) 1115.54/291.64 it(33) =< aux(187) 1115.54/291.64 it(35) =< aux(187) 1115.54/291.64 it(37) =< aux(187) 1115.54/291.64 it(38) =< aux(187) 1115.54/291.64 it(42) =< aux(187) 1115.54/291.64 it(43) =< aux(187) 1115.54/291.64 s(409) =< aux(187) 1115.54/291.64 aux(110) =< aux(188) 1115.54/291.64 it(38) =< aux(188) 1115.54/291.64 it(42) =< aux(188) 1115.54/291.64 it(43) =< aux(188) 1115.54/291.64 aux(108) =< aux(189) 1115.54/291.64 aux(110) =< aux(189) 1115.54/291.64 it(38) =< aux(189) 1115.54/291.64 s(409) =< aux(188) 1115.54/291.64 aux(108) =< aux(190) 1115.54/291.64 aux(110) =< aux(190) 1115.54/291.64 it(35) =< aux(190) 1115.54/291.64 it(42) =< aux(190) 1115.54/291.64 s(409) =< aux(190) 1115.54/291.64 it(37) =< aux(190) 1115.54/291.64 it(38) =< aux(190) 1115.54/291.64 it(43) =< aux(190) 1115.54/291.64 aux(112) =< aux(187) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(189)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(189)+aux(111) 1115.54/291.64 s(365) =< aux(187)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(187) 1115.54/291.64 aux(105) =< aux(187)+aux(187)+aux(124) 1115.54/291.64 it(42) =< aux(187)+aux(187)+aux(124) 1115.54/291.64 s(409) =< aux(187)+aux(187)+aux(124) 1115.54/291.64 it(43) =< aux(187)+aux(187)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(188) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(189) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],44,50]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+68*s(10)+44*s(11)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+12 1115.54/291.64 Such that:aux(191) =< 1 1115.54/291.64 aux(192) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(193) =< V1 1115.54/291.64 aux(194) =< 2*V1 1115.54/291.64 aux(195) =< 2*V1+2*V 1115.54/291.64 aux(196) =< 3*V1 1115.54/291.64 s(11) =< aux(191) 1115.54/291.64 s(10) =< aux(192) 1115.54/291.64 aux(105) =< aux(193) 1115.54/291.64 it(33) =< aux(193) 1115.54/291.64 it(35) =< aux(193) 1115.54/291.64 it(37) =< aux(193) 1115.54/291.64 it(38) =< aux(193) 1115.54/291.64 it(42) =< aux(193) 1115.54/291.64 it(43) =< aux(193) 1115.54/291.64 s(409) =< aux(193) 1115.54/291.64 aux(110) =< aux(194) 1115.54/291.64 it(38) =< aux(194) 1115.54/291.64 it(42) =< aux(194) 1115.54/291.64 it(43) =< aux(194) 1115.54/291.64 aux(108) =< aux(195) 1115.54/291.64 aux(110) =< aux(195) 1115.54/291.64 it(38) =< aux(195) 1115.54/291.64 s(409) =< aux(194) 1115.54/291.64 aux(108) =< aux(196) 1115.54/291.64 aux(110) =< aux(196) 1115.54/291.64 it(35) =< aux(196) 1115.54/291.64 it(42) =< aux(196) 1115.54/291.64 s(409) =< aux(196) 1115.54/291.64 it(37) =< aux(196) 1115.54/291.64 it(38) =< aux(196) 1115.54/291.64 it(43) =< aux(196) 1115.54/291.64 aux(112) =< aux(193) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(195)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(195)+aux(111) 1115.54/291.64 s(365) =< aux(193)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(193) 1115.54/291.64 aux(105) =< aux(193)+aux(193)+aux(124) 1115.54/291.64 it(42) =< aux(193)+aux(193)+aux(124) 1115.54/291.64 s(409) =< aux(193)+aux(193)+aux(124) 1115.54/291.64 it(43) =< aux(193)+aux(193)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(194) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(195) 1115.54/291.64 s(368) =< aux(196) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],44,49]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+3*s(541)+3*s(542)+12 1115.54/291.64 Such that:aux(199) =< 1 1115.54/291.64 aux(200) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(201) =< V1 1115.54/291.64 aux(202) =< 2*V1 1115.54/291.64 aux(203) =< 2*V1+2*V 1115.54/291.64 aux(204) =< 3*V1 1115.54/291.64 s(541) =< aux(199) 1115.54/291.64 s(542) =< aux(200) 1115.54/291.64 aux(105) =< aux(201) 1115.54/291.64 it(33) =< aux(201) 1115.54/291.64 it(35) =< aux(201) 1115.54/291.64 it(37) =< aux(201) 1115.54/291.64 it(38) =< aux(201) 1115.54/291.64 it(42) =< aux(201) 1115.54/291.64 it(43) =< aux(201) 1115.54/291.64 s(409) =< aux(201) 1115.54/291.64 aux(110) =< aux(202) 1115.54/291.64 it(38) =< aux(202) 1115.54/291.64 it(42) =< aux(202) 1115.54/291.64 it(43) =< aux(202) 1115.54/291.64 aux(108) =< aux(203) 1115.54/291.64 aux(110) =< aux(203) 1115.54/291.64 it(38) =< aux(203) 1115.54/291.64 s(409) =< aux(202) 1115.54/291.64 aux(108) =< aux(204) 1115.54/291.64 aux(110) =< aux(204) 1115.54/291.64 it(35) =< aux(204) 1115.54/291.64 it(42) =< aux(204) 1115.54/291.64 s(409) =< aux(204) 1115.54/291.64 it(37) =< aux(204) 1115.54/291.64 it(38) =< aux(204) 1115.54/291.64 it(43) =< aux(204) 1115.54/291.64 aux(112) =< aux(201) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(203)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(203)+aux(111) 1115.54/291.64 s(365) =< aux(201)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(201) 1115.54/291.64 aux(105) =< aux(201)+aux(201)+aux(124) 1115.54/291.64 it(42) =< aux(201)+aux(201)+aux(124) 1115.54/291.64 s(409) =< aux(201)+aux(201)+aux(124) 1115.54/291.64 it(43) =< aux(201)+aux(201)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(202) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(203) 1115.54/291.64 s(368) =< aux(204) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],41,50]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+44*s(10)+49*s(34)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+11 1115.54/291.64 Such that:aux(206) =< 1 1115.54/291.64 aux(207) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(208) =< V1 1115.54/291.64 aux(209) =< 2*V1 1115.54/291.64 aux(210) =< 2*V1+2*V 1115.54/291.64 aux(211) =< 3*V1 1115.54/291.64 s(10) =< aux(206) 1115.54/291.64 s(34) =< aux(207) 1115.54/291.64 aux(105) =< aux(208) 1115.54/291.64 it(33) =< aux(208) 1115.54/291.64 it(35) =< aux(208) 1115.54/291.64 it(37) =< aux(208) 1115.54/291.64 it(38) =< aux(208) 1115.54/291.64 it(42) =< aux(208) 1115.54/291.64 it(43) =< aux(208) 1115.54/291.64 s(409) =< aux(208) 1115.54/291.64 aux(110) =< aux(209) 1115.54/291.64 it(38) =< aux(209) 1115.54/291.64 it(42) =< aux(209) 1115.54/291.64 it(43) =< aux(209) 1115.54/291.64 aux(108) =< aux(210) 1115.54/291.64 aux(110) =< aux(210) 1115.54/291.64 it(38) =< aux(210) 1115.54/291.64 s(409) =< aux(209) 1115.54/291.64 aux(108) =< aux(211) 1115.54/291.64 aux(110) =< aux(211) 1115.54/291.64 it(35) =< aux(211) 1115.54/291.64 it(42) =< aux(211) 1115.54/291.64 s(409) =< aux(211) 1115.54/291.64 it(37) =< aux(211) 1115.54/291.64 it(38) =< aux(211) 1115.54/291.64 it(43) =< aux(211) 1115.54/291.64 aux(112) =< aux(208) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(210)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(210)+aux(111) 1115.54/291.64 s(365) =< aux(208)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(208) 1115.54/291.64 aux(105) =< aux(208)+aux(208)+aux(124) 1115.54/291.64 it(42) =< aux(208)+aux(208)+aux(124) 1115.54/291.64 s(409) =< aux(208)+aux(208)+aux(124) 1115.54/291.64 it(43) =< aux(208)+aux(208)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(209) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(210) 1115.54/291.64 s(368) =< aux(211) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],41,49]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+3*s(543)+1*s(552)+11 1115.54/291.64 Such that:aux(212) =< 1 1115.54/291.64 s(552) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(213) =< V1 1115.54/291.64 aux(214) =< 2*V1 1115.54/291.64 aux(215) =< 2*V1+2*V 1115.54/291.64 aux(216) =< 3*V1 1115.54/291.64 s(543) =< aux(212) 1115.54/291.64 aux(105) =< aux(213) 1115.54/291.64 it(33) =< aux(213) 1115.54/291.64 it(35) =< aux(213) 1115.54/291.64 it(37) =< aux(213) 1115.54/291.64 it(38) =< aux(213) 1115.54/291.64 it(42) =< aux(213) 1115.54/291.64 it(43) =< aux(213) 1115.54/291.64 s(409) =< aux(213) 1115.54/291.64 aux(110) =< aux(214) 1115.54/291.64 it(38) =< aux(214) 1115.54/291.64 it(42) =< aux(214) 1115.54/291.64 it(43) =< aux(214) 1115.54/291.64 aux(108) =< aux(215) 1115.54/291.64 aux(110) =< aux(215) 1115.54/291.64 it(38) =< aux(215) 1115.54/291.64 s(409) =< aux(214) 1115.54/291.64 aux(108) =< aux(216) 1115.54/291.64 aux(110) =< aux(216) 1115.54/291.64 it(35) =< aux(216) 1115.54/291.64 it(42) =< aux(216) 1115.54/291.64 s(409) =< aux(216) 1115.54/291.64 it(37) =< aux(216) 1115.54/291.64 it(38) =< aux(216) 1115.54/291.64 it(43) =< aux(216) 1115.54/291.64 aux(112) =< aux(213) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(215)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(215)+aux(111) 1115.54/291.64 s(365) =< aux(213)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(213) 1115.54/291.64 aux(105) =< aux(213)+aux(213)+aux(124) 1115.54/291.64 it(42) =< aux(213)+aux(213)+aux(124) 1115.54/291.64 s(409) =< aux(213)+aux(213)+aux(124) 1115.54/291.64 it(43) =< aux(213)+aux(213)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(214) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(215) 1115.54/291.64 s(368) =< aux(216) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],41,45]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+3*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+17*s(481)+9*s(509)+11 1115.54/291.64 Such that:aux(217) =< 1 1115.54/291.64 aux(218) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(219) =< V1 1115.54/291.64 aux(220) =< 2*V1 1115.54/291.64 aux(221) =< 2*V1+2*V 1115.54/291.64 aux(222) =< 3*V1 1115.54/291.64 s(509) =< aux(217) 1115.54/291.64 s(481) =< aux(218) 1115.54/291.64 aux(105) =< aux(219) 1115.54/291.64 it(33) =< aux(219) 1115.54/291.64 it(35) =< aux(219) 1115.54/291.64 it(37) =< aux(219) 1115.54/291.64 it(38) =< aux(219) 1115.54/291.64 it(42) =< aux(219) 1115.54/291.64 it(43) =< aux(219) 1115.54/291.64 s(409) =< aux(219) 1115.54/291.64 aux(110) =< aux(220) 1115.54/291.64 it(38) =< aux(220) 1115.54/291.64 it(42) =< aux(220) 1115.54/291.64 it(43) =< aux(220) 1115.54/291.64 aux(108) =< aux(221) 1115.54/291.64 aux(110) =< aux(221) 1115.54/291.64 it(38) =< aux(221) 1115.54/291.64 s(409) =< aux(220) 1115.54/291.64 aux(108) =< aux(222) 1115.54/291.64 aux(110) =< aux(222) 1115.54/291.64 it(35) =< aux(222) 1115.54/291.64 it(42) =< aux(222) 1115.54/291.64 s(409) =< aux(222) 1115.54/291.64 it(37) =< aux(222) 1115.54/291.64 it(38) =< aux(222) 1115.54/291.64 it(43) =< aux(222) 1115.54/291.64 aux(112) =< aux(219) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(221)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(221)+aux(111) 1115.54/291.64 s(365) =< aux(219)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(219) 1115.54/291.64 aux(105) =< aux(219)+aux(219)+aux(124) 1115.54/291.64 it(42) =< aux(219)+aux(219)+aux(124) 1115.54/291.64 s(409) =< aux(219)+aux(219)+aux(124) 1115.54/291.64 it(43) =< aux(219)+aux(219)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(220) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(380) =< aux(221) 1115.54/291.64 s(368) =< aux(222) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],40,50]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+42*s(10)+49*s(34)+25*s(136)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+12 1115.54/291.64 Such that:aux(223) =< 1 1115.54/291.64 aux(224) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(226) =< V1 1115.54/291.64 aux(227) =< 2*V1 1115.54/291.64 aux(228) =< 2*V1+2*V 1115.54/291.64 aux(229) =< 3*V1 1115.54/291.64 s(136) =< aux(223) 1115.54/291.64 s(34) =< aux(224) 1115.54/291.64 s(10) =< aux(228) 1115.54/291.64 aux(105) =< aux(226) 1115.54/291.64 it(33) =< aux(226) 1115.54/291.64 it(35) =< aux(226) 1115.54/291.64 it(37) =< aux(226) 1115.54/291.64 it(38) =< aux(226) 1115.54/291.64 it(42) =< aux(226) 1115.54/291.64 it(43) =< aux(226) 1115.54/291.64 s(409) =< aux(226) 1115.54/291.64 aux(110) =< aux(227) 1115.54/291.64 it(38) =< aux(227) 1115.54/291.64 it(42) =< aux(227) 1115.54/291.64 it(43) =< aux(227) 1115.54/291.64 aux(108) =< aux(228) 1115.54/291.64 aux(110) =< aux(228) 1115.54/291.64 it(38) =< aux(228) 1115.54/291.64 s(409) =< aux(227) 1115.54/291.64 aux(108) =< aux(229) 1115.54/291.64 aux(110) =< aux(229) 1115.54/291.64 it(35) =< aux(229) 1115.54/291.64 it(42) =< aux(229) 1115.54/291.64 s(409) =< aux(229) 1115.54/291.64 it(37) =< aux(229) 1115.54/291.64 it(38) =< aux(229) 1115.54/291.64 it(43) =< aux(229) 1115.54/291.64 aux(112) =< aux(226) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(228)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(228)+aux(111) 1115.54/291.64 s(365) =< aux(226)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(226) 1115.54/291.64 aux(105) =< aux(226)+aux(226)+aux(124) 1115.54/291.64 it(42) =< aux(226)+aux(226)+aux(124) 1115.54/291.64 s(409) =< aux(226)+aux(226)+aux(124) 1115.54/291.64 it(43) =< aux(226)+aux(226)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(227) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(229) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],40,49]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+8*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+1*s(553)+1*s(554)+12 1115.54/291.64 Such that:s(553) =< 1 1115.54/291.64 s(554) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(231) =< V1 1115.54/291.64 aux(232) =< 2*V1 1115.54/291.64 aux(233) =< 2*V1+2*V 1115.54/291.64 aux(234) =< 3*V1 1115.54/291.64 s(380) =< aux(233) 1115.54/291.64 aux(105) =< aux(231) 1115.54/291.64 it(33) =< aux(231) 1115.54/291.64 it(35) =< aux(231) 1115.54/291.64 it(37) =< aux(231) 1115.54/291.64 it(38) =< aux(231) 1115.54/291.64 it(42) =< aux(231) 1115.54/291.64 it(43) =< aux(231) 1115.54/291.64 s(409) =< aux(231) 1115.54/291.64 aux(110) =< aux(232) 1115.54/291.64 it(38) =< aux(232) 1115.54/291.64 it(42) =< aux(232) 1115.54/291.64 it(43) =< aux(232) 1115.54/291.64 aux(108) =< aux(233) 1115.54/291.64 aux(110) =< aux(233) 1115.54/291.64 it(38) =< aux(233) 1115.54/291.64 s(409) =< aux(232) 1115.54/291.64 aux(108) =< aux(234) 1115.54/291.64 aux(110) =< aux(234) 1115.54/291.64 it(35) =< aux(234) 1115.54/291.64 it(42) =< aux(234) 1115.54/291.64 s(409) =< aux(234) 1115.54/291.64 it(37) =< aux(234) 1115.54/291.64 it(38) =< aux(234) 1115.54/291.64 it(43) =< aux(234) 1115.54/291.64 aux(112) =< aux(231) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(233)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(233)+aux(111) 1115.54/291.64 s(365) =< aux(231)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(231) 1115.54/291.64 aux(105) =< aux(231)+aux(231)+aux(124) 1115.54/291.64 it(42) =< aux(231)+aux(231)+aux(124) 1115.54/291.64 s(409) =< aux(231)+aux(231)+aux(124) 1115.54/291.64 it(43) =< aux(231)+aux(231)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(232) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(234) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],39,50]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+42*s(10)+49*s(34)+25*s(136)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+11 1115.54/291.64 Such that:aux(235) =< 1 1115.54/291.64 aux(236) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(238) =< V1 1115.54/291.64 aux(239) =< 2*V1 1115.54/291.64 aux(240) =< 2*V1+2*V 1115.54/291.64 aux(241) =< 3*V1 1115.54/291.64 s(136) =< aux(235) 1115.54/291.64 s(34) =< aux(236) 1115.54/291.64 s(10) =< aux(240) 1115.54/291.64 aux(105) =< aux(238) 1115.54/291.64 it(33) =< aux(238) 1115.54/291.64 it(35) =< aux(238) 1115.54/291.64 it(37) =< aux(238) 1115.54/291.64 it(38) =< aux(238) 1115.54/291.64 it(42) =< aux(238) 1115.54/291.64 it(43) =< aux(238) 1115.54/291.64 s(409) =< aux(238) 1115.54/291.64 aux(110) =< aux(239) 1115.54/291.64 it(38) =< aux(239) 1115.54/291.64 it(42) =< aux(239) 1115.54/291.64 it(43) =< aux(239) 1115.54/291.64 aux(108) =< aux(240) 1115.54/291.64 aux(110) =< aux(240) 1115.54/291.64 it(38) =< aux(240) 1115.54/291.64 s(409) =< aux(239) 1115.54/291.64 aux(108) =< aux(241) 1115.54/291.64 aux(110) =< aux(241) 1115.54/291.64 it(35) =< aux(241) 1115.54/291.64 it(42) =< aux(241) 1115.54/291.64 s(409) =< aux(241) 1115.54/291.64 it(37) =< aux(241) 1115.54/291.64 it(38) =< aux(241) 1115.54/291.64 it(43) =< aux(241) 1115.54/291.64 aux(112) =< aux(238) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(240)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(240)+aux(111) 1115.54/291.64 s(365) =< aux(238)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(238) 1115.54/291.64 aux(105) =< aux(238)+aux(238)+aux(124) 1115.54/291.64 it(42) =< aux(238)+aux(238)+aux(124) 1115.54/291.64 s(409) =< aux(238)+aux(238)+aux(124) 1115.54/291.64 it(43) =< aux(238)+aux(238)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(239) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(241) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [[33,34,35,36,37,38,42,43],39,49]: 22*it(33)+12*it(35)+7*it(37)+6*it(38)+7*it(42)+7*it(43)+15*s(361)+3*s(362)+1*s(363)+6*s(368)+1*s(369)+2*s(379)+8*s(380)+2*s(387)+9*s(388)+1*s(399)+5*s(400)+3*s(401)+2*s(404)+1*s(556)+1*s(557)+11 1115.54/291.64 Such that:s(556) =< 1 1115.54/291.64 s(557) =< 2 1115.54/291.64 aux(111) =< 2*V1-V 1115.54/291.64 aux(82) =< 3*V1+4*V 1115.54/291.64 aux(81) =< 3*V1+4*V+2 1115.54/291.64 aux(84) =< V1/2+V 1115.54/291.64 aux(124) =< -V+1 1115.54/291.64 aux(243) =< V1 1115.54/291.64 aux(244) =< 2*V1 1115.54/291.64 aux(245) =< 2*V1+2*V 1115.54/291.64 aux(246) =< 3*V1 1115.54/291.64 s(380) =< aux(245) 1115.54/291.64 aux(105) =< aux(243) 1115.54/291.64 it(33) =< aux(243) 1115.54/291.64 it(35) =< aux(243) 1115.54/291.64 it(37) =< aux(243) 1115.54/291.64 it(38) =< aux(243) 1115.54/291.64 it(42) =< aux(243) 1115.54/291.64 it(43) =< aux(243) 1115.54/291.64 s(409) =< aux(243) 1115.54/291.64 aux(110) =< aux(244) 1115.54/291.64 it(38) =< aux(244) 1115.54/291.64 it(42) =< aux(244) 1115.54/291.64 it(43) =< aux(244) 1115.54/291.64 aux(108) =< aux(245) 1115.54/291.64 aux(110) =< aux(245) 1115.54/291.64 it(38) =< aux(245) 1115.54/291.64 s(409) =< aux(244) 1115.54/291.64 aux(108) =< aux(246) 1115.54/291.64 aux(110) =< aux(246) 1115.54/291.64 it(35) =< aux(246) 1115.54/291.64 it(42) =< aux(246) 1115.54/291.64 s(409) =< aux(246) 1115.54/291.64 it(37) =< aux(246) 1115.54/291.64 it(38) =< aux(246) 1115.54/291.64 it(43) =< aux(246) 1115.54/291.64 aux(112) =< aux(243) 1115.54/291.64 aux(87) =< aux(84)+1 1115.54/291.64 aux(92) =< aux(84) 1115.54/291.64 it(43) =< aux(110)+aux(108)+aux(108)+aux(245)+aux(111) 1115.54/291.64 s(402) =< aux(110)+aux(108)+aux(108)+aux(245)+aux(111) 1115.54/291.64 s(365) =< aux(243)*2 1115.54/291.64 s(363) =< it(33)*aux(84) 1115.54/291.64 s(364) =< it(33)*aux(243) 1115.54/291.64 aux(105) =< aux(243)+aux(243)+aux(124) 1115.54/291.64 it(42) =< aux(243)+aux(243)+aux(124) 1115.54/291.64 s(409) =< aux(243)+aux(243)+aux(124) 1115.54/291.64 it(43) =< aux(243)+aux(243)+aux(124) 1115.54/291.64 s(390) =< it(37)*aux(87) 1115.54/291.64 s(369) =< it(33)*aux(87) 1115.54/291.64 s(403) =< aux(105)*2 1115.54/291.64 s(402) =< it(42)*aux(112) 1115.54/291.64 s(399) =< aux(105) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(82) 1115.54/291.64 it(35) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 it(38) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(364) =< it(43)+it(42)+it(37)+it(33)+aux(81) 1115.54/291.64 s(382) =< it(35)*aux(92) 1115.54/291.64 s(404) =< s(409) 1115.54/291.64 s(400) =< s(403) 1115.54/291.64 s(388) =< aux(244) 1115.54/291.64 s(401) =< s(402) 1115.54/291.64 s(361) =< s(365) 1115.54/291.64 s(387) =< s(390) 1115.54/291.64 s(379) =< s(382) 1115.54/291.64 s(368) =< aux(246) 1115.54/291.64 s(362) =< s(364) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=3,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [50]: 19*s(10)+19*s(11)+120*s(24)+48*s(34)+24*s(136)+6 1115.54/291.64 Such that:aux(48) =< 1 1115.54/291.64 aux(49) =< 2 1115.54/291.64 aux(50) =< V1 1115.54/291.64 aux(51) =< V 1115.54/291.64 aux(52) =< V+1 1115.54/291.64 s(136) =< aux(48) 1115.54/291.64 s(34) =< aux(49) 1115.54/291.64 s(24) =< aux(50) 1115.54/291.64 s(11) =< aux(51) 1115.54/291.64 s(10) =< aux(52) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=0,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [49]: 2*s(543)+2*s(544)+6 1115.54/291.64 Such that:aux(197) =< V 1115.54/291.64 aux(198) =< V+1 1115.54/291.64 s(544) =< aux(197) 1115.54/291.64 s(543) =< aux(198) 1115.54/291.64 1115.54/291.64 with precondition: [V1=0,Out=1,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [48]: 36*s(410)+4*s(416)+4*s(419)+9*s(422)+7 1115.54/291.64 Such that:aux(147) =< 1 1115.54/291.64 aux(148) =< 2 1115.54/291.64 aux(149) =< V 1115.54/291.64 aux(150) =< V+1 1115.54/291.64 s(422) =< aux(148) 1115.54/291.64 s(419) =< aux(149) 1115.54/291.64 s(416) =< aux(150) 1115.54/291.64 s(410) =< aux(147) 1115.54/291.64 1115.54/291.64 with precondition: [V1=1,Out=0,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [47]: 4*s(463)+2*s(465)+1*s(468)+7 1115.54/291.64 Such that:s(468) =< 2 1115.54/291.64 aux(157) =< 1 1115.54/291.64 aux(158) =< V+1 1115.54/291.64 s(465) =< aux(158) 1115.54/291.64 s(463) =< aux(157) 1115.54/291.64 1115.54/291.64 with precondition: [V1=1,V=Out,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [46]: 4*s(470)+2*s(472)+1*s(475)+6 1115.54/291.64 Such that:s(475) =< 2 1115.54/291.64 aux(164) =< 1 1115.54/291.64 aux(165) =< V 1115.54/291.64 s(472) =< aux(165) 1115.54/291.64 s(470) =< aux(164) 1115.54/291.64 1115.54/291.64 with precondition: [V1=1,Out>=0,V>=Out+1] 1115.54/291.64 1115.54/291.64 * Chain [45]: 40*s(477)+16*s(481)+8*s(509)+6 1115.54/291.64 Such that:aux(184) =< 1 1115.54/291.64 aux(185) =< 2 1115.54/291.64 aux(186) =< V1 1115.54/291.64 s(509) =< aux(184) 1115.54/291.64 s(481) =< aux(185) 1115.54/291.64 s(477) =< aux(186) 1115.54/291.64 1115.54/291.64 with precondition: [V=0,Out=0,V1>=0] 1115.54/291.64 1115.54/291.64 * Chain [44,50]: 68*s(10)+44*s(11)+12 1115.54/291.64 Such that:aux(191) =< 1 1115.54/291.64 aux(192) =< 2 1115.54/291.64 s(11) =< aux(191) 1115.54/291.64 s(10) =< aux(192) 1115.54/291.64 1115.54/291.64 with precondition: [V=0,Out=0,V1>=2] 1115.54/291.64 1115.54/291.64 * Chain [44,49]: 3*s(541)+3*s(542)+12 1115.54/291.64 Such that:aux(199) =< 1 1115.54/291.64 aux(200) =< 2 1115.54/291.64 s(541) =< aux(199) 1115.54/291.64 s(542) =< aux(200) 1115.54/291.64 1115.54/291.64 with precondition: [V=0,Out=1,V1>=2] 1115.54/291.64 1115.54/291.64 * Chain [41,50]: 44*s(10)+49*s(34)+11 1115.54/291.64 Such that:aux(206) =< 1 1115.54/291.64 aux(207) =< 2 1115.54/291.64 s(10) =< aux(206) 1115.54/291.64 s(34) =< aux(207) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [41,49]: 3*s(543)+1*s(552)+11 1115.54/291.64 Such that:s(552) =< 2 1115.54/291.64 aux(212) =< 1 1115.54/291.64 s(543) =< aux(212) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [41,45]: 17*s(481)+9*s(509)+11 1115.54/291.64 Such that:aux(217) =< 1 1115.54/291.64 aux(218) =< 2 1115.54/291.64 s(509) =< aux(217) 1115.54/291.64 s(481) =< aux(218) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=0] 1115.54/291.64 1115.54/291.64 * Chain [40,50]: 19*s(10)+20*s(11)+49*s(34)+25*s(136)+12 1115.54/291.64 Such that:aux(52) =< V+2 1115.54/291.64 aux(223) =< 1 1115.54/291.64 aux(224) =< 2 1115.54/291.64 aux(225) =< V+1 1115.54/291.64 s(136) =< aux(223) 1115.54/291.64 s(34) =< aux(224) 1115.54/291.64 s(11) =< aux(225) 1115.54/291.64 s(10) =< aux(52) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [40,49]: 2*s(543)+3*s(544)+1*s(553)+1*s(554)+12 1115.54/291.64 Such that:s(553) =< 1 1115.54/291.64 s(554) =< 2 1115.54/291.64 aux(198) =< V+2 1115.54/291.64 aux(230) =< V+1 1115.54/291.64 s(544) =< aux(230) 1115.54/291.64 s(543) =< aux(198) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=2,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [39,50]: 19*s(10)+20*s(11)+49*s(34)+25*s(136)+11 1115.54/291.64 Such that:aux(52) =< V+1 1115.54/291.64 aux(235) =< 1 1115.54/291.64 aux(236) =< 2 1115.54/291.64 aux(237) =< V 1115.54/291.64 s(136) =< aux(235) 1115.54/291.64 s(34) =< aux(236) 1115.54/291.64 s(11) =< aux(237) 1115.54/291.64 s(10) =< aux(52) 1115.54/291.64 1115.54/291.64 with precondition: [Out=0,V1>=2,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [39,49]: 2*s(543)+3*s(544)+1*s(556)+1*s(557)+11 1115.54/291.64 Such that:s(556) =< 1 1115.54/291.64 s(557) =< 2 1115.54/291.64 aux(198) =< V+1 1115.54/291.64 aux(242) =< V 1115.54/291.64 s(544) =< aux(242) 1115.54/291.64 s(543) =< aux(198) 1115.54/291.64 1115.54/291.64 with precondition: [Out=1,V1>=2,V>=1] 1115.54/291.64 1115.54/291.64 1115.54/291.64 #### Cost of chains of start(V1,V,V16,V20): 1115.54/291.64 * Chain [58]: 54*s(1215)+4*s(1218)+900*s(1220)+1*s(1228)+925*s(1233)+1185*s(1250)+528*s(1254)+156*s(1256)+196*s(1257)+78*s(1258)+98*s(1259)+91*s(1260)+14*s(1269)+14*s(1272)+14*s(1274)+28*s(1276)+70*s(1277)+39*s(1279)+420*s(1280)+28*s(1281)+26*s(1282)+248*s(1283)+39*s(1284)+21*s(1285)+12*s(1348)+6*s(1349)+7*s(1350)+3*s(1357)+2*s(1358)+3*s(1359)+3*s(1360)+69*s(1408)+276*s(1429)+156*s(1431)+78*s(1433)+98*s(1434)+91*s(1435)+14*s(1444)+14*s(1447)+14*s(1449)+28*s(1451)+70*s(1452)+39*s(1454)+28*s(1456)+26*s(1457)+39*s(1459)+21*s(1460)+21*s(1461)+12*s(1517)+6*s(1518)+7*s(1519)+3*s(1526)+2*s(1527)+3*s(1528)+3*s(1529)+13 1115.54/291.64 Such that:s(1228) =< V1+1 1115.54/291.64 aux(288) =< 1 1115.54/291.64 aux(289) =< 2 1115.54/291.64 aux(290) =< V1 1115.54/291.64 aux(291) =< V1-V+1 1115.54/291.64 aux(292) =< 2*V1 1115.54/291.64 aux(293) =< 2*V1+2 1115.54/291.64 aux(294) =< 2*V1-V 1115.54/291.64 aux(295) =< 2*V1+2*V 1115.54/291.64 aux(296) =< 2*V1+2*V+2 1115.54/291.64 aux(297) =< 3*V1 1115.54/291.64 aux(298) =< 3*V1+2 1115.54/291.64 aux(299) =< 3*V1+4*V 1115.54/291.64 aux(300) =< 3*V1+4*V+2 1115.54/291.64 aux(301) =< V1/2 1115.54/291.64 aux(302) =< V1/2+V 1115.54/291.64 aux(303) =< -V+1 1115.54/291.64 aux(304) =< V 1115.54/291.64 aux(305) =< V+1 1115.54/291.64 aux(306) =< V+2 1115.54/291.64 s(1250) =< aux(289) 1115.54/291.64 s(1220) =< aux(290) 1115.54/291.64 s(1218) =< aux(291) 1115.54/291.64 s(1215) =< aux(304) 1115.54/291.64 s(1233) =< aux(288) 1115.54/291.64 s(1408) =< aux(305) 1115.54/291.64 s(1429) =< aux(295) 1115.54/291.64 s(1430) =< aux(290) 1115.54/291.64 s(1431) =< aux(290) 1115.54/291.64 s(1257) =< aux(290) 1115.54/291.64 s(1433) =< aux(290) 1115.54/291.64 s(1434) =< aux(290) 1115.54/291.64 s(1435) =< aux(290) 1115.54/291.64 s(1436) =< aux(290) 1115.54/291.64 s(1437) =< aux(292) 1115.54/291.64 s(1433) =< aux(292) 1115.54/291.64 s(1434) =< aux(292) 1115.54/291.64 s(1435) =< aux(292) 1115.54/291.64 s(1438) =< aux(295) 1115.54/291.64 s(1437) =< aux(295) 1115.54/291.64 s(1433) =< aux(295) 1115.54/291.64 s(1436) =< aux(292) 1115.54/291.64 s(1438) =< aux(297) 1115.54/291.64 s(1437) =< aux(297) 1115.54/291.64 s(1431) =< aux(297) 1115.54/291.64 s(1434) =< aux(297) 1115.54/291.64 s(1436) =< aux(297) 1115.54/291.64 s(1257) =< aux(297) 1115.54/291.64 s(1433) =< aux(297) 1115.54/291.64 s(1435) =< aux(297) 1115.54/291.64 s(1264) =< aux(290) 1115.54/291.64 s(1440) =< aux(302)+1 1115.54/291.64 s(1441) =< aux(302) 1115.54/291.64 s(1435) =< s(1437)+s(1438)+s(1438)+aux(295)+aux(294) 1115.54/291.64 s(1442) =< s(1437)+s(1438)+s(1438)+aux(295)+aux(294) 1115.54/291.64 s(1268) =< aux(290)*2 1115.54/291.64 s(1444) =< s(1220)*aux(302) 1115.54/291.64 s(1445) =< s(1220)*aux(290) 1115.54/291.64 s(1430) =< aux(290)+aux(290)+aux(303) 1115.54/291.64 s(1434) =< aux(290)+aux(290)+aux(303) 1115.54/291.64 s(1436) =< aux(290)+aux(290)+aux(303) 1115.54/291.64 s(1435) =< aux(290)+aux(290)+aux(303) 1115.54/291.64 s(1446) =< s(1257)*s(1440) 1115.54/291.64 s(1447) =< s(1220)*s(1440) 1115.54/291.64 s(1448) =< s(1430)*2 1115.54/291.64 s(1442) =< s(1434)*s(1264) 1115.54/291.64 s(1449) =< s(1430) 1115.54/291.64 s(1431) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1433) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1445) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1431) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1433) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1445) =< s(1435)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1450) =< s(1431)*s(1441) 1115.54/291.64 s(1451) =< s(1436) 1115.54/291.64 s(1452) =< s(1448) 1115.54/291.64 s(1254) =< aux(292) 1115.54/291.64 s(1454) =< s(1442) 1115.54/291.64 s(1280) =< s(1268) 1115.54/291.64 s(1456) =< s(1446) 1115.54/291.64 s(1457) =< s(1450) 1115.54/291.64 s(1283) =< aux(297) 1115.54/291.64 s(1459) =< s(1445) 1115.54/291.64 s(1460) =< aux(296) 1115.54/291.64 s(1461) =< aux(306) 1115.54/291.64 s(1517) =< aux(290) 1115.54/291.64 s(1518) =< aux(290) 1115.54/291.64 s(1519) =< aux(290) 1115.54/291.64 s(1520) =< aux(292) 1115.54/291.64 s(1518) =< aux(292) 1115.54/291.64 s(1519) =< aux(292) 1115.54/291.64 s(1521) =< aux(295) 1115.54/291.64 s(1522) =< aux(295) 1115.54/291.64 s(1520) =< aux(295) 1115.54/291.64 s(1518) =< aux(295) 1115.54/291.64 s(1521) =< aux(296) 1115.54/291.64 s(1522) =< aux(296) 1115.54/291.64 s(1520) =< aux(296) 1115.54/291.64 s(1518) =< aux(296) 1115.54/291.64 s(1522) =< aux(297) 1115.54/291.64 s(1520) =< aux(297) 1115.54/291.64 s(1517) =< aux(297) 1115.54/291.64 s(1518) =< aux(297) 1115.54/291.64 s(1519) =< aux(297) 1115.54/291.64 s(1519) =< s(1520)+s(1522)+s(1522)+s(1521)+aux(294) 1115.54/291.64 s(1523) =< s(1520)+s(1522)+s(1522)+s(1521)+aux(294) 1115.54/291.64 s(1524) =< s(1220)*aux(290) 1115.54/291.64 s(1519) =< aux(290)+aux(290)+aux(303) 1115.54/291.64 s(1523) =< s(1434)*s(1264) 1115.54/291.64 s(1517) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1518) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1524) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(299) 1115.54/291.64 s(1517) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1518) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1524) =< s(1519)+s(1434)+s(1257)+s(1220)+aux(300) 1115.54/291.64 s(1525) =< s(1517)*s(1441) 1115.54/291.64 s(1526) =< s(1523) 1115.54/291.64 s(1527) =< s(1525) 1115.54/291.64 s(1528) =< s(1521) 1115.54/291.64 s(1529) =< s(1524) 1115.54/291.64 s(1255) =< aux(290) 1115.54/291.64 s(1256) =< aux(290) 1115.54/291.64 s(1258) =< aux(290) 1115.54/291.64 s(1259) =< aux(290) 1115.54/291.64 s(1260) =< aux(290) 1115.54/291.64 s(1261) =< aux(290) 1115.54/291.64 s(1262) =< aux(292) 1115.54/291.64 s(1258) =< aux(292) 1115.54/291.64 s(1259) =< aux(292) 1115.54/291.64 s(1260) =< aux(292) 1115.54/291.64 s(1261) =< aux(292) 1115.54/291.64 s(1262) =< aux(297) 1115.54/291.64 s(1256) =< aux(297) 1115.54/291.64 s(1259) =< aux(297) 1115.54/291.64 s(1261) =< aux(297) 1115.54/291.64 s(1258) =< aux(297) 1115.54/291.64 s(1260) =< aux(297) 1115.54/291.64 s(1265) =< aux(301)+1 1115.54/291.64 s(1266) =< aux(301) 1115.54/291.64 s(1260) =< s(1262)+s(1262)+s(1262)+aux(292)+aux(292) 1115.54/291.64 s(1267) =< s(1262)+s(1262)+s(1262)+aux(292)+aux(292) 1115.54/291.64 s(1269) =< s(1220)*aux(301) 1115.54/291.64 s(1270) =< s(1220)*aux(290) 1115.54/291.64 s(1255) =< aux(290)+aux(290)+aux(288) 1115.54/291.64 s(1259) =< aux(290)+aux(290)+aux(288) 1115.54/291.64 s(1261) =< aux(290)+aux(290)+aux(288) 1115.54/291.64 s(1260) =< aux(290)+aux(290)+aux(288) 1115.54/291.64 s(1271) =< s(1257)*s(1265) 1115.54/291.64 s(1272) =< s(1220)*s(1265) 1115.54/291.64 s(1273) =< s(1255)*2 1115.54/291.64 s(1267) =< s(1259)*s(1264) 1115.54/291.64 s(1274) =< s(1255) 1115.54/291.64 s(1256) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1258) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1270) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1256) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1258) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1270) =< s(1260)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1275) =< s(1256)*s(1266) 1115.54/291.64 s(1276) =< s(1261) 1115.54/291.64 s(1277) =< s(1273) 1115.54/291.64 s(1279) =< s(1267) 1115.54/291.64 s(1281) =< s(1271) 1115.54/291.64 s(1282) =< s(1275) 1115.54/291.64 s(1284) =< s(1270) 1115.54/291.64 s(1218) =< aux(290) 1115.54/291.64 s(1285) =< aux(293) 1115.54/291.64 s(1348) =< aux(290) 1115.54/291.64 s(1349) =< aux(290) 1115.54/291.64 s(1350) =< aux(290) 1115.54/291.64 s(1351) =< aux(292) 1115.54/291.64 s(1349) =< aux(292) 1115.54/291.64 s(1350) =< aux(292) 1115.54/291.64 s(1352) =< aux(292) 1115.54/291.64 s(1352) =< aux(293) 1115.54/291.64 s(1351) =< aux(293) 1115.54/291.64 s(1349) =< aux(293) 1115.54/291.64 s(1351) =< aux(297) 1115.54/291.64 s(1348) =< aux(297) 1115.54/291.64 s(1349) =< aux(297) 1115.54/291.64 s(1350) =< aux(297) 1115.54/291.64 s(1350) =< s(1351)+s(1351)+s(1351)+s(1352)+aux(292) 1115.54/291.64 s(1354) =< s(1351)+s(1351)+s(1351)+s(1352)+aux(292) 1115.54/291.64 s(1355) =< s(1220)*aux(290) 1115.54/291.64 s(1350) =< aux(290)+aux(290)+aux(288) 1115.54/291.64 s(1354) =< s(1259)*s(1264) 1115.54/291.64 s(1348) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1349) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1355) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(297) 1115.54/291.64 s(1348) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1349) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1355) =< s(1350)+s(1259)+s(1257)+s(1220)+aux(298) 1115.54/291.64 s(1356) =< s(1348)*s(1266) 1115.54/291.64 s(1357) =< s(1354) 1115.54/291.64 s(1358) =< s(1356) 1115.54/291.64 s(1359) =< s(1352) 1115.54/291.64 s(1360) =< s(1355) 1115.54/291.64 1115.54/291.64 with precondition: [V1>=0] 1115.54/291.64 1115.54/291.64 * Chain [57]: 1 1115.54/291.64 with precondition: [V1=1,V>=0,V16>=0,V20>=0] 1115.54/291.64 1115.54/291.64 * Chain [56]: 2*s(1574)+2*s(1577)+8*s(1578)+2*s(1582)+7 1115.54/291.64 Such that:s(1581) =< V 1115.54/291.64 s(1576) =< V+1 1115.54/291.64 aux(307) =< 1 1115.54/291.64 aux(308) =< 2 1115.54/291.64 s(1574) =< aux(308) 1115.54/291.64 s(1577) =< s(1576) 1115.54/291.64 s(1578) =< aux(307) 1115.54/291.64 s(1582) =< s(1581) 1115.54/291.64 1115.54/291.64 with precondition: [V1=1,V>=1] 1115.54/291.64 1115.54/291.64 * Chain [55]: 1*s(1584)+4*s(1586)+2 1115.54/291.64 Such that:s(1584) =< 1 1115.54/291.64 s(1585) =< V1 1115.54/291.64 s(1586) =< s(1585) 1115.54/291.64 1115.54/291.64 with precondition: [V=1,V1>=1] 1115.54/291.64 1115.54/291.64 * Chain [54]: 48*s(1589)+69*s(1590)+402*s(1606)+540*s(1607)+428*s(1610)+276*s(1611)+156*s(1613)+98*s(1614)+78*s(1615)+98*s(1616)+91*s(1617)+14*s(1626)+14*s(1629)+14*s(1631)+28*s(1633)+70*s(1634)+126*s(1635)+39*s(1636)+210*s(1637)+28*s(1638)+26*s(1639)+124*s(1640)+39*s(1641)+21*s(1642)+21*s(1643)+12*s(1699)+6*s(1700)+7*s(1701)+3*s(1708)+2*s(1709)+3*s(1710)+3*s(1711)+13 1115.54/291.64 Such that:aux(311) =< 1 1115.54/291.64 aux(312) =< 2 1115.54/291.64 aux(313) =< V16 1115.54/291.64 aux(314) =< 2*V16 1115.54/291.64 aux(315) =< 2*V16-V20 1115.54/291.64 aux(316) =< 2*V16+2*V20 1115.54/291.64 aux(317) =< 2*V16+2*V20+2 1115.54/291.64 aux(318) =< 3*V16 1115.54/291.64 aux(319) =< 3*V16+4*V20 1115.54/291.64 aux(320) =< 3*V16+4*V20+2 1115.54/291.64 aux(321) =< V16/2+V20 1115.54/291.64 aux(322) =< -V20+1 1115.54/291.64 aux(323) =< V20 1115.54/291.64 aux(324) =< V20+1 1115.54/291.64 aux(325) =< V20+2 1115.54/291.64 s(1607) =< aux(312) 1115.54/291.64 s(1606) =< aux(311) 1115.54/291.64 s(1589) =< aux(323) 1115.54/291.64 s(1590) =< aux(324) 1115.54/291.64 s(1610) =< aux(313) 1115.54/291.64 s(1611) =< aux(316) 1115.54/291.64 s(1612) =< aux(313) 1115.54/291.64 s(1613) =< aux(313) 1115.54/291.64 s(1614) =< aux(313) 1115.54/291.64 s(1615) =< aux(313) 1115.54/291.64 s(1616) =< aux(313) 1115.54/291.64 s(1617) =< aux(313) 1115.54/291.64 s(1618) =< aux(313) 1115.54/291.64 s(1619) =< aux(314) 1115.54/291.64 s(1615) =< aux(314) 1115.54/291.64 s(1616) =< aux(314) 1115.54/291.64 s(1617) =< aux(314) 1115.54/291.64 s(1620) =< aux(316) 1115.54/291.64 s(1619) =< aux(316) 1115.54/291.64 s(1615) =< aux(316) 1115.54/291.64 s(1618) =< aux(314) 1115.54/291.64 s(1620) =< aux(318) 1115.54/291.64 s(1619) =< aux(318) 1115.54/291.64 s(1613) =< aux(318) 1115.54/291.64 s(1616) =< aux(318) 1115.54/291.64 s(1618) =< aux(318) 1115.54/291.64 s(1614) =< aux(318) 1115.54/291.64 s(1615) =< aux(318) 1115.54/291.64 s(1617) =< aux(318) 1115.54/291.64 s(1621) =< aux(313) 1115.54/291.64 s(1622) =< aux(321)+1 1115.54/291.64 s(1623) =< aux(321) 1115.54/291.64 s(1617) =< s(1619)+s(1620)+s(1620)+aux(316)+aux(315) 1115.54/291.64 s(1624) =< s(1619)+s(1620)+s(1620)+aux(316)+aux(315) 1115.54/291.64 s(1625) =< aux(313)*2 1115.54/291.64 s(1626) =< s(1610)*aux(321) 1115.54/291.64 s(1627) =< s(1610)*aux(313) 1115.54/291.64 s(1612) =< aux(313)+aux(313)+aux(322) 1115.54/291.64 s(1616) =< aux(313)+aux(313)+aux(322) 1115.54/291.64 s(1618) =< aux(313)+aux(313)+aux(322) 1115.54/291.64 s(1617) =< aux(313)+aux(313)+aux(322) 1115.54/291.64 s(1628) =< s(1614)*s(1622) 1115.54/291.64 s(1629) =< s(1610)*s(1622) 1115.54/291.64 s(1630) =< s(1612)*2 1115.54/291.64 s(1624) =< s(1616)*s(1621) 1115.54/291.64 s(1631) =< s(1612) 1115.54/291.64 s(1613) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1615) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1627) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1613) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1615) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1627) =< s(1617)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1632) =< s(1613)*s(1623) 1115.54/291.64 s(1633) =< s(1618) 1115.54/291.64 s(1634) =< s(1630) 1115.54/291.64 s(1635) =< aux(314) 1115.54/291.64 s(1636) =< s(1624) 1115.54/291.64 s(1637) =< s(1625) 1115.54/291.64 s(1638) =< s(1628) 1115.54/291.64 s(1639) =< s(1632) 1115.54/291.64 s(1640) =< aux(318) 1115.54/291.64 s(1641) =< s(1627) 1115.54/291.64 s(1642) =< aux(317) 1115.54/291.64 s(1643) =< aux(325) 1115.54/291.64 s(1699) =< aux(313) 1115.54/291.64 s(1700) =< aux(313) 1115.54/291.64 s(1701) =< aux(313) 1115.54/291.64 s(1702) =< aux(314) 1115.54/291.64 s(1700) =< aux(314) 1115.54/291.64 s(1701) =< aux(314) 1115.54/291.64 s(1703) =< aux(316) 1115.54/291.64 s(1704) =< aux(316) 1115.54/291.64 s(1702) =< aux(316) 1115.54/291.64 s(1700) =< aux(316) 1115.54/291.64 s(1703) =< aux(317) 1115.54/291.64 s(1704) =< aux(317) 1115.54/291.64 s(1702) =< aux(317) 1115.54/291.64 s(1700) =< aux(317) 1115.54/291.64 s(1704) =< aux(318) 1115.54/291.64 s(1702) =< aux(318) 1115.54/291.64 s(1699) =< aux(318) 1115.54/291.64 s(1700) =< aux(318) 1115.54/291.64 s(1701) =< aux(318) 1115.54/291.64 s(1701) =< s(1702)+s(1704)+s(1704)+s(1703)+aux(315) 1115.54/291.64 s(1705) =< s(1702)+s(1704)+s(1704)+s(1703)+aux(315) 1115.54/291.64 s(1706) =< s(1610)*aux(313) 1115.54/291.64 s(1701) =< aux(313)+aux(313)+aux(322) 1115.54/291.64 s(1705) =< s(1616)*s(1621) 1115.54/291.64 s(1699) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1700) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1706) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(319) 1115.54/291.64 s(1699) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1700) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1706) =< s(1701)+s(1616)+s(1614)+s(1610)+aux(320) 1115.54/291.64 s(1707) =< s(1699)*s(1623) 1115.54/291.64 s(1708) =< s(1705) 1115.54/291.64 s(1709) =< s(1707) 1115.54/291.64 s(1710) =< s(1703) 1115.54/291.64 s(1711) =< s(1706) 1115.54/291.64 1115.54/291.64 with precondition: [V1=2,V=2,V16>=0,V20>=0] 1115.54/291.64 1115.54/291.64 * Chain [53]: 2*s(1756)+2*s(1759)+8*s(1760)+2*s(1764)+8 1115.54/291.64 Such that:s(1763) =< V20 1115.54/291.64 s(1758) =< V20+1 1115.54/291.64 aux(326) =< 1 1115.54/291.64 aux(327) =< 2 1115.54/291.64 s(1756) =< aux(327) 1115.54/291.64 s(1759) =< s(1758) 1115.54/291.64 s(1760) =< aux(326) 1115.54/291.64 s(1764) =< s(1763) 1115.54/291.64 1115.54/291.64 with precondition: [V1=2,V=2,V16=1,V20>=1] 1115.54/291.64 1115.54/291.64 * Chain [52]: 52*s(1769)+84*s(1770)+40*s(1771)+13 1115.54/291.64 Such that:s(1767) =< 1 1115.54/291.64 s(1768) =< 2 1115.54/291.64 s(1766) =< V16 1115.54/291.64 s(1769) =< s(1767) 1115.54/291.64 s(1770) =< s(1768) 1115.54/291.64 s(1771) =< s(1766) 1115.54/291.64 1115.54/291.64 with precondition: [V1=2,V=2,V20=0,V16>=0] 1115.54/291.64 1115.54/291.64 * Chain [51]: 52*s(1775)+84*s(1776)+40*s(1777)+12 1115.54/291.64 Such that:s(1773) =< 1 1115.54/291.64 s(1774) =< 2 1115.54/291.64 s(1772) =< V1 1115.54/291.64 s(1775) =< s(1773) 1115.54/291.64 s(1776) =< s(1774) 1115.54/291.64 s(1777) =< s(1772) 1115.54/291.64 1115.54/291.64 with precondition: [V=0,V1>=0] 1115.54/291.64 1115.54/291.64 1115.54/291.64 Closed-form bounds of start(V1,V,V16,V20): 1115.54/291.64 ------------------------------------- 1115.54/291.64 * Chain [58] with precondition: [V1>=0] 1115.54/291.64 - Upper bound: 3616*V1+3308+84*V1*nat(V1/2+V)+V1/2*(84*V1)+nat(V)*54+1566*V1+870*V1+(V1+1)+nat(V+1)*69+nat(V+2)*21+(42*V1+42)+nat(2*V1+2*V)*405+nat(3*V1+4*V)*42+nat(2*V1+2*V+2)*21+nat(V1-V+1)*4+nat(2*V1-V)*42 1115.54/291.64 - Complexity: n^2 1115.54/291.64 * Chain [57] with precondition: [V1=1,V>=0,V16>=0,V20>=0] 1115.54/291.64 - Upper bound: 1 1115.54/291.64 - Complexity: constant 1115.54/291.64 * Chain [56] with precondition: [V1=1,V>=1] 1115.54/291.64 - Upper bound: 4*V+21 1115.54/291.64 - Complexity: n 1115.54/291.64 * Chain [55] with precondition: [V=1,V1>=1] 1115.54/291.64 - Upper bound: 4*V1+3 1115.54/291.64 - Complexity: n 1115.54/291.64 * Chain [54] with precondition: [V1=2,V=2,V16>=0,V20>=0] 1115.54/291.64 - Upper bound: 1786*V16+1495+(V16/2+V20)*(84*V16)+48*V20+336*V16+372*V16+(69*V20+69)+(21*V20+42)+(810*V16+810*V20)+(126*V16+168*V20)+(42*V16+42*V20+42)+nat(2*V16-V20)*42 1115.54/291.64 - Complexity: n^2 1115.54/291.64 * Chain [53] with precondition: [V1=2,V=2,V16=1,V20>=1] 1115.54/291.64 - Upper bound: 4*V20+22 1115.54/291.64 - Complexity: n 1115.54/291.64 * Chain [52] with precondition: [V1=2,V=2,V20=0,V16>=0] 1115.54/291.64 - Upper bound: 40*V16+233 1115.54/291.64 - Complexity: n 1115.54/291.64 * Chain [51] with precondition: [V=0,V1>=0] 1115.54/291.64 - Upper bound: 40*V1+232 1115.54/291.64 - Complexity: n 1115.54/291.64 1115.54/291.64 ### Maximum cost of start(V1,V,V16,V20): max([max([max([nat(V)*2+18+nat(V+1)*2,nat(V20)*2+19+nat(V20+1)*2]),nat(V16)*1746+1262+nat(V16)*84*nat(V16/2+V20)+nat(V20)*48+nat(2*V16)*168+nat(3*V16)*124+nat(V20+1)*69+nat(V20+2)*21+nat(2*V16+2*V20)*405+nat(3*V16+4*V20)*42+nat(2*V16+2*V20+2)*21+nat(2*V16-V20)*42+(nat(V16)*40+232)]),3576*V1+3076+84*V1*nat(V1/2+V)+V1/2*(84*V1)+nat(V)*54+1566*V1+870*V1+(V1+1)+nat(V+1)*69+nat(V+2)*21+(42*V1+42)+nat(2*V1+2*V)*405+nat(3*V1+4*V)*42+nat(2*V1+2*V+2)*21+nat(V1-V+1)*4+nat(2*V1-V)*42+(36*V1+229)+(4*V1+2)])+1 1115.54/291.64 Asymptotic class: n^2 1115.54/291.64 * Total analysis performed in 4889 ms. 1115.54/291.64 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (10) 1115.54/291.64 BOUNDS(1, n^2) 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (11) RenamingProof (BOTH BOUNDS(ID, ID)) 1115.54/291.64 Renamed function symbols to avoid clashes with predefined symbol. 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (12) 1115.54/291.64 Obligation: 1115.54/291.64 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1115.54/291.64 1115.54/291.64 1115.54/291.64 The TRS R consists of the following rules: 1115.54/291.64 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 S is empty. 1115.54/291.64 Rewrite Strategy: INNERMOST 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.54/291.64 Infered types. 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (14) 1115.54/291.64 Obligation: 1115.54/291.64 Innermost TRS: 1115.54/291.64 Rules: 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 Types: 1115.54/291.64 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 0' :: 0':s:logZeroError 1115.54/291.64 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.64 true :: true:false 1115.54/291.64 false :: true:false 1115.54/291.64 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logZeroError :: 0':s:logZeroError 1115.54/291.64 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.64 hole_true:false2_0 :: true:false 1115.54/291.64 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (15) OrderProof (LOWER BOUND(ID)) 1115.54/291.64 Heuristically decided to analyse the following defined symbols: 1115.54/291.64 minus, quot, le, inc, logIter 1115.54/291.64 1115.54/291.64 They will be analysed ascendingly in the following order: 1115.54/291.64 minus < quot 1115.54/291.64 quot < logIter 1115.54/291.64 le < logIter 1115.54/291.64 inc < logIter 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (16) 1115.54/291.64 Obligation: 1115.54/291.64 Innermost TRS: 1115.54/291.64 Rules: 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 Types: 1115.54/291.64 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 0' :: 0':s:logZeroError 1115.54/291.64 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.64 true :: true:false 1115.54/291.64 false :: true:false 1115.54/291.64 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logZeroError :: 0':s:logZeroError 1115.54/291.64 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.64 hole_true:false2_0 :: true:false 1115.54/291.64 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.64 1115.54/291.64 1115.54/291.64 Generator Equations: 1115.54/291.64 gen_0':s:logZeroError3_0(0) <=> 0' 1115.54/291.64 gen_0':s:logZeroError3_0(+(x, 1)) <=> s(gen_0':s:logZeroError3_0(x)) 1115.54/291.64 1115.54/291.64 1115.54/291.64 The following defined symbols remain to be analysed: 1115.54/291.64 minus, quot, le, inc, logIter 1115.54/291.64 1115.54/291.64 They will be analysed ascendingly in the following order: 1115.54/291.64 minus < quot 1115.54/291.64 quot < logIter 1115.54/291.64 le < logIter 1115.54/291.64 inc < logIter 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (17) RewriteLemmaProof (LOWER BOUND(ID)) 1115.54/291.64 Proved the following rewrite lemma: 1115.54/291.64 minus(gen_0':s:logZeroError3_0(n5_0), gen_0':s:logZeroError3_0(n5_0)) -> gen_0':s:logZeroError3_0(0), rt in Omega(1 + n5_0) 1115.54/291.64 1115.54/291.64 Induction Base: 1115.54/291.64 minus(gen_0':s:logZeroError3_0(0), gen_0':s:logZeroError3_0(0)) ->_R^Omega(1) 1115.54/291.64 gen_0':s:logZeroError3_0(0) 1115.54/291.64 1115.54/291.64 Induction Step: 1115.54/291.64 minus(gen_0':s:logZeroError3_0(+(n5_0, 1)), gen_0':s:logZeroError3_0(+(n5_0, 1))) ->_R^Omega(1) 1115.54/291.64 minus(gen_0':s:logZeroError3_0(n5_0), gen_0':s:logZeroError3_0(n5_0)) ->_IH 1115.54/291.64 gen_0':s:logZeroError3_0(0) 1115.54/291.64 1115.54/291.64 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (18) 1115.54/291.64 Complex Obligation (BEST) 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (19) 1115.54/291.64 Obligation: 1115.54/291.64 Proved the lower bound n^1 for the following obligation: 1115.54/291.64 1115.54/291.64 Innermost TRS: 1115.54/291.64 Rules: 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 Types: 1115.54/291.64 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 0' :: 0':s:logZeroError 1115.54/291.64 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.64 true :: true:false 1115.54/291.64 false :: true:false 1115.54/291.64 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logZeroError :: 0':s:logZeroError 1115.54/291.64 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.64 hole_true:false2_0 :: true:false 1115.54/291.64 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.64 1115.54/291.64 1115.54/291.64 Generator Equations: 1115.54/291.64 gen_0':s:logZeroError3_0(0) <=> 0' 1115.54/291.64 gen_0':s:logZeroError3_0(+(x, 1)) <=> s(gen_0':s:logZeroError3_0(x)) 1115.54/291.64 1115.54/291.64 1115.54/291.64 The following defined symbols remain to be analysed: 1115.54/291.64 minus, quot, le, inc, logIter 1115.54/291.64 1115.54/291.64 They will be analysed ascendingly in the following order: 1115.54/291.64 minus < quot 1115.54/291.64 quot < logIter 1115.54/291.64 le < logIter 1115.54/291.64 inc < logIter 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (20) LowerBoundPropagationProof (FINISHED) 1115.54/291.64 Propagated lower bound. 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (21) 1115.54/291.64 BOUNDS(n^1, INF) 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (22) 1115.54/291.64 Obligation: 1115.54/291.64 Innermost TRS: 1115.54/291.64 Rules: 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 Types: 1115.54/291.64 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 0' :: 0':s:logZeroError 1115.54/291.64 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.64 true :: true:false 1115.54/291.64 false :: true:false 1115.54/291.64 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logZeroError :: 0':s:logZeroError 1115.54/291.64 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.64 hole_true:false2_0 :: true:false 1115.54/291.64 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.64 1115.54/291.64 1115.54/291.64 Lemmas: 1115.54/291.64 minus(gen_0':s:logZeroError3_0(n5_0), gen_0':s:logZeroError3_0(n5_0)) -> gen_0':s:logZeroError3_0(0), rt in Omega(1 + n5_0) 1115.54/291.64 1115.54/291.64 1115.54/291.64 Generator Equations: 1115.54/291.64 gen_0':s:logZeroError3_0(0) <=> 0' 1115.54/291.64 gen_0':s:logZeroError3_0(+(x, 1)) <=> s(gen_0':s:logZeroError3_0(x)) 1115.54/291.64 1115.54/291.64 1115.54/291.64 The following defined symbols remain to be analysed: 1115.54/291.64 quot, le, inc, logIter 1115.54/291.64 1115.54/291.64 They will be analysed ascendingly in the following order: 1115.54/291.64 quot < logIter 1115.54/291.64 le < logIter 1115.54/291.64 inc < logIter 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (23) RewriteLemmaProof (LOWER BOUND(ID)) 1115.54/291.64 Proved the following rewrite lemma: 1115.54/291.64 le(gen_0':s:logZeroError3_0(n441_0), gen_0':s:logZeroError3_0(n441_0)) -> true, rt in Omega(1 + n441_0) 1115.54/291.64 1115.54/291.64 Induction Base: 1115.54/291.64 le(gen_0':s:logZeroError3_0(0), gen_0':s:logZeroError3_0(0)) ->_R^Omega(1) 1115.54/291.64 true 1115.54/291.64 1115.54/291.64 Induction Step: 1115.54/291.64 le(gen_0':s:logZeroError3_0(+(n441_0, 1)), gen_0':s:logZeroError3_0(+(n441_0, 1))) ->_R^Omega(1) 1115.54/291.64 le(gen_0':s:logZeroError3_0(n441_0), gen_0':s:logZeroError3_0(n441_0)) ->_IH 1115.54/291.64 true 1115.54/291.64 1115.54/291.64 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (24) 1115.54/291.64 Obligation: 1115.54/291.64 Innermost TRS: 1115.54/291.64 Rules: 1115.54/291.64 minus(x, 0') -> x 1115.54/291.64 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.64 quot(0', s(y)) -> 0' 1115.54/291.64 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.64 le(0', y) -> true 1115.54/291.64 le(s(x), 0') -> false 1115.54/291.64 le(s(x), s(y)) -> le(x, y) 1115.54/291.64 inc(s(x)) -> s(inc(x)) 1115.54/291.64 inc(0') -> s(0') 1115.54/291.64 log(x) -> logIter(x, 0') 1115.54/291.64 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.64 if(false, b, x, y) -> logZeroError 1115.54/291.64 if(true, false, x, s(y)) -> y 1115.54/291.64 if(true, true, x, y) -> logIter(x, y) 1115.54/291.64 1115.54/291.64 Types: 1115.54/291.64 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 0' :: 0':s:logZeroError 1115.54/291.64 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.64 true :: true:false 1115.54/291.64 false :: true:false 1115.54/291.64 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.64 logZeroError :: 0':s:logZeroError 1115.54/291.64 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.64 hole_true:false2_0 :: true:false 1115.54/291.64 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.64 1115.54/291.64 1115.54/291.64 Lemmas: 1115.54/291.64 minus(gen_0':s:logZeroError3_0(n5_0), gen_0':s:logZeroError3_0(n5_0)) -> gen_0':s:logZeroError3_0(0), rt in Omega(1 + n5_0) 1115.54/291.64 le(gen_0':s:logZeroError3_0(n441_0), gen_0':s:logZeroError3_0(n441_0)) -> true, rt in Omega(1 + n441_0) 1115.54/291.64 1115.54/291.64 1115.54/291.64 Generator Equations: 1115.54/291.64 gen_0':s:logZeroError3_0(0) <=> 0' 1115.54/291.64 gen_0':s:logZeroError3_0(+(x, 1)) <=> s(gen_0':s:logZeroError3_0(x)) 1115.54/291.64 1115.54/291.64 1115.54/291.64 The following defined symbols remain to be analysed: 1115.54/291.64 inc, logIter 1115.54/291.64 1115.54/291.64 They will be analysed ascendingly in the following order: 1115.54/291.64 inc < logIter 1115.54/291.64 1115.54/291.64 ---------------------------------------- 1115.54/291.64 1115.54/291.64 (25) RewriteLemmaProof (LOWER BOUND(ID)) 1115.54/291.64 Proved the following rewrite lemma: 1115.54/291.64 inc(gen_0':s:logZeroError3_0(n784_0)) -> gen_0':s:logZeroError3_0(+(1, n784_0)), rt in Omega(1 + n784_0) 1115.54/291.64 1115.54/291.64 Induction Base: 1115.54/291.64 inc(gen_0':s:logZeroError3_0(0)) ->_R^Omega(1) 1115.54/291.64 s(0') 1115.54/291.64 1115.54/291.64 Induction Step: 1115.54/291.64 inc(gen_0':s:logZeroError3_0(+(n784_0, 1))) ->_R^Omega(1) 1115.54/291.64 s(inc(gen_0':s:logZeroError3_0(n784_0))) ->_IH 1115.54/291.64 s(gen_0':s:logZeroError3_0(+(1, c785_0))) 1115.54/291.64 1115.54/291.64 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 1115.54/291.65 ---------------------------------------- 1115.54/291.65 1115.54/291.65 (26) 1115.54/291.65 Obligation: 1115.54/291.65 Innermost TRS: 1115.54/291.65 Rules: 1115.54/291.65 minus(x, 0') -> x 1115.54/291.65 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.65 quot(0', s(y)) -> 0' 1115.54/291.65 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.65 le(0', y) -> true 1115.54/291.65 le(s(x), 0') -> false 1115.54/291.65 le(s(x), s(y)) -> le(x, y) 1115.54/291.65 inc(s(x)) -> s(inc(x)) 1115.54/291.65 inc(0') -> s(0') 1115.54/291.65 log(x) -> logIter(x, 0') 1115.54/291.65 logIter(x, y) -> if(le(s(0'), x), le(s(s(0')), x), quot(x, s(s(0'))), inc(y)) 1115.54/291.65 if(false, b, x, y) -> logZeroError 1115.54/291.65 if(true, false, x, s(y)) -> y 1115.54/291.65 if(true, true, x, y) -> logIter(x, y) 1115.54/291.65 1115.54/291.65 Types: 1115.54/291.65 minus :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 0' :: 0':s:logZeroError 1115.54/291.65 s :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 quot :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 le :: 0':s:logZeroError -> 0':s:logZeroError -> true:false 1115.54/291.65 true :: true:false 1115.54/291.65 false :: true:false 1115.54/291.65 inc :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 log :: 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 logIter :: 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 if :: true:false -> true:false -> 0':s:logZeroError -> 0':s:logZeroError -> 0':s:logZeroError 1115.54/291.65 logZeroError :: 0':s:logZeroError 1115.54/291.65 hole_0':s:logZeroError1_0 :: 0':s:logZeroError 1115.54/291.65 hole_true:false2_0 :: true:false 1115.54/291.65 gen_0':s:logZeroError3_0 :: Nat -> 0':s:logZeroError 1115.54/291.65 1115.54/291.65 1115.54/291.65 Lemmas: 1115.54/291.65 minus(gen_0':s:logZeroError3_0(n5_0), gen_0':s:logZeroError3_0(n5_0)) -> gen_0':s:logZeroError3_0(0), rt in Omega(1 + n5_0) 1115.54/291.65 le(gen_0':s:logZeroError3_0(n441_0), gen_0':s:logZeroError3_0(n441_0)) -> true, rt in Omega(1 + n441_0) 1115.54/291.65 inc(gen_0':s:logZeroError3_0(n784_0)) -> gen_0':s:logZeroError3_0(+(1, n784_0)), rt in Omega(1 + n784_0) 1115.54/291.65 1115.54/291.65 1115.54/291.65 Generator Equations: 1115.54/291.65 gen_0':s:logZeroError3_0(0) <=> 0' 1115.54/291.65 gen_0':s:logZeroError3_0(+(x, 1)) <=> s(gen_0':s:logZeroError3_0(x)) 1115.54/291.65 1115.54/291.65 1115.54/291.65 The following defined symbols remain to be analysed: 1115.54/291.65 logIter 1115.76/291.70 EOF