1131.48/294.58 WORST_CASE(Omega(n^1), O(n^2)) 1131.48/294.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1131.48/294.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1131.48/294.61 1131.48/294.61 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.61 1131.48/294.61 (0) CpxTRS 1131.48/294.61 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.48/294.61 (2) CpxWeightedTrs 1131.48/294.61 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.48/294.61 (4) CpxTypedWeightedTrs 1131.48/294.61 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1131.48/294.61 (6) CpxTypedWeightedCompleteTrs 1131.48/294.61 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1131.48/294.61 (8) CpxRNTS 1131.48/294.61 (9) CompleteCoflocoProof [FINISHED, 7724 ms] 1131.48/294.61 (10) BOUNDS(1, n^2) 1131.48/294.61 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1131.48/294.61 (12) TRS for Loop Detection 1131.48/294.61 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1131.48/294.61 (14) BEST 1131.48/294.61 (15) proven lower bound 1131.48/294.61 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.48/294.61 (17) BOUNDS(n^1, INF) 1131.48/294.61 (18) TRS for Loop Detection 1131.48/294.61 1131.48/294.61 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (0) 1131.48/294.61 Obligation: 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.61 1131.48/294.61 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 1131.48/294.61 plus(x, 0) -> x 1131.48/294.61 plus(x, s(y)) -> s(plus(x, y)) 1131.48/294.61 length(nil) -> 0 1131.48/294.61 length(cons(x, y)) -> s(length(y)) 1131.48/294.61 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 1131.48/294.61 ge(x, 0) -> true 1131.48/294.61 ge(0, s(x)) -> false 1131.48/294.61 ge(s(x), s(y)) -> ge(x, y) 1131.48/294.61 if(true, c, l, ys, zs) -> nil 1131.48/294.61 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 1131.48/294.61 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 1131.48/294.61 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 1131.48/294.61 helpc(true, ys, zs) -> ys 1131.48/294.61 helpc(false, ys, zs) -> zs 1131.48/294.61 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 1131.48/294.61 1131.48/294.61 S is empty. 1131.48/294.61 Rewrite Strategy: INNERMOST 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1131.48/294.61 Transformed relative TRS to weighted TRS 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (2) 1131.48/294.61 Obligation: 1131.48/294.61 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1131.48/294.61 1131.48/294.61 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] 1131.48/294.61 plus(x, 0) -> x [1] 1131.48/294.61 plus(x, s(y)) -> s(plus(x, y)) [1] 1131.48/294.61 length(nil) -> 0 [1] 1131.48/294.61 length(cons(x, y)) -> s(length(y)) [1] 1131.48/294.61 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] 1131.48/294.61 ge(x, 0) -> true [1] 1131.48/294.61 ge(0, s(x)) -> false [1] 1131.48/294.61 ge(s(x), s(y)) -> ge(x, y) [1] 1131.48/294.61 if(true, c, l, ys, zs) -> nil [1] 1131.48/294.61 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] 1131.48/294.61 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] 1131.48/294.61 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] 1131.48/294.61 helpc(true, ys, zs) -> ys [1] 1131.48/294.61 helpc(false, ys, zs) -> zs [1] 1131.48/294.61 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] 1131.48/294.61 1131.48/294.61 Rewrite Strategy: INNERMOST 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1131.48/294.61 Infered types. 1131.48/294.61 ---------------------------------------- 1131.48/294.61 1131.48/294.61 (4) 1131.48/294.61 Obligation: 1131.48/294.61 Runtime Complexity Weighted TRS with Types. 1131.48/294.61 The TRS R consists of the following rules: 1131.48/294.61 1131.48/294.61 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] 1131.48/294.61 plus(x, 0) -> x [1] 1131.48/294.61 plus(x, s(y)) -> s(plus(x, y)) [1] 1131.48/294.61 length(nil) -> 0 [1] 1131.48/294.61 length(cons(x, y)) -> s(length(y)) [1] 1131.48/294.61 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] 1131.48/294.61 ge(x, 0) -> true [1] 1131.48/294.61 ge(0, s(x)) -> false [1] 1131.48/294.61 ge(s(x), s(y)) -> ge(x, y) [1] 1131.48/294.61 if(true, c, l, ys, zs) -> nil [1] 1131.48/294.61 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] 1131.48/294.61 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] 1131.48/294.61 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] 1131.48/294.61 helpc(true, ys, zs) -> ys [1] 1131.48/294.61 helpc(false, ys, zs) -> zs [1] 1131.48/294.61 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] 1131.48/294.61 1131.48/294.61 The TRS has the following type information: 1131.48/294.61 app :: nil:cons -> nil:cons -> nil:cons 1131.48/294.61 helpa :: 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons 1131.48/294.61 0 :: 0:s 1131.48/294.62 plus :: 0:s -> 0:s -> 0:s 1131.48/294.62 length :: nil:cons -> 0:s 1131.48/294.62 s :: 0:s -> 0:s 1131.48/294.62 nil :: nil:cons 1131.48/294.62 cons :: a -> nil:cons -> nil:cons 1131.48/294.62 if :: true:false -> 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons 1131.48/294.62 ge :: 0:s -> 0:s -> true:false 1131.48/294.62 true :: true:false 1131.48/294.62 false :: true:false 1131.48/294.62 helpb :: 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons 1131.48/294.62 greater :: nil:cons -> nil:cons -> nil:cons 1131.48/294.62 smaller :: nil:cons -> nil:cons -> nil:cons 1131.48/294.62 helpc :: true:false -> nil:cons -> nil:cons -> nil:cons 1131.48/294.62 1131.48/294.62 Rewrite Strategy: INNERMOST 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (5) CompletionProof (UPPER BOUND(ID)) 1131.48/294.62 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 1131.48/294.62 1131.48/294.62 helpb(v0, v1, v2, v3) -> null_helpb [0] 1131.48/294.62 length(v0) -> null_length [0] 1131.48/294.62 plus(v0, v1) -> null_plus [0] 1131.48/294.62 ge(v0, v1) -> null_ge [0] 1131.48/294.62 if(v0, v1, v2, v3, v4) -> null_if [0] 1131.48/294.62 helpc(v0, v1, v2) -> null_helpc [0] 1131.48/294.62 1131.48/294.62 And the following fresh constants: null_helpb, null_length, null_plus, null_ge, null_if, null_helpc, const 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (6) 1131.48/294.62 Obligation: 1131.48/294.62 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 1131.48/294.62 1131.48/294.62 Runtime Complexity Weighted TRS with Types. 1131.48/294.62 The TRS R consists of the following rules: 1131.48/294.62 1131.48/294.62 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] 1131.48/294.62 plus(x, 0) -> x [1] 1131.48/294.62 plus(x, s(y)) -> s(plus(x, y)) [1] 1131.48/294.62 length(nil) -> 0 [1] 1131.48/294.62 length(cons(x, y)) -> s(length(y)) [1] 1131.48/294.62 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] 1131.48/294.62 ge(x, 0) -> true [1] 1131.48/294.62 ge(0, s(x)) -> false [1] 1131.48/294.62 ge(s(x), s(y)) -> ge(x, y) [1] 1131.48/294.62 if(true, c, l, ys, zs) -> nil [1] 1131.48/294.62 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] 1131.48/294.62 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] 1131.48/294.62 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] 1131.48/294.62 helpc(true, ys, zs) -> ys [1] 1131.48/294.62 helpc(false, ys, zs) -> zs [1] 1131.48/294.62 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] 1131.48/294.62 helpb(v0, v1, v2, v3) -> null_helpb [0] 1131.48/294.62 length(v0) -> null_length [0] 1131.48/294.62 plus(v0, v1) -> null_plus [0] 1131.48/294.62 ge(v0, v1) -> null_ge [0] 1131.48/294.62 if(v0, v1, v2, v3, v4) -> null_if [0] 1131.48/294.62 helpc(v0, v1, v2) -> null_helpc [0] 1131.48/294.62 1131.48/294.62 The TRS has the following type information: 1131.48/294.62 app :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 helpa :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 0 :: 0:s:null_length:null_plus 1131.48/294.62 plus :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> 0:s:null_length:null_plus 1131.48/294.62 length :: nil:cons:null_helpb:null_if:null_helpc -> 0:s:null_length:null_plus 1131.48/294.62 s :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus 1131.48/294.62 nil :: nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 cons :: a -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 if :: true:false:null_ge -> 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 ge :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> true:false:null_ge 1131.48/294.62 true :: true:false:null_ge 1131.48/294.62 false :: true:false:null_ge 1131.48/294.62 helpb :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 greater :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 smaller :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 helpc :: true:false:null_ge -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 null_helpb :: nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 null_length :: 0:s:null_length:null_plus 1131.48/294.62 null_plus :: 0:s:null_length:null_plus 1131.48/294.62 null_ge :: true:false:null_ge 1131.48/294.62 null_if :: nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 null_helpc :: nil:cons:null_helpb:null_if:null_helpc 1131.48/294.62 const :: a 1131.48/294.62 1131.48/294.62 Rewrite Strategy: INNERMOST 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) 1131.48/294.62 Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. 1131.48/294.62 The constant constructors are abstracted as follows: 1131.48/294.62 1131.48/294.62 0 => 0 1131.48/294.62 nil => 0 1131.48/294.62 true => 2 1131.48/294.62 false => 1 1131.48/294.62 null_helpb => 0 1131.48/294.62 null_length => 0 1131.48/294.62 null_plus => 0 1131.48/294.62 null_ge => 0 1131.48/294.62 null_if => 0 1131.48/294.62 null_helpc => 0 1131.48/294.62 const => 0 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (8) 1131.48/294.62 Obligation: 1131.48/294.62 Complexity RNTS consisting of the following rules: 1131.48/294.62 1131.48/294.62 app(z, z') -{ 1 }-> helpa(0, plus(length(x), length(y)), x, y) :|: x >= 0, y >= 0, z = x, z' = y 1131.48/294.62 ge(z, z') -{ 1 }-> ge(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1131.48/294.62 ge(z, z') -{ 1 }-> 2 :|: x >= 0, z = x, z' = 0 1131.48/294.62 ge(z, z') -{ 1 }-> 1 :|: z' = 1 + x, x >= 0, z = 0 1131.48/294.62 ge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1131.48/294.62 greater(z, z') -{ 1 }-> helpc(ge(length(ys), length(zs)), ys, zs) :|: z = ys, z' = zs, ys >= 0, zs >= 0 1131.48/294.62 helpa(z, z', z'', z1) -{ 1 }-> if(ge(c, l), c, l, ys, zs) :|: z' = l, c >= 0, ys >= 0, zs >= 0, z'' = ys, z = c, l >= 0, z1 = zs 1131.48/294.62 helpb(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 1131.48/294.62 helpb(z, z', z'', z1) -{ 1 }-> 1 + y + helpa(1 + c, l, ys, zs) :|: z' = l, z'' = 1 + y + ys, c >= 0, ys >= 0, zs >= 0, y >= 0, z = c, l >= 0, z1 = zs 1131.48/294.62 helpc(z, z', z'') -{ 1 }-> ys :|: z = 2, z' = ys, ys >= 0, zs >= 0, z'' = zs 1131.48/294.62 helpc(z, z', z'') -{ 1 }-> zs :|: z' = ys, z = 1, ys >= 0, zs >= 0, z'' = zs 1131.48/294.62 helpc(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 1131.48/294.62 if(z, z', z'', z1, z2) -{ 1 }-> helpb(c, l, greater(ys, zs), smaller(ys, zs)) :|: z2 = zs, c >= 0, z = 1, ys >= 0, zs >= 0, l >= 0, z' = c, z'' = l, z1 = ys 1131.48/294.62 if(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z = 2, z2 = zs, c >= 0, ys >= 0, zs >= 0, l >= 0, z' = c, z'' = l, z1 = ys 1131.48/294.62 if(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 1131.48/294.62 length(z) -{ 1 }-> 0 :|: z = 0 1131.48/294.62 length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 1131.48/294.62 length(z) -{ 1 }-> 1 + length(y) :|: z = 1 + x + y, x >= 0, y >= 0 1131.48/294.62 plus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 1131.48/294.62 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1131.48/294.62 plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = x 1131.48/294.62 smaller(z, z') -{ 1 }-> helpc(ge(length(ys), length(zs)), zs, ys) :|: z = ys, z' = zs, ys >= 0, zs >= 0 1131.48/294.62 1131.48/294.62 Only complete derivations are relevant for the runtime complexity. 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (9) CompleteCoflocoProof (FINISHED) 1131.48/294.62 Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: 1131.48/294.62 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[app(V1, V, Out)],[V1 >= 0,V >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[plus(V1, V, Out)],[V1 >= 0,V >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[length(V1, Out)],[V1 >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[helpa(V1, V, V9, V14, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[ge(V1, V, Out)],[V1 >= 0,V >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[if(V1, V, V9, V14, V22, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0,V22 >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[greater(V1, V, Out)],[V1 >= 0,V >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[smaller(V1, V, Out)],[V1 >= 0,V >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[helpc(V1, V, V9, Out)],[V1 >= 0,V >= 0,V9 >= 0]). 1131.48/294.62 eq(start(V1, V, V9, V14, V22),0,[helpb(V1, V, V9, V14, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0]). 1131.48/294.62 eq(app(V1, V, Out),1,[length(V3, Ret10),length(V2, Ret11),plus(Ret10, Ret11, Ret1),helpa(0, Ret1, V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = V3,V = V2]). 1131.48/294.62 eq(plus(V1, V, Out),1,[],[Out = V4,V4 >= 0,V1 = V4,V = 0]). 1131.48/294.62 eq(plus(V1, V, Out),1,[plus(V5, V6, Ret12)],[Out = 1 + Ret12,V = 1 + V6,V5 >= 0,V6 >= 0,V1 = V5]). 1131.48/294.62 eq(length(V1, Out),1,[],[Out = 0,V1 = 0]). 1131.48/294.62 eq(length(V1, Out),1,[length(V8, Ret13)],[Out = 1 + Ret13,V1 = 1 + V7 + V8,V7 >= 0,V8 >= 0]). 1131.48/294.62 eq(helpa(V1, V, V9, V14, Out),1,[ge(V10, V11, Ret0),if(Ret0, V10, V11, V12, V13, Ret2)],[Out = Ret2,V = V11,V10 >= 0,V12 >= 0,V13 >= 0,V9 = V12,V1 = V10,V11 >= 0,V14 = V13]). 1131.48/294.62 eq(ge(V1, V, Out),1,[],[Out = 2,V15 >= 0,V1 = V15,V = 0]). 1131.48/294.62 eq(ge(V1, V, Out),1,[],[Out = 1,V = 1 + V16,V16 >= 0,V1 = 0]). 1131.48/294.62 eq(ge(V1, V, Out),1,[ge(V18, V17, Ret3)],[Out = Ret3,V = 1 + V17,V18 >= 0,V17 >= 0,V1 = 1 + V18]). 1131.48/294.62 eq(if(V1, V, V9, V14, V22, Out),1,[],[Out = 0,V1 = 2,V22 = V21,V19 >= 0,V20 >= 0,V21 >= 0,V23 >= 0,V = V19,V9 = V23,V14 = V20]). 1131.48/294.62 eq(if(V1, V, V9, V14, V22, Out),1,[greater(V26, V25, Ret21),smaller(V26, V25, Ret31),helpb(V24, V27, Ret21, Ret31, Ret4)],[Out = Ret4,V22 = V25,V24 >= 0,V1 = 1,V26 >= 0,V25 >= 0,V27 >= 0,V = V24,V9 = V27,V14 = V26]). 1131.48/294.62 eq(greater(V1, V, Out),1,[length(V28, Ret00),length(V29, Ret01),ge(Ret00, Ret01, Ret02),helpc(Ret02, V28, V29, Ret5)],[Out = Ret5,V1 = V28,V = V29,V28 >= 0,V29 >= 0]). 1131.48/294.62 eq(smaller(V1, V, Out),1,[length(V30, Ret001),length(V31, Ret011),ge(Ret001, Ret011, Ret03),helpc(Ret03, V31, V30, Ret6)],[Out = Ret6,V1 = V30,V = V31,V30 >= 0,V31 >= 0]). 1131.48/294.62 eq(helpc(V1, V, V9, Out),1,[],[Out = V32,V1 = 2,V = V32,V32 >= 0,V33 >= 0,V9 = V33]). 1131.48/294.62 eq(helpc(V1, V, V9, Out),1,[],[Out = V34,V = V35,V1 = 1,V35 >= 0,V34 >= 0,V9 = V34]). 1131.48/294.62 eq(helpb(V1, V, V9, V14, Out),1,[helpa(1 + V39, V40, V37, V38, Ret14)],[Out = 1 + Ret14 + V36,V = V40,V9 = 1 + V36 + V37,V39 >= 0,V37 >= 0,V38 >= 0,V36 >= 0,V1 = V39,V40 >= 0,V14 = V38]). 1131.48/294.62 eq(helpb(V1, V, V9, V14, Out),0,[],[Out = 0,V14 = V43,V42 >= 0,V9 = V44,V41 >= 0,V1 = V42,V = V41,V44 >= 0,V43 >= 0]). 1131.48/294.62 eq(length(V1, Out),0,[],[Out = 0,V45 >= 0,V1 = V45]). 1131.48/294.62 eq(plus(V1, V, Out),0,[],[Out = 0,V47 >= 0,V46 >= 0,V1 = V47,V = V46]). 1131.48/294.62 eq(ge(V1, V, Out),0,[],[Out = 0,V48 >= 0,V49 >= 0,V1 = V48,V = V49]). 1131.48/294.62 eq(if(V1, V, V9, V14, V22, Out),0,[],[Out = 0,V14 = V54,V50 >= 0,V53 >= 0,V9 = V51,V52 >= 0,V1 = V50,V = V52,V22 = V53,V51 >= 0,V54 >= 0]). 1131.48/294.62 eq(helpc(V1, V, V9, Out),0,[],[Out = 0,V56 >= 0,V9 = V57,V55 >= 0,V1 = V56,V = V55,V57 >= 0]). 1131.48/294.62 input_output_vars(app(V1,V,Out),[V1,V],[Out]). 1131.48/294.62 input_output_vars(plus(V1,V,Out),[V1,V],[Out]). 1131.48/294.62 input_output_vars(length(V1,Out),[V1],[Out]). 1131.48/294.62 input_output_vars(helpa(V1,V,V9,V14,Out),[V1,V,V9,V14],[Out]). 1131.48/294.62 input_output_vars(ge(V1,V,Out),[V1,V],[Out]). 1131.48/294.62 input_output_vars(if(V1,V,V9,V14,V22,Out),[V1,V,V9,V14,V22],[Out]). 1131.48/294.62 input_output_vars(greater(V1,V,Out),[V1,V],[Out]). 1131.48/294.62 input_output_vars(smaller(V1,V,Out),[V1,V],[Out]). 1131.48/294.62 input_output_vars(helpc(V1,V,V9,Out),[V1,V,V9],[Out]). 1131.48/294.62 input_output_vars(helpb(V1,V,V9,V14,Out),[V1,V,V9,V14],[Out]). 1131.48/294.62 1131.48/294.62 1131.48/294.62 CoFloCo proof output: 1131.48/294.62 Preprocessing Cost Relations 1131.48/294.62 ===================================== 1131.48/294.62 1131.48/294.62 #### Computed strongly connected components 1131.48/294.62 0. recursive : [ge/3] 1131.48/294.62 1. non_recursive : [helpc/4] 1131.48/294.62 2. recursive : [length/2] 1131.48/294.62 3. non_recursive : [greater/3] 1131.48/294.62 4. non_recursive : [smaller/3] 1131.48/294.62 5. recursive : [helpa/5,helpb/5,if/6] 1131.48/294.62 6. recursive : [plus/3] 1131.48/294.62 7. non_recursive : [app/3] 1131.48/294.62 8. non_recursive : [start/5] 1131.48/294.62 1131.48/294.62 #### Obtained direct recursion through partial evaluation 1131.48/294.62 0. SCC is partially evaluated into ge/3 1131.48/294.62 1. SCC is partially evaluated into helpc/4 1131.48/294.62 2. SCC is partially evaluated into length/2 1131.48/294.62 3. SCC is partially evaluated into greater/3 1131.48/294.62 4. SCC is partially evaluated into smaller/3 1131.48/294.62 5. SCC is partially evaluated into helpa/5 1131.48/294.62 6. SCC is partially evaluated into plus/3 1131.48/294.62 7. SCC is partially evaluated into app/3 1131.48/294.62 8. SCC is partially evaluated into start/5 1131.48/294.62 1131.48/294.62 Control-Flow Refinement of Cost Relations 1131.48/294.62 ===================================== 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations ge/3 1131.48/294.62 * CE 30 is refined into CE [34] 1131.48/294.62 * CE 27 is refined into CE [35] 1131.48/294.62 * CE 28 is refined into CE [36] 1131.48/294.62 * CE 29 is refined into CE [37] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of ge/3 1131.48/294.62 * CEs [37] --> Loop 20 1131.48/294.62 * CEs [34] --> Loop 21 1131.48/294.62 * CEs [35] --> Loop 22 1131.48/294.62 * CEs [36] --> Loop 23 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR ge(V1,V,Out) 1131.48/294.62 * RF of phase [20]: [V,V1] 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR ge(V1,V,Out) 1131.48/294.62 * Partial RF of phase [20]: 1131.48/294.62 - RF of loop [20:1]: 1131.48/294.62 V 1131.48/294.62 V1 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations helpc/4 1131.48/294.62 * CE 33 is refined into CE [38] 1131.48/294.62 * CE 31 is refined into CE [39] 1131.48/294.62 * CE 32 is refined into CE [40] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of helpc/4 1131.48/294.62 * CEs [38] --> Loop 24 1131.48/294.62 * CEs [39] --> Loop 25 1131.48/294.62 * CEs [40] --> Loop 26 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR helpc(V1,V,V9,Out) 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR helpc(V1,V,V9,Out) 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations length/2 1131.48/294.62 * CE 24 is refined into CE [41] 1131.48/294.62 * CE 26 is refined into CE [42] 1131.48/294.62 * CE 25 is refined into CE [43] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of length/2 1131.48/294.62 * CEs [43] --> Loop 27 1131.48/294.62 * CEs [41,42] --> Loop 28 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR length(V1,Out) 1131.48/294.62 * RF of phase [27]: [V1] 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR length(V1,Out) 1131.48/294.62 * Partial RF of phase [27]: 1131.48/294.62 - RF of loop [27:1]: 1131.48/294.62 V1 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations greater/3 1131.48/294.62 * CE 14 is refined into CE [44,45,46,47,48,49,50,51,52,53,54,55,56,57] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of greater/3 1131.48/294.62 * CEs [47,54] --> Loop 29 1131.48/294.62 * CEs [44,50,56] --> Loop 30 1131.48/294.62 * CEs [45,46,48,49,51,52,53,55,57] --> Loop 31 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR greater(V1,V,Out) 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR greater(V1,V,Out) 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations smaller/3 1131.48/294.62 * CE 15 is refined into CE [58,59,60,61,62,63,64,65,66,67,68,69,70,71] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of smaller/3 1131.48/294.62 * CEs [58,64,70] --> Loop 32 1131.48/294.62 * CEs [61,68] --> Loop 33 1131.48/294.62 * CEs [59,60,62,63,65,66,67,69,71] --> Loop 34 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR smaller(V1,V,Out) 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR smaller(V1,V,Out) 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations helpa/5 1131.48/294.62 * CE 16 is refined into CE [72,73,74,75,76] 1131.48/294.62 * CE 17 is refined into CE [77,78] 1131.48/294.62 * CE 19 is refined into CE [79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96] 1131.48/294.62 * CE 18 is refined into CE [97,98,99,100,101,102,103,104,105,106,107,108] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of helpa/5 1131.48/294.62 * CEs [108] --> Loop 35 1131.48/294.62 * CEs [105] --> Loop 36 1131.48/294.62 * CEs [107] --> Loop 37 1131.48/294.62 * CEs [104] --> Loop 38 1131.48/294.62 * CEs [106] --> Loop 39 1131.48/294.62 * CEs [103] --> Loop 40 1131.48/294.62 * CEs [102] --> Loop 41 1131.48/294.62 * CEs [99] --> Loop 42 1131.48/294.62 * CEs [101] --> Loop 43 1131.48/294.62 * CEs [98] --> Loop 44 1131.48/294.62 * CEs [100] --> Loop 45 1131.48/294.62 * CEs [97] --> Loop 46 1131.48/294.62 * CEs [73,77] --> Loop 47 1131.48/294.62 * CEs [72,74,75,76,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96] --> Loop 48 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR helpa(V1,V,V9,V14,Out) 1131.48/294.62 * RF of phase [35,36,37,38,39,40]: [-V1+V] 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR helpa(V1,V,V9,V14,Out) 1131.48/294.62 * Partial RF of phase [35,36,37,38,39,40]: 1131.48/294.62 - RF of loop [35:1,36:1,37:1,38:1,39:1,40:1]: 1131.48/294.62 -V1+V 1131.48/294.62 - RF of loop [36:1,38:1,40:1]: 1131.48/294.62 V9 depends on loops [35:1,37:1,39:1] 1131.48/294.62 - RF of loop [37:1,39:1]: 1131.48/294.62 V9+V14 depends on loops [35:1,38:1] 1131.48/294.62 - RF of loop [39:1]: 1131.48/294.62 V14 depends on loops [37:1,38:1] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations plus/3 1131.48/294.62 * CE 23 is refined into CE [109] 1131.48/294.62 * CE 21 is refined into CE [110] 1131.48/294.62 * CE 22 is refined into CE [111] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of plus/3 1131.48/294.62 * CEs [111] --> Loop 49 1131.48/294.62 * CEs [109] --> Loop 50 1131.48/294.62 * CEs [110] --> Loop 51 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR plus(V1,V,Out) 1131.48/294.62 * RF of phase [49]: [V] 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR plus(V1,V,Out) 1131.48/294.62 * Partial RF of phase [49]: 1131.48/294.62 - RF of loop [49:1]: 1131.48/294.62 V 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations app/3 1131.48/294.62 * CE 20 is refined into CE [112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of app/3 1131.48/294.62 * CEs [116,121,126,133,138] --> Loop 52 1131.48/294.62 * CEs [128] --> Loop 53 1131.48/294.62 * CEs [127,134,135] --> Loop 54 1131.48/294.62 * CEs [115,120,125,132,137] --> Loop 55 1131.48/294.62 * CEs [117,118,122,123,139,140] --> Loop 56 1131.48/294.62 * CEs [112,113,114,119,124,129,130,131,136,141] --> Loop 57 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR app(V1,V,Out) 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR app(V1,V,Out) 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Specialization of cost equations start/5 1131.48/294.62 * CE 2 is refined into CE [142] 1131.48/294.62 * CE 1 is refined into CE [143] 1131.48/294.62 * CE 3 is refined into CE [144,145,146,147,148,149,150,151,152,153,154,155] 1131.48/294.62 * CE 4 is refined into CE [156,157,158,159,160,161,162,163,164] 1131.48/294.62 * CE 5 is refined into CE [165,166] 1131.48/294.62 * CE 6 is refined into CE [167,168,169,170,171,172] 1131.48/294.62 * CE 7 is refined into CE [173,174,175,176] 1131.48/294.62 * CE 8 is refined into CE [177,178] 1131.48/294.62 * CE 9 is refined into CE [179,180,181,182,183,184] 1131.48/294.62 * CE 10 is refined into CE [185,186,187,188,189] 1131.48/294.62 * CE 11 is refined into CE [190,191,192] 1131.48/294.62 * CE 12 is refined into CE [193,194,195] 1131.48/294.62 * CE 13 is refined into CE [196,197,198] 1131.48/294.62 1131.48/294.62 1131.48/294.62 ### Cost equations --> "Loop" of start/5 1131.48/294.62 * CEs [173,186] --> Loop 58 1131.48/294.62 * CEs [142,197] --> Loop 59 1131.48/294.62 * CEs [144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,196] --> Loop 60 1131.48/294.62 * CEs [143,165,166,167,168,169,170,171,172,174,175,176,177,178,179,180,181,182,183,184,185,187,188,189,190,191,192,193,194,195,198] --> Loop 61 1131.48/294.62 1131.48/294.62 ### Ranking functions of CR start(V1,V,V9,V14,V22) 1131.48/294.62 1131.48/294.62 #### Partial ranking functions of CR start(V1,V,V9,V14,V22) 1131.48/294.62 1131.48/294.62 1131.48/294.62 Computing Bounds 1131.48/294.62 ===================================== 1131.48/294.62 1131.48/294.62 #### Cost of chains of ge(V1,V,Out): 1131.48/294.62 * Chain [[20],23]: 1*it(20)+1 1131.48/294.62 Such that:it(20) =< V1 1131.48/294.62 1131.48/294.62 with precondition: [Out=1,V1>=1,V>=V1+1] 1131.48/294.62 1131.48/294.62 * Chain [[20],22]: 1*it(20)+1 1131.48/294.62 Such that:it(20) =< V 1131.48/294.62 1131.48/294.62 with precondition: [Out=2,V>=1,V1>=V] 1131.48/294.62 1131.48/294.62 * Chain [[20],21]: 1*it(20)+0 1131.48/294.62 Such that:it(20) =< V 1131.48/294.62 1131.48/294.62 with precondition: [Out=0,V1>=1,V>=1] 1131.48/294.62 1131.48/294.62 * Chain [23]: 1 1131.48/294.62 with precondition: [V1=0,Out=1,V>=1] 1131.48/294.62 1131.48/294.62 * Chain [22]: 1 1131.48/294.62 with precondition: [V=0,Out=2,V1>=0] 1131.48/294.62 1131.48/294.62 * Chain [21]: 0 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of helpc(V1,V,V9,Out): 1131.48/294.62 * Chain [26]: 1 1131.48/294.62 with precondition: [V1=1,V9=Out,V>=0,V9>=0] 1131.48/294.62 1131.48/294.62 * Chain [25]: 1 1131.48/294.62 with precondition: [V1=2,V=Out,V>=0,V9>=0] 1131.48/294.62 1131.48/294.62 * Chain [24]: 0 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0,V9>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of length(V1,Out): 1131.48/294.62 * Chain [[27],28]: 1*it(27)+1 1131.48/294.62 Such that:it(27) =< V1 1131.48/294.62 1131.48/294.62 with precondition: [Out>=1,V1>=Out] 1131.48/294.62 1131.48/294.62 * Chain [28]: 1 1131.48/294.62 with precondition: [Out=0,V1>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of greater(V1,V,Out): 1131.48/294.62 * Chain [31]: 9*s(3)+5*s(6)+4 1131.48/294.62 Such that:aux(5) =< V1 1131.48/294.62 aux(6) =< V 1131.48/294.62 s(6) =< aux(5) 1131.48/294.62 s(3) =< aux(6) 1131.48/294.62 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 * Chain [30]: 2*s(18)+2*s(20)+5 1131.48/294.62 Such that:aux(7) =< V 1131.48/294.62 aux(8) =< V1 1131.48/294.62 s(18) =< aux(8) 1131.48/294.62 s(20) =< aux(7) 1131.48/294.62 1131.48/294.62 with precondition: [V1=Out,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 * Chain [29]: 3*s(22)+1*s(23)+5 1131.48/294.62 Such that:s(23) =< V1 1131.48/294.62 aux(10) =< V 1131.48/294.62 s(22) =< aux(10) 1131.48/294.62 1131.48/294.62 with precondition: [V=Out,V1>=0,V>=1] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of smaller(V1,V,Out): 1131.48/294.62 * Chain [34]: 9*s(27)+5*s(30)+4 1131.48/294.62 Such that:aux(15) =< V1 1131.48/294.62 aux(16) =< V 1131.48/294.62 s(30) =< aux(15) 1131.48/294.62 s(27) =< aux(16) 1131.48/294.62 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 * Chain [33]: 3*s(42)+1*s(43)+5 1131.48/294.62 Such that:s(43) =< V1 1131.48/294.62 aux(18) =< V 1131.48/294.62 s(42) =< aux(18) 1131.48/294.62 1131.48/294.62 with precondition: [V1=Out,V1>=0,V>=1] 1131.48/294.62 1131.48/294.62 * Chain [32]: 2*s(46)+2*s(48)+5 1131.48/294.62 Such that:aux(19) =< V 1131.48/294.62 aux(20) =< V1 1131.48/294.62 s(46) =< aux(20) 1131.48/294.62 s(48) =< aux(19) 1131.48/294.62 1131.48/294.62 with precondition: [V=Out,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of helpa(V1,V,V9,V14,Out): 1131.48/294.62 * Chain [[35,36,37,38,39,40],48]: 69*it(35)+13*it(39)+13*s(50)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+13 1131.48/294.62 Such that:aux(118) =< V1+V9+V14 1131.48/294.62 aux(143) =< V+2*V9+2*V14 1131.48/294.62 aux(149) =< -V1+V 1131.48/294.62 aux(150) =< V 1131.48/294.62 aux(151) =< V9+V14 1131.48/294.62 aux(152) =< V14 1131.48/294.62 s(50) =< aux(150) 1131.48/294.62 s(56) =< aux(151) 1131.48/294.62 it(35) =< aux(149) 1131.48/294.62 it(39) =< aux(149) 1131.48/294.62 aux(87) =< aux(151) 1131.48/294.62 aux(86) =< aux(150) 1131.48/294.62 aux(113) =< aux(151)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(151) 1131.48/294.62 s(274) =< it(35)*aux(150) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77)+aux(152) 1131.48/294.62 s(302) =< aux(105)+aux(77)+aux(152) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(118) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(118) 1131.48/294.62 it(39) =< aux(105)+aux(77)+aux(152) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=1,V9>=0,V14>=0,Out>=1,V>=V1+1,V9+V14>=1] 1131.48/294.62 1131.48/294.62 * Chain [48]: 3*s(50)+10*s(51)+96*s(56)+168*s(57)+13 1131.48/294.62 Such that:aux(57) =< V1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(59) =< V9 1131.48/294.62 aux(60) =< V14 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(57) =< aux(60) 1131.48/294.62 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0,V9>=0,V14>=0] 1131.48/294.62 1131.48/294.62 * Chain [47]: 3 1131.48/294.62 with precondition: [V=0,Out=0,V1>=0,V9>=0,V14>=0] 1131.48/294.62 1131.48/294.62 * Chain [46,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+271*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+11*s(307)+26 1131.48/294.62 Such that:aux(143) =< V+2*V9 1131.48/294.62 aux(154) =< V14 1131.48/294.62 aux(155) =< V 1131.48/294.62 aux(156) =< V9 1131.48/294.62 it(35) =< aux(155) 1131.48/294.62 s(56) =< aux(156) 1131.48/294.62 it(39) =< aux(155) 1131.48/294.62 aux(87) =< aux(156) 1131.48/294.62 aux(86) =< aux(155) 1131.48/294.62 aux(113) =< aux(156)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(156) 1131.48/294.62 s(274) =< it(35)*aux(155) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77) 1131.48/294.62 s(302) =< aux(105)+aux(77) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(156) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(156) 1131.48/294.62 it(39) =< aux(105)+aux(77) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(307) =< aux(154) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=2,V14>=0,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [46,48]: 3*s(50)+10*s(51)+96*s(56)+7*s(306)+11*s(307)+26 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(153) =< V9 1131.48/294.62 aux(59) =< V9-Out 1131.48/294.62 aux(154) =< V14 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(306) =< aux(153) 1131.48/294.62 s(307) =< aux(154) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V14>=0,Out>=1,V9>=Out] 1131.48/294.62 1131.48/294.62 * Chain [45,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+276*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+6*s(312)+26 1131.48/294.62 Such that:aux(143) =< V+2*V14 1131.48/294.62 aux(157) =< V9 1131.48/294.62 aux(159) =< V 1131.48/294.62 aux(160) =< V14 1131.48/294.62 it(35) =< aux(159) 1131.48/294.62 s(56) =< aux(160) 1131.48/294.62 it(39) =< aux(159) 1131.48/294.62 aux(87) =< aux(160) 1131.48/294.62 aux(86) =< aux(159) 1131.48/294.62 aux(113) =< aux(160)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(160) 1131.48/294.62 s(274) =< it(35)*aux(159) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77) 1131.48/294.62 s(302) =< aux(105)+aux(77) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(160) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(160) 1131.48/294.62 it(39) =< aux(105)+aux(77) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(312) =< aux(157) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=0,V14>=2,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [45,48]: 3*s(50)+10*s(51)+96*s(56)+6*s(312)+12*s(314)+26 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(157) =< V9 1131.48/294.62 aux(158) =< V14 1131.48/294.62 aux(59) =< V14-Out 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(312) =< aux(157) 1131.48/294.62 s(314) =< aux(158) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] 1131.48/294.62 1131.48/294.62 * Chain [44,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+3*s(321)+5*s(322)+27 1131.48/294.62 Such that:aux(143) =< V+4*V9 1131.48/294.62 aux(161) =< V14 1131.48/294.62 aux(163) =< V 1131.48/294.62 aux(164) =< V9 1131.48/294.62 aux(165) =< 2*V9 1131.48/294.62 it(35) =< aux(163) 1131.48/294.62 s(56) =< aux(165) 1131.48/294.62 it(39) =< aux(163) 1131.48/294.62 aux(87) =< aux(165) 1131.48/294.62 aux(86) =< aux(163) 1131.48/294.62 aux(113) =< aux(165)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(165) 1131.48/294.62 s(274) =< it(35)*aux(163) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77)+aux(164) 1131.48/294.62 s(302) =< aux(105)+aux(77)+aux(164) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(165) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(165) 1131.48/294.62 it(39) =< aux(105)+aux(77)+aux(164) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(321) =< aux(164) 1131.48/294.62 s(322) =< aux(161) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=1,V14>=1,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [44,48]: 3*s(50)+10*s(51)+96*s(56)+171*s(57)+5*s(322)+27 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(59) =< V9-Out 1131.48/294.62 aux(161) =< V14 1131.48/294.62 aux(166) =< V9 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(57) =< aux(166) 1131.48/294.62 s(322) =< aux(161) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V14>=1,Out>=1,V9>=Out] 1131.48/294.62 1131.48/294.62 * Chain [43,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+2*s(326)+6*s(328)+27 1131.48/294.62 Such that:aux(143) =< V+2*V9+2*V14 1131.48/294.62 aux(167) =< V14 1131.48/294.62 aux(169) =< V 1131.48/294.62 aux(170) =< V9 1131.48/294.62 aux(171) =< V9+V14 1131.48/294.62 it(35) =< aux(169) 1131.48/294.62 s(56) =< aux(171) 1131.48/294.62 it(39) =< aux(169) 1131.48/294.62 aux(87) =< aux(171) 1131.48/294.62 aux(86) =< aux(169) 1131.48/294.62 aux(113) =< aux(171)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(171) 1131.48/294.62 s(274) =< it(35)*aux(169) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77)+aux(170) 1131.48/294.62 s(302) =< aux(105)+aux(77)+aux(170) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(171) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(171) 1131.48/294.62 it(39) =< aux(105)+aux(77)+aux(170) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(326) =< aux(170) 1131.48/294.62 s(328) =< aux(167) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=0,V14>=1,Out>=2,V9+V14>=2] 1131.48/294.62 1131.48/294.62 * Chain [43,48]: 3*s(50)+10*s(51)+96*s(56)+170*s(57)+6*s(328)+27 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(167) =< V14 1131.48/294.62 aux(59) =< V14-Out 1131.48/294.62 aux(172) =< V9 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(57) =< aux(172) 1131.48/294.62 s(328) =< aux(167) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] 1131.48/294.62 1131.48/294.62 * Chain [42,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+4*s(334)+4*s(335)+27 1131.48/294.62 Such that:aux(143) =< V+2*V9+2*V14 1131.48/294.62 aux(173) =< V9 1131.48/294.62 aux(175) =< V 1131.48/294.62 aux(176) =< V9+V14 1131.48/294.62 aux(177) =< V14 1131.48/294.62 it(35) =< aux(175) 1131.48/294.62 s(56) =< aux(176) 1131.48/294.62 it(39) =< aux(175) 1131.48/294.62 aux(87) =< aux(176) 1131.48/294.62 aux(86) =< aux(175) 1131.48/294.62 aux(113) =< aux(176)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(176) 1131.48/294.62 s(274) =< it(35)*aux(175) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77)+aux(177) 1131.48/294.62 s(302) =< aux(105)+aux(77)+aux(177) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(176) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(176) 1131.48/294.62 it(39) =< aux(105)+aux(77)+aux(177) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(334) =< aux(173) 1131.48/294.62 s(335) =< aux(177) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=1,V14>=0,Out>=2,V9+V14>=2] 1131.48/294.62 1131.48/294.62 * Chain [42,48]: 3*s(50)+10*s(51)+96*s(56)+172*s(57)+4*s(334)+27 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(173) =< V9 1131.48/294.62 aux(59) =< V9-Out 1131.48/294.62 aux(178) =< V14 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(57) =< aux(178) 1131.48/294.62 s(334) =< aux(173) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V14>=0,Out>=1,V9>=Out] 1131.48/294.62 1131.48/294.62 * Chain [41,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+3*s(340)+5*s(342)+27 1131.48/294.62 Such that:aux(143) =< V+4*V14 1131.48/294.62 aux(179) =< V9 1131.48/294.62 aux(181) =< V 1131.48/294.62 aux(182) =< V14 1131.48/294.62 aux(183) =< 2*V14 1131.48/294.62 it(35) =< aux(181) 1131.48/294.62 s(56) =< aux(183) 1131.48/294.62 it(39) =< aux(181) 1131.48/294.62 aux(87) =< aux(183) 1131.48/294.62 aux(86) =< aux(181) 1131.48/294.62 aux(113) =< aux(183)-1 1131.48/294.62 aux(116) =< it(35)*aux(143) 1131.48/294.62 aux(77) =< it(35)*aux(183) 1131.48/294.62 s(274) =< it(35)*aux(181) 1131.48/294.62 aux(126) =< it(35)*aux(87) 1131.48/294.62 s(279) =< it(35)*aux(86) 1131.48/294.62 aux(105) =< it(35)*aux(113) 1131.48/294.62 s(297) =< aux(105)+aux(77)+aux(182) 1131.48/294.62 s(302) =< aux(105)+aux(77)+aux(182) 1131.48/294.62 s(298) =< aux(116)+aux(116)+aux(183) 1131.48/294.62 s(302) =< aux(116)+aux(116)+aux(183) 1131.48/294.62 it(39) =< aux(105)+aux(77)+aux(182) 1131.48/294.62 s(297) =< it(39)*aux(87) 1131.48/294.62 s(298) =< it(39)*aux(87) 1131.48/294.62 s(294) =< it(39)*aux(86) 1131.48/294.62 s(280) =< aux(126) 1131.48/294.62 s(301) =< s(302) 1131.48/294.62 s(295) =< s(298) 1131.48/294.62 s(296) =< s(297) 1131.48/294.62 s(275) =< aux(77) 1131.48/294.62 s(340) =< aux(179) 1131.48/294.62 s(342) =< aux(182) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=2,V9>=0,V14>=1,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [41,48]: 3*s(50)+10*s(51)+96*s(56)+173*s(57)+3*s(340)+27 1131.48/294.62 Such that:aux(57) =< 1 1131.48/294.62 aux(58) =< V 1131.48/294.62 aux(179) =< V9 1131.48/294.62 aux(59) =< V14-Out 1131.48/294.62 aux(184) =< V14 1131.48/294.62 s(51) =< aux(57) 1131.48/294.62 s(50) =< aux(58) 1131.48/294.62 s(56) =< aux(59) 1131.48/294.62 s(57) =< aux(184) 1131.48/294.62 s(340) =< aux(179) 1131.48/294.62 1131.48/294.62 with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of plus(V1,V,Out): 1131.48/294.62 * Chain [[49],51]: 1*it(49)+1 1131.48/294.62 Such that:it(49) =< V 1131.48/294.62 1131.48/294.62 with precondition: [V+V1=Out,V1>=0,V>=1] 1131.48/294.62 1131.48/294.62 * Chain [[49],50]: 1*it(49)+0 1131.48/294.62 Such that:it(49) =< Out 1131.48/294.62 1131.48/294.62 with precondition: [V1>=0,Out>=1,V>=Out] 1131.48/294.62 1131.48/294.62 * Chain [51]: 1 1131.48/294.62 with precondition: [V=0,V1=Out,V1>=0] 1131.48/294.62 1131.48/294.62 * Chain [50]: 0 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of app(V1,V,Out): 1131.48/294.62 * Chain [57]: 968*s(585)+1699*s(586)+3*s(660)+17 1131.48/294.62 Such that:s(656) =< V1+V 1131.48/294.62 aux(217) =< V1 1131.48/294.62 aux(218) =< V 1131.48/294.62 s(585) =< aux(217) 1131.48/294.62 s(586) =< aux(218) 1131.48/294.62 s(660) =< s(656) 1131.48/294.62 1131.48/294.62 with precondition: [Out=0,V1>=0,V>=0] 1131.48/294.62 1131.48/294.62 * Chain [56]: 2409*s(674)+1584*s(687)+39*s(688)+18*s(694)+72*s(696)+3*s(701)+186*s(702)+33*s(703)+18*s(704)+36*s(705)+48*s(706)+869*s(707)+792*s(709)+39*s(710)+3*s(720)+93*s(721)+33*s(722)+18*s(723)+36*s(724)+24*s(725)+39*s(726)+3*s(736)+93*s(737)+33*s(738)+18*s(739)+36*s(740)+24*s(741)+792*s(742)+39*s(743)+3*s(753)+93*s(754)+33*s(755)+18*s(756)+36*s(757)+24*s(758)+39*s(769)+3*s(782)+93*s(783)+33*s(784)+18*s(785)+36*s(786)+24*s(787)+39*s(790)+3*s(800)+33*s(802)+18*s(803)+36*s(804)+31 1131.48/294.62 Such that:aux(227) =< V1 1131.48/294.62 aux(228) =< V1+V 1131.48/294.62 aux(229) =< 2*V1 1131.48/294.62 aux(230) =< 2*V1+V 1131.48/294.62 aux(231) =< 2*V1+3*V 1131.48/294.62 aux(232) =< 4*V1+V 1131.48/294.62 aux(233) =< V 1131.48/294.62 aux(234) =< 2*V 1131.48/294.62 aux(235) =< 3*V 1131.48/294.62 aux(236) =< 5*V 1131.48/294.62 s(674) =< aux(233) 1131.48/294.62 s(687) =< aux(228) 1131.48/294.62 s(688) =< aux(233) 1131.48/294.62 s(689) =< aux(228) 1131.48/294.62 s(690) =< aux(233) 1131.48/294.62 s(691) =< aux(228)-1 1131.48/294.62 s(692) =< s(674)*aux(231) 1131.48/294.62 s(693) =< s(674)*aux(228) 1131.48/294.62 s(694) =< s(674)*aux(233) 1131.48/294.62 s(695) =< s(674)*s(689) 1131.48/294.62 s(696) =< s(674)*s(690) 1131.48/294.62 s(697) =< s(674)*s(691) 1131.48/294.62 s(698) =< s(697)+s(693)+aux(227) 1131.48/294.62 s(699) =< s(697)+s(693)+aux(227) 1131.48/294.62 s(700) =< s(692)+s(692)+aux(228) 1131.48/294.62 s(699) =< s(692)+s(692)+aux(228) 1131.48/294.62 s(688) =< s(697)+s(693)+aux(227) 1131.48/294.62 s(698) =< s(688)*s(689) 1131.48/294.62 s(700) =< s(688)*s(689) 1131.48/294.62 s(701) =< s(688)*s(690) 1131.48/294.62 s(702) =< s(695) 1131.48/294.62 s(703) =< s(699) 1131.48/294.62 s(704) =< s(700) 1131.48/294.62 s(705) =< s(698) 1131.48/294.62 s(706) =< s(693) 1131.48/294.62 s(707) =< aux(227) 1131.48/294.62 s(709) =< aux(229) 1131.48/294.62 s(710) =< aux(233) 1131.48/294.62 s(711) =< aux(229) 1131.48/294.62 s(712) =< aux(229)-1 1131.48/294.62 s(713) =< s(674)*aux(232) 1131.48/294.62 s(714) =< s(674)*aux(229) 1131.48/294.62 s(715) =< s(674)*s(711) 1131.48/294.62 s(716) =< s(674)*s(712) 1131.48/294.62 s(717) =< s(716)+s(714)+aux(227) 1131.48/294.62 s(718) =< s(716)+s(714)+aux(227) 1131.48/294.62 s(719) =< s(713)+s(713)+aux(229) 1131.48/294.62 s(718) =< s(713)+s(713)+aux(229) 1131.48/294.62 s(710) =< s(716)+s(714)+aux(227) 1131.48/294.62 s(717) =< s(710)*s(711) 1131.48/294.62 s(719) =< s(710)*s(711) 1131.48/294.62 s(720) =< s(710)*s(690) 1131.48/294.62 s(721) =< s(715) 1131.48/294.62 s(722) =< s(718) 1131.48/294.62 s(723) =< s(719) 1131.48/294.62 s(724) =< s(717) 1131.48/294.62 s(725) =< s(714) 1131.48/294.62 s(726) =< aux(233) 1131.48/294.62 s(728) =< aux(233)-1 1131.48/294.62 s(729) =< s(674)*aux(235) 1131.48/294.62 s(730) =< s(674)*aux(233) 1131.48/294.62 s(731) =< s(674)*s(690) 1131.48/294.62 s(732) =< s(674)*s(728) 1131.48/294.62 s(733) =< s(732)+s(730) 1131.48/294.62 s(734) =< s(732)+s(730) 1131.48/294.62 s(735) =< s(729)+s(729)+aux(233) 1131.48/294.62 s(734) =< s(729)+s(729)+aux(233) 1131.48/294.62 s(726) =< s(732)+s(730) 1131.48/294.62 s(733) =< s(726)*s(690) 1131.48/294.62 s(735) =< s(726)*s(690) 1131.48/294.62 s(736) =< s(726)*s(690) 1131.48/294.62 s(737) =< s(731) 1131.48/294.62 s(738) =< s(734) 1131.48/294.62 s(739) =< s(735) 1131.48/294.62 s(740) =< s(733) 1131.48/294.62 s(741) =< s(730) 1131.48/294.62 s(742) =< aux(234) 1131.48/294.62 s(743) =< aux(233) 1131.48/294.62 s(744) =< aux(234) 1131.48/294.62 s(745) =< aux(234)-1 1131.48/294.62 s(746) =< s(674)*aux(236) 1131.48/294.62 s(747) =< s(674)*aux(234) 1131.48/294.62 s(748) =< s(674)*s(744) 1131.48/294.62 s(749) =< s(674)*s(745) 1131.48/294.62 s(750) =< s(749)+s(747)+aux(233) 1131.48/294.62 s(751) =< s(749)+s(747)+aux(233) 1131.48/294.62 s(752) =< s(746)+s(746)+aux(234) 1131.48/294.62 s(751) =< s(746)+s(746)+aux(234) 1131.48/294.62 s(743) =< s(749)+s(747)+aux(233) 1131.48/294.62 s(750) =< s(743)*s(744) 1131.48/294.62 s(752) =< s(743)*s(744) 1131.48/294.62 s(753) =< s(743)*s(690) 1131.48/294.62 s(754) =< s(748) 1131.48/294.62 s(755) =< s(751) 1131.48/294.62 s(756) =< s(752) 1131.48/294.62 s(757) =< s(750) 1131.48/294.62 s(758) =< s(747) 1131.48/294.62 s(769) =< aux(233) 1131.48/294.62 s(770) =< aux(227) 1131.48/294.62 s(772) =< aux(227)-1 1131.48/294.62 s(773) =< s(674)*aux(230) 1131.48/294.62 s(774) =< s(674)*aux(227) 1131.48/294.62 s(776) =< s(674)*s(770) 1131.48/294.62 s(778) =< s(674)*s(772) 1131.48/294.62 s(779) =< s(778)+s(774) 1131.48/294.62 s(780) =< s(778)+s(774) 1131.48/294.62 s(781) =< s(773)+s(773)+aux(227) 1131.48/294.62 s(780) =< s(773)+s(773)+aux(227) 1131.48/294.62 s(769) =< s(778)+s(774) 1131.48/294.62 s(779) =< s(769)*s(770) 1131.48/294.62 s(781) =< s(769)*s(770) 1131.48/294.62 s(782) =< s(769)*s(690) 1131.48/294.62 s(783) =< s(776) 1131.48/294.62 s(784) =< s(780) 1131.48/294.62 s(785) =< s(781) 1131.48/294.62 s(786) =< s(779) 1131.48/294.62 s(787) =< s(774) 1131.48/294.62 s(790) =< aux(233) 1131.48/294.62 s(797) =< s(697)+s(693)+aux(233) 1131.48/294.62 s(798) =< s(697)+s(693)+aux(233) 1131.48/294.62 s(799) =< s(692)+s(692)+aux(228) 1131.48/294.62 s(798) =< s(692)+s(692)+aux(228) 1131.48/294.62 s(790) =< s(697)+s(693)+aux(233) 1131.48/294.62 s(797) =< s(790)*s(689) 1131.48/294.62 s(799) =< s(790)*s(689) 1131.48/294.62 s(800) =< s(790)*s(690) 1131.48/294.62 s(802) =< s(798) 1131.48/294.62 s(803) =< s(799) 1131.48/294.62 s(804) =< s(797) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=0,V>=2,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [55]: 2430*s(1072)+150*s(1079)+907*s(1083)+9*s(1116)+31 1131.48/294.62 Such that:s(1111) =< V1+V 1131.48/294.62 aux(245) =< 1 1131.48/294.62 aux(246) =< V1 1131.48/294.62 aux(247) =< V 1131.48/294.62 s(1072) =< aux(247) 1131.48/294.62 s(1079) =< aux(245) 1131.48/294.62 s(1083) =< aux(246) 1131.48/294.62 s(1116) =< s(1111) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=0,Out>=1,V>=Out] 1131.48/294.62 1131.48/294.62 * Chain [54]: 634*s(1133)+1284*s(1145)+13*s(1146)+4*s(1152)+16*s(1154)+1*s(1159)+31*s(1160)+11*s(1161)+6*s(1162)+12*s(1163)+8*s(1164)+603*s(1166)+528*s(1167)+13*s(1168)+1*s(1178)+31*s(1179)+11*s(1180)+6*s(1181)+12*s(1182)+8*s(1183)+13*s(1184)+1*s(1194)+31*s(1195)+11*s(1196)+6*s(1197)+12*s(1198)+8*s(1199)+528*s(1200)+13*s(1201)+1*s(1211)+31*s(1212)+11*s(1213)+6*s(1214)+12*s(1215)+8*s(1216)+13*s(1232)+6*s(1238)+24*s(1240)+1*s(1245)+62*s(1246)+11*s(1247)+6*s(1248)+12*s(1249)+16*s(1250)+13*s(1254)+1*s(1264)+31*s(1265)+11*s(1266)+6*s(1267)+12*s(1268)+8*s(1269)+13*s(1270)+1*s(1280)+31*s(1281)+11*s(1282)+6*s(1283)+12*s(1284)+8*s(1285)+13*s(1287)+1*s(1297)+31*s(1298)+11*s(1299)+6*s(1300)+12*s(1301)+8*s(1302)+13*s(1314)+1*s(1327)+31*s(1328)+11*s(1329)+6*s(1330)+12*s(1331)+8*s(1332)+13*s(1335)+1*s(1345)+11*s(1347)+6*s(1348)+12*s(1349)+31 1131.48/294.62 Such that:s(1136) =< V1+2*V 1131.48/294.62 s(1222) =< V1+3*V 1131.48/294.62 s(1137) =< V1+4*V 1131.48/294.62 s(1223) =< V1+5*V 1131.48/294.62 s(1306) =< 3*V1+V 1131.48/294.62 s(1134) =< 3*V1+2*V 1131.48/294.62 s(1135) =< 5*V1 1131.48/294.62 s(1221) =< 5*V1+V 1131.48/294.62 aux(255) =< V1 1131.48/294.62 aux(256) =< V1+V 1131.48/294.62 aux(257) =< 2*V1 1131.48/294.62 aux(258) =< 3*V1+3*V 1131.48/294.62 aux(259) =< V 1131.48/294.62 aux(260) =< 2*V 1131.48/294.62 s(1133) =< aux(255) 1131.48/294.62 s(1145) =< aux(256) 1131.48/294.62 s(1146) =< aux(255) 1131.48/294.62 s(1147) =< aux(256) 1131.48/294.62 s(1148) =< aux(255) 1131.48/294.62 s(1149) =< aux(256)-1 1131.48/294.62 s(1150) =< s(1133)*s(1134) 1131.48/294.62 s(1151) =< s(1133)*aux(256) 1131.48/294.62 s(1152) =< s(1133)*aux(255) 1131.48/294.62 s(1153) =< s(1133)*s(1147) 1131.48/294.62 s(1154) =< s(1133)*s(1148) 1131.48/294.62 s(1155) =< s(1133)*s(1149) 1131.48/294.62 s(1156) =< s(1155)+s(1151)+aux(255) 1131.48/294.62 s(1157) =< s(1155)+s(1151)+aux(255) 1131.48/294.62 s(1158) =< s(1150)+s(1150)+aux(256) 1131.48/294.62 s(1157) =< s(1150)+s(1150)+aux(256) 1131.48/294.62 s(1146) =< s(1155)+s(1151)+aux(255) 1131.48/294.62 s(1156) =< s(1146)*s(1147) 1131.48/294.62 s(1158) =< s(1146)*s(1147) 1131.48/294.62 s(1159) =< s(1146)*s(1148) 1131.48/294.62 s(1160) =< s(1153) 1131.48/294.62 s(1161) =< s(1157) 1131.48/294.62 s(1162) =< s(1158) 1131.48/294.62 s(1163) =< s(1156) 1131.48/294.62 s(1164) =< s(1151) 1131.48/294.62 s(1166) =< aux(259) 1131.48/294.62 s(1167) =< aux(257) 1131.48/294.62 s(1168) =< aux(255) 1131.48/294.62 s(1169) =< aux(257) 1131.48/294.62 s(1170) =< aux(257)-1 1131.48/294.62 s(1171) =< s(1133)*s(1135) 1131.48/294.62 s(1172) =< s(1133)*aux(257) 1131.48/294.62 s(1173) =< s(1133)*s(1169) 1131.48/294.62 s(1174) =< s(1133)*s(1170) 1131.48/294.62 s(1175) =< s(1174)+s(1172)+aux(255) 1131.48/294.62 s(1176) =< s(1174)+s(1172)+aux(255) 1131.48/294.62 s(1177) =< s(1171)+s(1171)+aux(257) 1131.48/294.62 s(1176) =< s(1171)+s(1171)+aux(257) 1131.48/294.62 s(1168) =< s(1174)+s(1172)+aux(255) 1131.48/294.62 s(1175) =< s(1168)*s(1169) 1131.48/294.62 s(1177) =< s(1168)*s(1169) 1131.48/294.62 s(1178) =< s(1168)*s(1148) 1131.48/294.62 s(1179) =< s(1173) 1131.48/294.62 s(1180) =< s(1176) 1131.48/294.62 s(1181) =< s(1177) 1131.48/294.62 s(1182) =< s(1175) 1131.48/294.62 s(1183) =< s(1172) 1131.48/294.62 s(1184) =< aux(255) 1131.48/294.62 s(1185) =< aux(259) 1131.48/294.62 s(1186) =< aux(259)-1 1131.48/294.62 s(1187) =< s(1133)*s(1136) 1131.48/294.62 s(1188) =< s(1133)*aux(259) 1131.48/294.62 s(1189) =< s(1133)*s(1185) 1131.48/294.62 s(1190) =< s(1133)*s(1186) 1131.48/294.62 s(1191) =< s(1190)+s(1188) 1131.48/294.62 s(1192) =< s(1190)+s(1188) 1131.48/294.62 s(1193) =< s(1187)+s(1187)+aux(259) 1131.48/294.62 s(1192) =< s(1187)+s(1187)+aux(259) 1131.48/294.62 s(1184) =< s(1190)+s(1188) 1131.48/294.62 s(1191) =< s(1184)*s(1185) 1131.48/294.62 s(1193) =< s(1184)*s(1185) 1131.48/294.62 s(1194) =< s(1184)*s(1148) 1131.48/294.62 s(1195) =< s(1189) 1131.48/294.62 s(1196) =< s(1192) 1131.48/294.62 s(1197) =< s(1193) 1131.48/294.62 s(1198) =< s(1191) 1131.48/294.62 s(1199) =< s(1188) 1131.48/294.62 s(1200) =< aux(260) 1131.48/294.62 s(1201) =< aux(255) 1131.48/294.62 s(1202) =< aux(260) 1131.48/294.62 s(1203) =< aux(260)-1 1131.48/294.62 s(1204) =< s(1133)*s(1137) 1131.48/294.62 s(1205) =< s(1133)*aux(260) 1131.48/294.62 s(1206) =< s(1133)*s(1202) 1131.48/294.62 s(1207) =< s(1133)*s(1203) 1131.48/294.62 s(1208) =< s(1207)+s(1205)+aux(259) 1131.48/294.62 s(1209) =< s(1207)+s(1205)+aux(259) 1131.48/294.62 s(1210) =< s(1204)+s(1204)+aux(260) 1131.48/294.62 s(1209) =< s(1204)+s(1204)+aux(260) 1131.48/294.62 s(1201) =< s(1207)+s(1205)+aux(259) 1131.48/294.62 s(1208) =< s(1201)*s(1202) 1131.48/294.62 s(1210) =< s(1201)*s(1202) 1131.48/294.62 s(1211) =< s(1201)*s(1148) 1131.48/294.62 s(1212) =< s(1206) 1131.48/294.62 s(1213) =< s(1209) 1131.48/294.62 s(1214) =< s(1210) 1131.48/294.62 s(1215) =< s(1208) 1131.48/294.62 s(1216) =< s(1205) 1131.48/294.62 s(1232) =< aux(256) 1131.48/294.62 s(1236) =< s(1145)*aux(258) 1131.48/294.62 s(1237) =< s(1145)*aux(256) 1131.48/294.62 s(1238) =< s(1145)*aux(256) 1131.48/294.62 s(1239) =< s(1145)*s(1147) 1131.48/294.62 s(1240) =< s(1145)*s(1147) 1131.48/294.62 s(1241) =< s(1145)*s(1149) 1131.48/294.62 s(1242) =< s(1241)+s(1237)+aux(255) 1131.48/294.62 s(1243) =< s(1241)+s(1237)+aux(255) 1131.48/294.62 s(1244) =< s(1236)+s(1236)+aux(256) 1131.48/294.62 s(1243) =< s(1236)+s(1236)+aux(256) 1131.48/294.62 s(1232) =< s(1241)+s(1237)+aux(255) 1131.48/294.62 s(1242) =< s(1232)*s(1147) 1131.48/294.62 s(1244) =< s(1232)*s(1147) 1131.48/294.62 s(1245) =< s(1232)*s(1147) 1131.48/294.62 s(1246) =< s(1239) 1131.48/294.62 s(1247) =< s(1243) 1131.48/294.62 s(1248) =< s(1244) 1131.48/294.62 s(1249) =< s(1242) 1131.48/294.62 s(1250) =< s(1237) 1131.48/294.62 s(1254) =< aux(256) 1131.48/294.62 s(1257) =< s(1145)*s(1221) 1131.48/294.62 s(1258) =< s(1145)*aux(257) 1131.48/294.62 s(1259) =< s(1145)*s(1169) 1131.48/294.62 s(1260) =< s(1145)*s(1170) 1131.48/294.62 s(1261) =< s(1260)+s(1258)+aux(255) 1131.48/294.62 s(1262) =< s(1260)+s(1258)+aux(255) 1131.48/294.62 s(1263) =< s(1257)+s(1257)+aux(257) 1131.48/294.62 s(1262) =< s(1257)+s(1257)+aux(257) 1131.48/294.62 s(1254) =< s(1260)+s(1258)+aux(255) 1131.48/294.62 s(1261) =< s(1254)*s(1169) 1131.48/294.62 s(1263) =< s(1254)*s(1169) 1131.48/294.62 s(1264) =< s(1254)*s(1147) 1131.48/294.62 s(1265) =< s(1259) 1131.48/294.62 s(1266) =< s(1262) 1131.48/294.62 s(1267) =< s(1263) 1131.48/294.62 s(1268) =< s(1261) 1131.48/294.62 s(1269) =< s(1258) 1131.48/294.62 s(1270) =< aux(256) 1131.48/294.62 s(1273) =< s(1145)*s(1222) 1131.48/294.62 s(1274) =< s(1145)*aux(259) 1131.48/294.62 s(1275) =< s(1145)*s(1185) 1131.48/294.62 s(1276) =< s(1145)*s(1186) 1131.48/294.62 s(1277) =< s(1276)+s(1274) 1131.48/294.62 s(1278) =< s(1276)+s(1274) 1131.48/294.62 s(1279) =< s(1273)+s(1273)+aux(259) 1131.48/294.62 s(1278) =< s(1273)+s(1273)+aux(259) 1131.48/294.62 s(1270) =< s(1276)+s(1274) 1131.48/294.62 s(1277) =< s(1270)*s(1185) 1131.48/294.62 s(1279) =< s(1270)*s(1185) 1131.48/294.62 s(1280) =< s(1270)*s(1147) 1131.48/294.62 s(1281) =< s(1275) 1131.48/294.62 s(1282) =< s(1278) 1131.48/294.62 s(1283) =< s(1279) 1131.48/294.62 s(1284) =< s(1277) 1131.48/294.62 s(1285) =< s(1274) 1131.48/294.62 s(1287) =< aux(256) 1131.48/294.62 s(1290) =< s(1145)*s(1223) 1131.48/294.62 s(1291) =< s(1145)*aux(260) 1131.48/294.62 s(1292) =< s(1145)*s(1202) 1131.48/294.62 s(1293) =< s(1145)*s(1203) 1131.48/294.62 s(1294) =< s(1293)+s(1291)+aux(259) 1131.48/294.62 s(1295) =< s(1293)+s(1291)+aux(259) 1131.48/294.62 s(1296) =< s(1290)+s(1290)+aux(260) 1131.48/294.62 s(1295) =< s(1290)+s(1290)+aux(260) 1131.48/294.62 s(1287) =< s(1293)+s(1291)+aux(259) 1131.48/294.62 s(1294) =< s(1287)*s(1202) 1131.48/294.62 s(1296) =< s(1287)*s(1202) 1131.48/294.62 s(1297) =< s(1287)*s(1147) 1131.48/294.62 s(1298) =< s(1292) 1131.48/294.62 s(1299) =< s(1295) 1131.48/294.62 s(1300) =< s(1296) 1131.48/294.62 s(1301) =< s(1294) 1131.48/294.62 s(1302) =< s(1291) 1131.48/294.62 s(1314) =< aux(256) 1131.48/294.62 s(1317) =< aux(255)-1 1131.48/294.62 s(1318) =< s(1145)*s(1306) 1131.48/294.62 s(1319) =< s(1145)*aux(255) 1131.48/294.62 s(1321) =< s(1145)*s(1148) 1131.48/294.62 s(1323) =< s(1145)*s(1317) 1131.48/294.62 s(1324) =< s(1323)+s(1319) 1131.48/294.62 s(1325) =< s(1323)+s(1319) 1131.48/294.62 s(1326) =< s(1318)+s(1318)+aux(255) 1131.48/294.62 s(1325) =< s(1318)+s(1318)+aux(255) 1131.48/294.62 s(1314) =< s(1323)+s(1319) 1131.48/294.62 s(1324) =< s(1314)*s(1148) 1131.48/294.62 s(1326) =< s(1314)*s(1148) 1131.48/294.62 s(1327) =< s(1314)*s(1147) 1131.48/294.62 s(1328) =< s(1321) 1131.48/294.62 s(1329) =< s(1325) 1131.48/294.62 s(1330) =< s(1326) 1131.48/294.62 s(1331) =< s(1324) 1131.48/294.62 s(1332) =< s(1319) 1131.48/294.62 s(1335) =< aux(256) 1131.48/294.62 s(1342) =< s(1241)+s(1237)+aux(259) 1131.48/294.62 s(1343) =< s(1241)+s(1237)+aux(259) 1131.48/294.62 s(1344) =< s(1236)+s(1236)+aux(256) 1131.48/294.62 s(1343) =< s(1236)+s(1236)+aux(256) 1131.48/294.62 s(1335) =< s(1241)+s(1237)+aux(259) 1131.48/294.62 s(1342) =< s(1335)*s(1147) 1131.48/294.62 s(1344) =< s(1335)*s(1147) 1131.48/294.62 s(1345) =< s(1335)*s(1147) 1131.48/294.62 s(1347) =< s(1343) 1131.48/294.62 s(1348) =< s(1344) 1131.48/294.62 s(1349) =< s(1342) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=1,V>=1,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [53]: 440*s(1351)+13*s(1360)+2*s(1366)+8*s(1368)+1*s(1373)+31*s(1374)+11*s(1375)+6*s(1376)+12*s(1377)+8*s(1378)+15*s(1379)+264*s(1380)+13*s(1381)+1*s(1391)+31*s(1392)+11*s(1393)+6*s(1394)+12*s(1395)+8*s(1396)+31 1131.48/294.62 Such that:s(1354) =< V1+V 1131.48/294.62 s(1352) =< 3*V1 1131.48/294.62 s(1353) =< 3*V1+2*V 1131.48/294.62 s(1357) =< V 1131.48/294.62 aux(261) =< V1 1131.48/294.62 s(1351) =< aux(261) 1131.48/294.62 s(1360) =< aux(261) 1131.48/294.62 s(1361) =< aux(261) 1131.48/294.62 s(1363) =< aux(261)-1 1131.48/294.62 s(1364) =< s(1351)*s(1352) 1131.48/294.62 s(1365) =< s(1351)*aux(261) 1131.48/294.62 s(1366) =< s(1351)*aux(261) 1131.48/294.62 s(1367) =< s(1351)*s(1361) 1131.48/294.62 s(1368) =< s(1351)*s(1361) 1131.48/294.62 s(1369) =< s(1351)*s(1363) 1131.48/294.62 s(1370) =< s(1369)+s(1365) 1131.48/294.62 s(1371) =< s(1369)+s(1365) 1131.48/294.62 s(1372) =< s(1364)+s(1364)+aux(261) 1131.48/294.62 s(1371) =< s(1364)+s(1364)+aux(261) 1131.48/294.62 s(1360) =< s(1369)+s(1365) 1131.48/294.62 s(1370) =< s(1360)*s(1361) 1131.48/294.62 s(1372) =< s(1360)*s(1361) 1131.48/294.62 s(1373) =< s(1360)*s(1361) 1131.48/294.62 s(1374) =< s(1367) 1131.48/294.62 s(1375) =< s(1371) 1131.48/294.62 s(1376) =< s(1372) 1131.48/294.62 s(1377) =< s(1370) 1131.48/294.62 s(1378) =< s(1365) 1131.48/294.62 s(1379) =< s(1357) 1131.48/294.62 s(1380) =< s(1354) 1131.48/294.62 s(1381) =< aux(261) 1131.48/294.62 s(1382) =< s(1354) 1131.48/294.62 s(1383) =< s(1354)-1 1131.48/294.62 s(1384) =< s(1351)*s(1353) 1131.48/294.62 s(1385) =< s(1351)*s(1354) 1131.48/294.62 s(1386) =< s(1351)*s(1382) 1131.48/294.62 s(1387) =< s(1351)*s(1383) 1131.48/294.62 s(1388) =< s(1387)+s(1385)+s(1357) 1131.48/294.62 s(1389) =< s(1387)+s(1385)+s(1357) 1131.48/294.62 s(1390) =< s(1384)+s(1384)+s(1354) 1131.48/294.62 s(1389) =< s(1384)+s(1384)+s(1354) 1131.48/294.62 s(1381) =< s(1387)+s(1385)+s(1357) 1131.48/294.62 s(1388) =< s(1381)*s(1382) 1131.48/294.62 s(1390) =< s(1381)*s(1382) 1131.48/294.62 s(1391) =< s(1381)*s(1361) 1131.48/294.62 s(1392) =< s(1386) 1131.48/294.62 s(1393) =< s(1389) 1131.48/294.62 s(1394) =< s(1390) 1131.48/294.62 s(1395) =< s(1388) 1131.48/294.62 s(1396) =< s(1385) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=2,V>=0,Out>=2] 1131.48/294.62 1131.48/294.62 * Chain [52]: 975*s(1397)+150*s(1404)+2362*s(1406)+9*s(1441)+31 1131.48/294.62 Such that:s(1436) =< V1+V 1131.48/294.62 aux(271) =< 1 1131.48/294.62 aux(272) =< V1 1131.48/294.62 aux(273) =< V 1131.48/294.62 s(1397) =< aux(273) 1131.48/294.62 s(1404) =< aux(271) 1131.48/294.62 s(1406) =< aux(272) 1131.48/294.62 s(1441) =< s(1436) 1131.48/294.62 1131.48/294.62 with precondition: [V>=0,Out>=1,V1>=Out] 1131.48/294.62 1131.48/294.62 1131.48/294.62 #### Cost of chains of start(V1,V,V9,V14,V22): 1131.48/294.62 * Chain [61]: 10*s(1462)+8705*s(1463)+1130*s(1464)+1310*s(1465)+1056*s(1473)+138*s(1474)+26*s(1475)+2*s(1481)+8*s(1483)+2*s(1488)+62*s(1489)+22*s(1490)+12*s(1491)+24*s(1492)+16*s(1493)+6208*s(1497)+3153*s(1499)+39*s(1512)+24*s(1518)+96*s(1520)+3*s(1525)+186*s(1526)+33*s(1527)+18*s(1528)+36*s(1529)+48*s(1530)+1320*s(1532)+39*s(1533)+3*s(1543)+93*s(1544)+33*s(1545)+18*s(1546)+36*s(1547)+24*s(1548)+39*s(1549)+3*s(1558)+93*s(1559)+33*s(1560)+18*s(1561)+36*s(1562)+24*s(1563)+1320*s(1564)+39*s(1565)+3*s(1575)+93*s(1576)+33*s(1577)+18*s(1578)+36*s(1579)+24*s(1580)+39*s(1581)+3*s(1591)+93*s(1592)+33*s(1593)+18*s(1594)+36*s(1595)+24*s(1596)+39*s(1597)+3*s(1601)+33*s(1602)+18*s(1603)+36*s(1604)+360*s(1610)+13*s(1629)+6*s(1635)+24*s(1637)+1*s(1642)+62*s(1643)+11*s(1644)+6*s(1645)+12*s(1646)+16*s(1647)+13*s(1650)+1*s(1660)+31*s(1661)+11*s(1662)+6*s(1663)+12*s(1664)+8*s(1665)+13*s(1666)+1*s(1676)+31*s(1677)+11*s(1678)+6*s(1679)+12*s(1680)+8*s(1681)+13*s(1683)+1*s(1693)+31*s(1694)+11*s(1695)+6*s(1696)+12*s(1697)+8*s(1698)+13*s(1699)+6*s(1702)+24*s(1704)+1*s(1709)+62*s(1710)+11*s(1711)+6*s(1712)+12*s(1713)+16*s(1714)+13*s(1715)+1*s(1723)+31*s(1724)+11*s(1725)+6*s(1726)+12*s(1727)+8*s(1728)+13*s(1729)+1*s(1737)+31*s(1738)+11*s(1739)+6*s(1740)+12*s(1741)+8*s(1742)+13*s(1743)+1*s(1751)+31*s(1752)+11*s(1753)+6*s(1754)+12*s(1755)+8*s(1756)+13*s(1757)+1*s(1766)+31*s(1767)+11*s(1768)+6*s(1769)+12*s(1770)+8*s(1771)+13*s(1772)+1*s(1776)+11*s(1777)+6*s(1778)+12*s(1779)+13*s(1786)+1*s(1798)+31*s(1799)+11*s(1800)+6*s(1801)+12*s(1802)+8*s(1803)+13*s(1806)+1*s(1816)+11*s(1818)+6*s(1819)+12*s(1820)+13*s(1865)+1*s(1878)+62*s(1879)+11*s(1880)+6*s(1881)+12*s(1882)+16*s(1883)+264*s(1886)+13*s(1887)+1*s(1897)+31*s(1898)+11*s(1899)+6*s(1900)+12*s(1901)+8*s(1902)+13*s(1903)+1*s(1913)+31*s(1914)+11*s(1915)+6*s(1916)+12*s(1917)+8*s(1918)+264*s(1919)+13*s(1920)+1*s(1930)+31*s(1931)+11*s(1932)+6*s(1933)+12*s(1934)+8*s(1935)+13*s(1944)+1*s(1957)+31*s(1958)+11*s(1959)+6*s(1960)+12*s(1961)+8*s(1962)+13*s(1965)+1*s(1975)+11*s(1977)+6*s(1978)+12*s(1979)+31 1131.48/294.62 Such that:s(1458) =< V1+1 1131.48/294.62 s(1613) =< V1+2*V 1131.48/294.62 s(1614) =< V1+3*V 1131.48/294.62 s(1615) =< V1+4*V 1131.48/294.62 s(1616) =< V1+5*V 1131.48/294.62 s(1503) =< 2*V1+V 1131.48/294.62 s(1504) =< 2*V1+3*V 1131.48/294.62 s(1781) =< 3*V1 1131.48/294.62 s(1617) =< 3*V1+V 1131.48/294.62 s(1624) =< 3*V1+3*V 1131.48/294.62 s(1505) =< 4*V1+V 1131.48/294.62 s(1619) =< 5*V1 1131.48/294.62 s(1620) =< 5*V1+V 1131.48/294.62 s(1936) =< V+2*V9 1131.48/294.62 s(1854) =< V+4*V9 1131.48/294.62 s(1855) =< V+2*V14 1131.48/294.62 s(1856) =< V+4*V14 1131.48/294.62 s(1508) =< 3*V 1131.48/294.62 s(1509) =< 5*V 1131.48/294.62 s(1858) =< 2*V9 1131.48/294.62 s(1859) =< 2*V14 1131.48/294.62 aux(276) =< 1 1131.48/294.62 aux(277) =< -V1+V 1131.48/294.62 aux(278) =< V1 1131.48/294.62 aux(279) =< V1+V 1131.48/294.62 aux(280) =< V1+V9+V14 1131.48/294.62 aux(281) =< 2*V1 1131.48/294.62 aux(282) =< 3*V1+2*V 1131.48/294.62 aux(283) =< V 1131.48/294.62 aux(284) =< V+2*V9+2*V14 1131.48/294.62 aux(285) =< 2*V 1131.48/294.62 aux(286) =< V9 1131.48/294.62 aux(287) =< V9+V14 1131.48/294.62 aux(288) =< V14 1131.48/294.62 s(1497) =< aux(278) 1131.48/294.62 s(1463) =< aux(283) 1131.48/294.62 s(1610) =< aux(276) 1131.48/294.62 s(1499) =< aux(279) 1131.48/294.62 s(1465) =< aux(288) 1131.48/294.62 s(1464) =< aux(286) 1131.48/294.62 s(1473) =< aux(287) 1131.48/294.62 s(1474) =< aux(277) 1131.48/294.62 s(1475) =< aux(277) 1131.48/294.62 s(1476) =< aux(287) 1131.48/294.62 s(1477) =< aux(283) 1131.48/294.62 s(1478) =< aux(287)-1 1131.48/294.62 s(1479) =< s(1474)*aux(284) 1131.48/294.62 s(1480) =< s(1474)*aux(287) 1131.48/294.62 s(1481) =< s(1474)*aux(283) 1131.48/294.62 s(1482) =< s(1474)*s(1476) 1131.48/294.62 s(1483) =< s(1474)*s(1477) 1131.48/294.62 s(1484) =< s(1474)*s(1478) 1131.48/294.62 s(1485) =< s(1484)+s(1480)+aux(288) 1131.48/294.62 s(1486) =< s(1484)+s(1480)+aux(288) 1131.48/294.62 s(1487) =< s(1479)+s(1479)+aux(280) 1131.48/294.62 s(1486) =< s(1479)+s(1479)+aux(280) 1131.48/294.62 s(1475) =< s(1484)+s(1480)+aux(288) 1131.48/294.62 s(1485) =< s(1475)*s(1476) 1131.48/294.62 s(1487) =< s(1475)*s(1476) 1131.48/294.62 s(1488) =< s(1475)*s(1477) 1131.48/294.62 s(1489) =< s(1482) 1131.48/294.62 s(1490) =< s(1486) 1131.48/294.62 s(1491) =< s(1487) 1131.48/294.62 s(1492) =< s(1485) 1131.48/294.62 s(1493) =< s(1480) 1131.48/294.62 s(1512) =< aux(283) 1131.48/294.62 s(1513) =< aux(279) 1131.48/294.62 s(1515) =< aux(279)-1 1131.48/294.62 s(1516) =< s(1463)*s(1504) 1131.48/294.62 s(1517) =< s(1463)*aux(279) 1131.48/294.62 s(1518) =< s(1463)*aux(283) 1131.48/294.62 s(1519) =< s(1463)*s(1513) 1131.48/294.62 s(1520) =< s(1463)*s(1477) 1131.48/294.62 s(1521) =< s(1463)*s(1515) 1131.48/294.62 s(1522) =< s(1521)+s(1517)+aux(278) 1131.48/294.62 s(1523) =< s(1521)+s(1517)+aux(278) 1131.48/294.62 s(1524) =< s(1516)+s(1516)+aux(279) 1131.48/294.62 s(1523) =< s(1516)+s(1516)+aux(279) 1131.48/294.62 s(1512) =< s(1521)+s(1517)+aux(278) 1131.48/294.62 s(1522) =< s(1512)*s(1513) 1131.48/294.62 s(1524) =< s(1512)*s(1513) 1131.48/294.62 s(1525) =< s(1512)*s(1477) 1131.48/294.62 s(1526) =< s(1519) 1131.48/294.62 s(1527) =< s(1523) 1131.48/294.62 s(1528) =< s(1524) 1131.48/294.62 s(1529) =< s(1522) 1131.48/294.62 s(1530) =< s(1517) 1131.48/294.62 s(1532) =< aux(281) 1131.48/294.62 s(1533) =< aux(283) 1131.48/294.62 s(1534) =< aux(281) 1131.48/294.62 s(1535) =< aux(281)-1 1131.48/294.62 s(1536) =< s(1463)*s(1505) 1131.48/294.62 s(1537) =< s(1463)*aux(281) 1131.48/294.62 s(1538) =< s(1463)*s(1534) 1131.48/294.62 s(1539) =< s(1463)*s(1535) 1131.48/294.62 s(1540) =< s(1539)+s(1537)+aux(278) 1131.48/294.62 s(1541) =< s(1539)+s(1537)+aux(278) 1131.48/294.62 s(1542) =< s(1536)+s(1536)+aux(281) 1131.48/294.62 s(1541) =< s(1536)+s(1536)+aux(281) 1131.48/294.62 s(1533) =< s(1539)+s(1537)+aux(278) 1131.48/294.62 s(1540) =< s(1533)*s(1534) 1131.48/294.62 s(1542) =< s(1533)*s(1534) 1131.48/294.62 s(1543) =< s(1533)*s(1477) 1131.48/294.62 s(1544) =< s(1538) 1131.48/294.62 s(1545) =< s(1541) 1131.48/294.62 s(1546) =< s(1542) 1131.48/294.62 s(1547) =< s(1540) 1131.48/294.62 s(1548) =< s(1537) 1131.48/294.62 s(1549) =< aux(283) 1131.48/294.62 s(1550) =< aux(283)-1 1131.48/294.62 s(1551) =< s(1463)*s(1508) 1131.48/294.62 s(1552) =< s(1463)*aux(283) 1131.48/294.62 s(1553) =< s(1463)*s(1477) 1131.48/294.62 s(1554) =< s(1463)*s(1550) 1131.48/294.62 s(1555) =< s(1554)+s(1552) 1131.48/294.62 s(1556) =< s(1554)+s(1552) 1131.48/294.62 s(1557) =< s(1551)+s(1551)+aux(283) 1131.48/294.62 s(1556) =< s(1551)+s(1551)+aux(283) 1131.48/294.62 s(1549) =< s(1554)+s(1552) 1131.48/294.62 s(1555) =< s(1549)*s(1477) 1131.48/294.62 s(1557) =< s(1549)*s(1477) 1131.48/294.62 s(1558) =< s(1549)*s(1477) 1131.48/294.62 s(1559) =< s(1553) 1131.48/294.62 s(1560) =< s(1556) 1131.48/294.62 s(1561) =< s(1557) 1131.48/294.62 s(1562) =< s(1555) 1131.48/294.62 s(1563) =< s(1552) 1131.48/294.62 s(1564) =< aux(285) 1131.48/294.62 s(1565) =< aux(283) 1131.48/294.62 s(1566) =< aux(285) 1131.48/294.62 s(1567) =< aux(285)-1 1131.48/294.62 s(1568) =< s(1463)*s(1509) 1131.48/294.62 s(1569) =< s(1463)*aux(285) 1131.48/294.62 s(1570) =< s(1463)*s(1566) 1131.48/294.62 s(1571) =< s(1463)*s(1567) 1131.48/294.62 s(1572) =< s(1571)+s(1569)+aux(283) 1131.48/294.62 s(1573) =< s(1571)+s(1569)+aux(283) 1131.48/294.62 s(1574) =< s(1568)+s(1568)+aux(285) 1131.48/294.62 s(1573) =< s(1568)+s(1568)+aux(285) 1131.48/294.62 s(1565) =< s(1571)+s(1569)+aux(283) 1131.48/294.62 s(1572) =< s(1565)*s(1566) 1131.48/294.62 s(1574) =< s(1565)*s(1566) 1131.48/294.62 s(1575) =< s(1565)*s(1477) 1131.48/294.62 s(1576) =< s(1570) 1131.48/294.62 s(1577) =< s(1573) 1131.48/294.62 s(1578) =< s(1574) 1131.48/294.62 s(1579) =< s(1572) 1131.48/294.62 s(1580) =< s(1569) 1131.48/294.62 s(1581) =< aux(283) 1131.48/294.62 s(1582) =< aux(278) 1131.48/294.62 s(1583) =< aux(278)-1 1131.48/294.62 s(1584) =< s(1463)*s(1503) 1131.48/294.62 s(1585) =< s(1463)*aux(278) 1131.48/294.62 s(1586) =< s(1463)*s(1582) 1131.48/294.62 s(1587) =< s(1463)*s(1583) 1131.48/294.62 s(1588) =< s(1587)+s(1585) 1131.48/294.62 s(1589) =< s(1587)+s(1585) 1131.48/294.62 s(1590) =< s(1584)+s(1584)+aux(278) 1131.48/294.62 s(1589) =< s(1584)+s(1584)+aux(278) 1131.48/294.62 s(1581) =< s(1587)+s(1585) 1131.48/294.62 s(1588) =< s(1581)*s(1582) 1131.48/294.62 s(1590) =< s(1581)*s(1582) 1131.48/294.62 s(1591) =< s(1581)*s(1477) 1131.48/294.62 s(1592) =< s(1586) 1131.48/294.62 s(1593) =< s(1589) 1131.48/294.62 s(1594) =< s(1590) 1131.48/294.62 s(1595) =< s(1588) 1131.48/294.62 s(1596) =< s(1585) 1131.48/294.62 s(1597) =< aux(283) 1131.48/294.62 s(1598) =< s(1521)+s(1517)+aux(283) 1131.48/294.62 s(1599) =< s(1521)+s(1517)+aux(283) 1131.48/294.62 s(1600) =< s(1516)+s(1516)+aux(279) 1131.48/294.62 s(1599) =< s(1516)+s(1516)+aux(279) 1131.48/294.62 s(1597) =< s(1521)+s(1517)+aux(283) 1131.48/294.62 s(1598) =< s(1597)*s(1513) 1131.48/294.62 s(1600) =< s(1597)*s(1513) 1131.48/294.62 s(1601) =< s(1597)*s(1477) 1131.48/294.62 s(1602) =< s(1599) 1131.48/294.62 s(1603) =< s(1600) 1131.48/294.62 s(1604) =< s(1598) 1131.48/294.62 s(1629) =< aux(278) 1131.48/294.62 s(1633) =< s(1497)*aux(282) 1131.48/294.62 s(1634) =< s(1497)*aux(279) 1131.48/294.62 s(1635) =< s(1497)*aux(278) 1131.48/294.62 s(1636) =< s(1497)*s(1513) 1131.48/294.62 s(1637) =< s(1497)*s(1582) 1131.48/294.62 s(1638) =< s(1497)*s(1515) 1131.48/294.62 s(1639) =< s(1638)+s(1634)+aux(278) 1131.48/294.62 s(1640) =< s(1638)+s(1634)+aux(278) 1131.48/294.62 s(1641) =< s(1633)+s(1633)+aux(279) 1131.48/294.62 s(1640) =< s(1633)+s(1633)+aux(279) 1131.48/294.62 s(1629) =< s(1638)+s(1634)+aux(278) 1131.48/294.62 s(1639) =< s(1629)*s(1513) 1131.48/294.62 s(1641) =< s(1629)*s(1513) 1131.48/294.62 s(1642) =< s(1629)*s(1582) 1131.48/294.62 s(1643) =< s(1636) 1131.48/294.62 s(1644) =< s(1640) 1131.48/294.62 s(1645) =< s(1641) 1131.48/294.62 s(1646) =< s(1639) 1131.48/294.62 s(1647) =< s(1634) 1131.48/294.62 s(1650) =< aux(278) 1131.48/294.62 s(1653) =< s(1497)*s(1619) 1131.48/294.62 s(1654) =< s(1497)*aux(281) 1131.48/294.62 s(1655) =< s(1497)*s(1534) 1131.48/294.62 s(1656) =< s(1497)*s(1535) 1131.48/294.62 s(1657) =< s(1656)+s(1654)+aux(278) 1131.48/294.62 s(1658) =< s(1656)+s(1654)+aux(278) 1131.48/294.62 s(1659) =< s(1653)+s(1653)+aux(281) 1131.48/294.62 s(1658) =< s(1653)+s(1653)+aux(281) 1131.48/294.62 s(1650) =< s(1656)+s(1654)+aux(278) 1131.48/294.62 s(1657) =< s(1650)*s(1534) 1131.48/294.62 s(1659) =< s(1650)*s(1534) 1131.48/294.62 s(1660) =< s(1650)*s(1582) 1131.48/294.62 s(1661) =< s(1655) 1131.48/294.62 s(1662) =< s(1658) 1131.48/294.62 s(1663) =< s(1659) 1131.48/294.62 s(1664) =< s(1657) 1131.48/294.62 s(1665) =< s(1654) 1131.48/294.62 s(1666) =< aux(278) 1131.48/294.62 s(1669) =< s(1497)*s(1613) 1131.48/294.62 s(1670) =< s(1497)*aux(283) 1131.48/294.62 s(1671) =< s(1497)*s(1477) 1131.48/294.62 s(1672) =< s(1497)*s(1550) 1131.48/294.62 s(1673) =< s(1672)+s(1670) 1131.48/294.62 s(1674) =< s(1672)+s(1670) 1131.48/294.62 s(1675) =< s(1669)+s(1669)+aux(283) 1131.48/294.62 s(1674) =< s(1669)+s(1669)+aux(283) 1131.48/294.62 s(1666) =< s(1672)+s(1670) 1131.48/294.62 s(1673) =< s(1666)*s(1477) 1131.48/294.62 s(1675) =< s(1666)*s(1477) 1131.48/294.62 s(1676) =< s(1666)*s(1582) 1131.48/294.62 s(1677) =< s(1671) 1131.48/294.62 s(1678) =< s(1674) 1131.48/294.62 s(1679) =< s(1675) 1131.48/294.62 s(1680) =< s(1673) 1131.48/294.62 s(1681) =< s(1670) 1131.48/294.62 s(1683) =< aux(278) 1131.48/294.62 s(1686) =< s(1497)*s(1615) 1131.48/294.62 s(1687) =< s(1497)*aux(285) 1131.48/294.62 s(1688) =< s(1497)*s(1566) 1131.48/294.62 s(1689) =< s(1497)*s(1567) 1131.48/294.62 s(1690) =< s(1689)+s(1687)+aux(283) 1131.48/294.62 s(1691) =< s(1689)+s(1687)+aux(283) 1131.48/294.62 s(1692) =< s(1686)+s(1686)+aux(285) 1131.48/294.62 s(1691) =< s(1686)+s(1686)+aux(285) 1131.48/294.62 s(1683) =< s(1689)+s(1687)+aux(283) 1131.48/294.62 s(1690) =< s(1683)*s(1566) 1131.48/294.62 s(1692) =< s(1683)*s(1566) 1131.48/294.62 s(1693) =< s(1683)*s(1582) 1131.48/294.62 s(1694) =< s(1688) 1131.48/294.62 s(1695) =< s(1691) 1131.48/294.62 s(1696) =< s(1692) 1131.48/294.62 s(1697) =< s(1690) 1131.48/294.62 s(1698) =< s(1687) 1131.48/294.62 s(1699) =< aux(279) 1131.48/294.62 s(1700) =< s(1499)*s(1624) 1131.48/294.62 s(1701) =< s(1499)*aux(279) 1131.48/294.62 s(1702) =< s(1499)*aux(279) 1131.48/294.62 s(1703) =< s(1499)*s(1513) 1131.48/294.62 s(1704) =< s(1499)*s(1513) 1131.48/294.62 s(1705) =< s(1499)*s(1515) 1131.48/294.62 s(1706) =< s(1705)+s(1701)+aux(278) 1131.48/294.62 s(1707) =< s(1705)+s(1701)+aux(278) 1131.48/294.62 s(1708) =< s(1700)+s(1700)+aux(279) 1131.48/294.62 s(1707) =< s(1700)+s(1700)+aux(279) 1131.48/294.62 s(1699) =< s(1705)+s(1701)+aux(278) 1131.48/294.62 s(1706) =< s(1699)*s(1513) 1131.48/294.62 s(1708) =< s(1699)*s(1513) 1131.48/294.62 s(1709) =< s(1699)*s(1513) 1131.48/294.62 s(1710) =< s(1703) 1131.48/294.62 s(1711) =< s(1707) 1131.48/294.62 s(1712) =< s(1708) 1131.48/294.62 s(1713) =< s(1706) 1131.48/294.62 s(1714) =< s(1701) 1131.48/294.62 s(1715) =< aux(279) 1131.48/294.62 s(1716) =< s(1499)*s(1620) 1131.48/294.62 s(1717) =< s(1499)*aux(281) 1131.48/294.62 s(1718) =< s(1499)*s(1534) 1131.48/294.62 s(1719) =< s(1499)*s(1535) 1131.48/294.62 s(1720) =< s(1719)+s(1717)+aux(278) 1131.48/294.62 s(1721) =< s(1719)+s(1717)+aux(278) 1131.48/294.62 s(1722) =< s(1716)+s(1716)+aux(281) 1131.48/294.62 s(1721) =< s(1716)+s(1716)+aux(281) 1131.48/294.62 s(1715) =< s(1719)+s(1717)+aux(278) 1131.48/294.62 s(1720) =< s(1715)*s(1534) 1131.48/294.62 s(1722) =< s(1715)*s(1534) 1131.48/294.62 s(1723) =< s(1715)*s(1513) 1131.48/294.62 s(1724) =< s(1718) 1131.48/294.62 s(1725) =< s(1721) 1131.48/294.62 s(1726) =< s(1722) 1131.48/294.62 s(1727) =< s(1720) 1131.48/294.62 s(1728) =< s(1717) 1131.48/294.62 s(1729) =< aux(279) 1131.48/294.62 s(1730) =< s(1499)*s(1614) 1131.48/294.62 s(1731) =< s(1499)*aux(283) 1131.48/294.62 s(1732) =< s(1499)*s(1477) 1131.48/294.62 s(1733) =< s(1499)*s(1550) 1131.48/294.62 s(1734) =< s(1733)+s(1731) 1131.48/294.62 s(1735) =< s(1733)+s(1731) 1131.48/294.62 s(1736) =< s(1730)+s(1730)+aux(283) 1131.48/294.62 s(1735) =< s(1730)+s(1730)+aux(283) 1131.48/294.62 s(1729) =< s(1733)+s(1731) 1131.48/294.62 s(1734) =< s(1729)*s(1477) 1131.48/294.62 s(1736) =< s(1729)*s(1477) 1131.48/294.62 s(1737) =< s(1729)*s(1513) 1131.48/294.62 s(1738) =< s(1732) 1131.48/294.62 s(1739) =< s(1735) 1131.48/294.62 s(1740) =< s(1736) 1131.48/294.62 s(1741) =< s(1734) 1131.48/294.62 s(1742) =< s(1731) 1131.48/294.62 s(1743) =< aux(279) 1131.48/294.62 s(1744) =< s(1499)*s(1616) 1131.48/294.62 s(1745) =< s(1499)*aux(285) 1131.48/294.62 s(1746) =< s(1499)*s(1566) 1131.48/294.62 s(1747) =< s(1499)*s(1567) 1131.48/294.62 s(1748) =< s(1747)+s(1745)+aux(283) 1131.48/294.62 s(1749) =< s(1747)+s(1745)+aux(283) 1131.48/294.62 s(1750) =< s(1744)+s(1744)+aux(285) 1131.48/294.62 s(1749) =< s(1744)+s(1744)+aux(285) 1131.48/294.62 s(1743) =< s(1747)+s(1745)+aux(283) 1131.48/294.62 s(1748) =< s(1743)*s(1566) 1131.48/294.62 s(1750) =< s(1743)*s(1566) 1131.48/294.62 s(1751) =< s(1743)*s(1513) 1131.48/294.62 s(1752) =< s(1746) 1131.48/294.62 s(1753) =< s(1749) 1131.48/294.62 s(1754) =< s(1750) 1131.48/294.62 s(1755) =< s(1748) 1131.48/294.62 s(1756) =< s(1745) 1131.48/294.62 s(1757) =< aux(279) 1131.48/294.62 s(1759) =< s(1499)*s(1617) 1131.48/294.62 s(1760) =< s(1499)*aux(278) 1131.48/294.62 s(1761) =< s(1499)*s(1582) 1131.48/294.62 s(1762) =< s(1499)*s(1583) 1131.48/294.62 s(1763) =< s(1762)+s(1760) 1131.48/294.62 s(1764) =< s(1762)+s(1760) 1131.48/294.62 s(1765) =< s(1759)+s(1759)+aux(278) 1131.48/294.62 s(1764) =< s(1759)+s(1759)+aux(278) 1131.48/294.62 s(1757) =< s(1762)+s(1760) 1131.48/294.62 s(1763) =< s(1757)*s(1582) 1131.48/294.62 s(1765) =< s(1757)*s(1582) 1131.48/294.62 s(1766) =< s(1757)*s(1513) 1131.48/294.62 s(1767) =< s(1761) 1131.48/294.62 s(1768) =< s(1764) 1131.48/294.62 s(1769) =< s(1765) 1131.48/294.62 s(1770) =< s(1763) 1131.48/294.62 s(1771) =< s(1760) 1131.48/294.62 s(1772) =< aux(279) 1131.48/294.62 s(1773) =< s(1705)+s(1701)+aux(283) 1131.48/294.62 s(1774) =< s(1705)+s(1701)+aux(283) 1131.48/294.62 s(1775) =< s(1700)+s(1700)+aux(279) 1131.48/294.62 s(1774) =< s(1700)+s(1700)+aux(279) 1131.48/294.62 s(1772) =< s(1705)+s(1701)+aux(283) 1131.48/294.62 s(1773) =< s(1772)*s(1513) 1131.48/294.62 s(1775) =< s(1772)*s(1513) 1131.48/294.62 s(1776) =< s(1772)*s(1513) 1131.48/294.62 s(1777) =< s(1774) 1131.48/294.62 s(1778) =< s(1775) 1131.48/294.62 s(1779) =< s(1773) 1131.48/294.62 s(1786) =< aux(278) 1131.48/294.62 s(1789) =< s(1497)*s(1781) 1131.48/294.62 s(1790) =< s(1497)*aux(278) 1131.48/294.62 s(1792) =< s(1497)*s(1582) 1131.48/294.62 s(1794) =< s(1497)*s(1583) 1131.48/294.62 s(1795) =< s(1794)+s(1790) 1131.48/294.62 s(1796) =< s(1794)+s(1790) 1131.48/294.62 s(1797) =< s(1789)+s(1789)+aux(278) 1131.48/294.62 s(1796) =< s(1789)+s(1789)+aux(278) 1131.48/294.62 s(1786) =< s(1794)+s(1790) 1131.48/294.62 s(1795) =< s(1786)*s(1582) 1131.48/294.62 s(1797) =< s(1786)*s(1582) 1131.48/294.62 s(1798) =< s(1786)*s(1582) 1131.48/294.62 s(1799) =< s(1792) 1131.48/294.62 s(1800) =< s(1796) 1131.48/294.62 s(1801) =< s(1797) 1131.48/294.62 s(1802) =< s(1795) 1131.48/294.62 s(1803) =< s(1790) 1131.48/294.62 s(1806) =< aux(278) 1131.48/294.62 s(1813) =< s(1638)+s(1634)+aux(283) 1131.48/294.62 s(1814) =< s(1638)+s(1634)+aux(283) 1131.48/294.62 s(1815) =< s(1633)+s(1633)+aux(279) 1131.48/294.62 s(1814) =< s(1633)+s(1633)+aux(279) 1131.48/294.62 s(1806) =< s(1638)+s(1634)+aux(283) 1131.48/294.62 s(1813) =< s(1806)*s(1513) 1131.48/294.62 s(1815) =< s(1806)*s(1513) 1131.48/294.62 s(1816) =< s(1806)*s(1582) 1131.48/294.62 s(1818) =< s(1814) 1131.48/294.62 s(1819) =< s(1815) 1131.48/294.62 s(1820) =< s(1813) 1131.48/294.62 s(1462) =< s(1458) 1131.48/294.62 s(1865) =< aux(283) 1131.48/294.62 s(1869) =< s(1463)*aux(284) 1131.48/294.62 s(1870) =< s(1463)*aux(287) 1131.48/294.62 s(1872) =< s(1463)*s(1476) 1131.48/294.62 s(1874) =< s(1463)*s(1478) 1131.48/294.62 s(1875) =< s(1874)+s(1870)+aux(286) 1131.48/294.62 s(1876) =< s(1874)+s(1870)+aux(286) 1131.48/294.62 s(1877) =< s(1869)+s(1869)+aux(287) 1131.48/294.62 s(1876) =< s(1869)+s(1869)+aux(287) 1131.48/294.62 s(1865) =< s(1874)+s(1870)+aux(286) 1131.48/294.62 s(1875) =< s(1865)*s(1476) 1131.48/294.62 s(1877) =< s(1865)*s(1476) 1131.48/294.62 s(1878) =< s(1865)*s(1477) 1131.48/294.62 s(1879) =< s(1872) 1131.48/294.62 s(1880) =< s(1876) 1131.48/294.62 s(1881) =< s(1877) 1131.48/294.62 s(1882) =< s(1875) 1131.48/294.62 s(1883) =< s(1870) 1131.48/294.62 s(1886) =< s(1858) 1131.48/294.62 s(1887) =< aux(283) 1131.48/294.62 s(1888) =< s(1858) 1131.48/294.62 s(1889) =< s(1858)-1 1131.48/294.62 s(1890) =< s(1463)*s(1854) 1131.48/294.62 s(1891) =< s(1463)*s(1858) 1131.48/294.62 s(1892) =< s(1463)*s(1888) 1131.48/294.62 s(1893) =< s(1463)*s(1889) 1131.48/294.62 s(1894) =< s(1893)+s(1891)+aux(286) 1131.48/294.62 s(1895) =< s(1893)+s(1891)+aux(286) 1131.48/294.62 s(1896) =< s(1890)+s(1890)+s(1858) 1131.48/294.62 s(1895) =< s(1890)+s(1890)+s(1858) 1131.48/294.62 s(1887) =< s(1893)+s(1891)+aux(286) 1131.48/294.62 s(1894) =< s(1887)*s(1888) 1131.48/294.62 s(1896) =< s(1887)*s(1888) 1131.48/294.62 s(1897) =< s(1887)*s(1477) 1131.48/294.62 s(1898) =< s(1892) 1131.48/294.62 s(1899) =< s(1895) 1131.48/294.62 s(1900) =< s(1896) 1131.48/294.62 s(1901) =< s(1894) 1131.48/294.62 s(1902) =< s(1891) 1131.48/294.62 s(1903) =< aux(283) 1131.48/294.62 s(1904) =< aux(288) 1131.48/294.62 s(1905) =< aux(288)-1 1131.48/294.62 s(1906) =< s(1463)*s(1855) 1131.48/294.62 s(1907) =< s(1463)*aux(288) 1131.48/294.62 s(1908) =< s(1463)*s(1904) 1131.48/294.62 s(1909) =< s(1463)*s(1905) 1131.48/294.62 s(1910) =< s(1909)+s(1907) 1131.48/294.62 s(1911) =< s(1909)+s(1907) 1131.48/294.62 s(1912) =< s(1906)+s(1906)+aux(288) 1131.48/294.62 s(1911) =< s(1906)+s(1906)+aux(288) 1131.48/294.62 s(1903) =< s(1909)+s(1907) 1131.48/294.62 s(1910) =< s(1903)*s(1904) 1131.48/294.62 s(1912) =< s(1903)*s(1904) 1131.48/294.62 s(1913) =< s(1903)*s(1477) 1131.48/294.62 s(1914) =< s(1908) 1131.48/294.62 s(1915) =< s(1911) 1131.48/294.62 s(1916) =< s(1912) 1131.48/294.62 s(1917) =< s(1910) 1131.48/294.62 s(1918) =< s(1907) 1131.48/294.62 s(1919) =< s(1859) 1131.48/294.62 s(1920) =< aux(283) 1131.48/294.62 s(1921) =< s(1859) 1131.48/294.62 s(1922) =< s(1859)-1 1131.48/294.62 s(1923) =< s(1463)*s(1856) 1131.48/294.62 s(1924) =< s(1463)*s(1859) 1131.48/294.62 s(1925) =< s(1463)*s(1921) 1131.48/294.62 s(1926) =< s(1463)*s(1922) 1131.48/294.62 s(1927) =< s(1926)+s(1924)+aux(288) 1131.48/294.62 s(1928) =< s(1926)+s(1924)+aux(288) 1131.48/294.62 s(1929) =< s(1923)+s(1923)+s(1859) 1131.48/294.62 s(1928) =< s(1923)+s(1923)+s(1859) 1131.48/294.62 s(1920) =< s(1926)+s(1924)+aux(288) 1131.48/294.62 s(1927) =< s(1920)*s(1921) 1131.48/294.62 s(1929) =< s(1920)*s(1921) 1131.48/294.62 s(1930) =< s(1920)*s(1477) 1131.48/294.62 s(1931) =< s(1925) 1131.48/294.62 s(1932) =< s(1928) 1131.48/294.62 s(1933) =< s(1929) 1131.48/294.62 s(1934) =< s(1927) 1131.48/294.62 s(1935) =< s(1924) 1131.48/294.62 s(1944) =< aux(283) 1131.48/294.62 s(1945) =< aux(286) 1131.48/294.62 s(1947) =< aux(286)-1 1131.48/294.62 s(1948) =< s(1463)*s(1936) 1131.48/294.62 s(1949) =< s(1463)*aux(286) 1131.48/294.62 s(1951) =< s(1463)*s(1945) 1131.48/294.62 s(1953) =< s(1463)*s(1947) 1131.48/294.62 s(1954) =< s(1953)+s(1949) 1131.48/294.62 s(1955) =< s(1953)+s(1949) 1131.48/294.62 s(1956) =< s(1948)+s(1948)+aux(286) 1131.48/294.62 s(1955) =< s(1948)+s(1948)+aux(286) 1131.48/294.62 s(1944) =< s(1953)+s(1949) 1131.48/294.62 s(1954) =< s(1944)*s(1945) 1131.48/294.62 s(1956) =< s(1944)*s(1945) 1131.48/294.62 s(1957) =< s(1944)*s(1477) 1131.48/294.62 s(1958) =< s(1951) 1131.48/294.62 s(1959) =< s(1955) 1131.48/294.62 s(1960) =< s(1956) 1131.48/294.62 s(1961) =< s(1954) 1131.48/294.62 s(1962) =< s(1949) 1131.48/294.62 s(1965) =< aux(283) 1131.48/294.62 s(1972) =< s(1874)+s(1870)+aux(288) 1131.48/294.62 s(1973) =< s(1874)+s(1870)+aux(288) 1131.48/294.62 s(1974) =< s(1869)+s(1869)+aux(287) 1131.48/294.62 s(1973) =< s(1869)+s(1869)+aux(287) 1131.48/294.62 s(1965) =< s(1874)+s(1870)+aux(288) 1131.48/294.62 s(1972) =< s(1965)*s(1476) 1131.48/294.62 s(1974) =< s(1965)*s(1476) 1131.48/294.62 s(1975) =< s(1965)*s(1477) 1131.48/294.62 s(1977) =< s(1973) 1131.48/294.62 s(1978) =< s(1974) 1131.48/294.62 s(1979) =< s(1972) 1131.48/294.62 1131.48/294.62 with precondition: [V1>=0] 1131.48/294.62 1131.48/294.62 * Chain [60]: 986*s(2044)+1058*s(2045)+60*s(2054)+96*s(2055)+414*s(2074)+13*s(2075)+6*s(2081)+24*s(2083)+1*s(2088)+31*s(2089)+11*s(2090)+6*s(2091)+12*s(2092)+8*s(2093)+264*s(2123)+13*s(2125)+1*s(2138)+31*s(2139)+11*s(2140)+6*s(2141)+12*s(2142)+8*s(2143)+528*s(2175)+13*s(2177)+1*s(2190)+62*s(2191)+11*s(2192)+6*s(2193)+12*s(2194)+16*s(2195)+13*s(2227)+1*s(2240)+31*s(2241)+11*s(2242)+6*s(2243)+12*s(2244)+8*s(2245)+13*s(2275)+1*s(2288)+11*s(2290)+6*s(2291)+12*s(2292)+264*s(2323)+13*s(2325)+1*s(2338)+31*s(2339)+11*s(2340)+6*s(2341)+12*s(2342)+8*s(2343)+25 1131.48/294.62 Such that:s(2066) =< V+V14 1131.48/294.62 s(2116) =< V+2*V14 1131.48/294.62 s(2218) =< V+V22 1131.48/294.62 s(2316) =< V+2*V22 1131.48/294.62 s(2067) =< V9+2*V14 1131.48/294.62 s(2117) =< V9+4*V14 1131.48/294.62 s(2219) =< V9+2*V22 1131.48/294.62 s(2317) =< V9+4*V22 1131.48/294.62 s(2120) =< 2*V14 1131.48/294.62 s(2320) =< 2*V22 1131.48/294.62 aux(331) =< -V+V9 1131.48/294.62 aux(332) =< V+1 1131.48/294.62 aux(333) =< V+V14+V22 1131.48/294.62 aux(334) =< V9 1131.48/294.62 aux(335) =< V9+2*V14+2*V22 1131.48/294.62 aux(336) =< V14 1131.48/294.62 aux(337) =< V14+V22 1131.48/294.62 aux(338) =< V22 1131.48/294.62 s(2055) =< aux(334) 1131.48/294.62 s(2044) =< aux(336) 1131.48/294.62 s(2074) =< aux(331) 1131.48/294.62 s(2075) =< aux(331) 1131.48/294.62 s(2076) =< aux(336) 1131.48/294.62 s(2077) =< aux(334) 1131.48/294.62 s(2078) =< aux(336)-1 1131.48/294.62 s(2079) =< s(2074)*s(2067) 1131.48/294.62 s(2080) =< s(2074)*aux(336) 1131.48/294.62 s(2081) =< s(2074)*aux(334) 1131.48/294.62 s(2082) =< s(2074)*s(2076) 1131.48/294.62 s(2083) =< s(2074)*s(2077) 1131.48/294.62 s(2084) =< s(2074)*s(2078) 1131.48/294.62 s(2085) =< s(2084)+s(2080) 1131.48/294.62 s(2086) =< s(2084)+s(2080) 1131.48/294.62 s(2087) =< s(2079)+s(2079)+s(2066) 1131.48/294.62 s(2086) =< s(2079)+s(2079)+s(2066) 1131.48/294.62 s(2075) =< s(2084)+s(2080) 1131.48/294.62 s(2085) =< s(2075)*s(2076) 1131.48/294.62 s(2087) =< s(2075)*s(2076) 1131.48/294.62 s(2088) =< s(2075)*s(2077) 1131.48/294.62 s(2089) =< s(2082) 1131.48/294.62 s(2090) =< s(2086) 1131.48/294.62 s(2091) =< s(2087) 1131.48/294.62 s(2092) =< s(2085) 1131.48/294.62 s(2093) =< s(2080) 1131.48/294.62 s(2045) =< aux(338) 1131.48/294.62 s(2123) =< s(2120) 1131.48/294.62 s(2125) =< aux(331) 1131.48/294.62 s(2126) =< s(2120) 1131.48/294.62 s(2128) =< s(2120)-1 1131.48/294.62 s(2129) =< s(2074)*s(2117) 1131.48/294.62 s(2130) =< s(2074)*s(2120) 1131.48/294.62 s(2132) =< s(2074)*s(2126) 1131.48/294.62 s(2134) =< s(2074)*s(2128) 1131.48/294.62 s(2135) =< s(2134)+s(2130)+aux(336) 1131.48/294.62 s(2136) =< s(2134)+s(2130)+aux(336) 1131.48/294.62 s(2137) =< s(2129)+s(2129)+s(2116) 1131.48/294.62 s(2136) =< s(2129)+s(2129)+s(2116) 1131.48/294.62 s(2125) =< s(2134)+s(2130)+aux(336) 1131.48/294.62 s(2135) =< s(2125)*s(2126) 1131.48/294.62 s(2137) =< s(2125)*s(2126) 1131.48/294.62 s(2138) =< s(2125)*s(2077) 1131.48/294.62 s(2139) =< s(2132) 1131.48/294.62 s(2140) =< s(2136) 1131.48/294.62 s(2141) =< s(2137) 1131.48/294.62 s(2142) =< s(2135) 1131.48/294.62 s(2143) =< s(2130) 1131.48/294.62 s(2175) =< aux(337) 1131.48/294.62 s(2177) =< aux(331) 1131.48/294.62 s(2178) =< aux(337) 1131.48/294.62 s(2180) =< aux(337)-1 1131.48/294.62 s(2181) =< s(2074)*aux(335) 1131.48/294.62 s(2182) =< s(2074)*aux(337) 1131.48/294.62 s(2184) =< s(2074)*s(2178) 1131.48/294.62 s(2186) =< s(2074)*s(2180) 1131.48/294.62 s(2187) =< s(2186)+s(2182)+aux(338) 1131.48/294.62 s(2188) =< s(2186)+s(2182)+aux(338) 1131.48/294.62 s(2189) =< s(2181)+s(2181)+aux(333) 1131.48/294.62 s(2188) =< s(2181)+s(2181)+aux(333) 1131.48/294.62 s(2177) =< s(2186)+s(2182)+aux(338) 1131.48/294.62 s(2187) =< s(2177)*s(2178) 1131.48/294.62 s(2189) =< s(2177)*s(2178) 1131.48/294.62 s(2190) =< s(2177)*s(2077) 1131.48/294.62 s(2191) =< s(2184) 1131.48/294.62 s(2192) =< s(2188) 1131.48/294.62 s(2193) =< s(2189) 1131.48/294.62 s(2194) =< s(2187) 1131.48/294.62 s(2195) =< s(2182) 1131.48/294.62 s(2227) =< aux(331) 1131.48/294.62 s(2228) =< aux(338) 1131.48/294.62 s(2230) =< aux(338)-1 1131.48/294.62 s(2231) =< s(2074)*s(2219) 1131.48/294.62 s(2232) =< s(2074)*aux(338) 1131.48/294.62 s(2234) =< s(2074)*s(2228) 1131.48/294.62 s(2236) =< s(2074)*s(2230) 1131.48/294.62 s(2237) =< s(2236)+s(2232) 1131.48/294.62 s(2238) =< s(2236)+s(2232) 1131.48/294.62 s(2239) =< s(2231)+s(2231)+s(2218) 1131.48/294.62 s(2238) =< s(2231)+s(2231)+s(2218) 1131.48/294.62 s(2227) =< s(2236)+s(2232) 1131.48/294.62 s(2237) =< s(2227)*s(2228) 1131.48/294.62 s(2239) =< s(2227)*s(2228) 1131.48/294.62 s(2240) =< s(2227)*s(2077) 1131.48/294.62 s(2241) =< s(2234) 1131.48/294.62 s(2242) =< s(2238) 1131.48/294.62 s(2243) =< s(2239) 1131.48/294.62 s(2244) =< s(2237) 1131.48/294.62 s(2245) =< s(2232) 1131.48/294.62 s(2275) =< aux(331) 1131.48/294.62 s(2285) =< s(2186)+s(2182)+aux(336) 1131.48/294.62 s(2286) =< s(2186)+s(2182)+aux(336) 1131.48/294.62 s(2287) =< s(2181)+s(2181)+aux(333) 1131.48/294.62 s(2286) =< s(2181)+s(2181)+aux(333) 1131.48/294.62 s(2275) =< s(2186)+s(2182)+aux(336) 1131.48/294.62 s(2285) =< s(2275)*s(2178) 1131.48/294.62 s(2287) =< s(2275)*s(2178) 1131.48/294.62 s(2288) =< s(2275)*s(2077) 1131.48/294.62 s(2290) =< s(2286) 1131.48/294.62 s(2291) =< s(2287) 1131.48/294.62 s(2292) =< s(2285) 1131.48/294.62 s(2323) =< s(2320) 1131.48/294.62 s(2325) =< aux(331) 1131.48/294.62 s(2326) =< s(2320) 1131.48/294.62 s(2328) =< s(2320)-1 1131.48/294.62 s(2329) =< s(2074)*s(2317) 1131.48/294.62 s(2330) =< s(2074)*s(2320) 1131.48/294.62 s(2332) =< s(2074)*s(2326) 1131.48/294.62 s(2334) =< s(2074)*s(2328) 1131.48/294.62 s(2335) =< s(2334)+s(2330)+aux(338) 1131.48/294.62 s(2336) =< s(2334)+s(2330)+aux(338) 1131.48/294.62 s(2337) =< s(2329)+s(2329)+s(2316) 1131.48/294.62 s(2336) =< s(2329)+s(2329)+s(2316) 1131.48/294.62 s(2325) =< s(2334)+s(2330)+aux(338) 1131.48/294.62 s(2335) =< s(2325)*s(2326) 1131.48/294.62 s(2337) =< s(2325)*s(2326) 1131.48/294.62 s(2338) =< s(2325)*s(2077) 1131.48/294.62 s(2339) =< s(2332) 1131.48/294.62 s(2340) =< s(2336) 1131.48/294.62 s(2341) =< s(2337) 1131.48/294.62 s(2342) =< s(2335) 1131.48/294.62 s(2343) =< s(2330) 1131.48/294.62 s(2054) =< aux(332) 1131.48/294.62 1131.48/294.62 with precondition: [V1=1,V>=0,V9>=0] 1131.48/294.62 1131.48/294.62 * Chain [59]: 1 1131.48/294.62 with precondition: [V1=2,V>=0,V9>=0] 1131.48/294.62 1131.48/294.62 * Chain [58]: 1 1131.48/294.62 with precondition: [V=0,V1>=0] 1131.48/294.62 1131.48/294.62 1131.48/294.62 Closed-form bounds of start(V1,V,V9,V14,V22): 1131.48/294.62 ------------------------------------- 1131.48/294.62 * Chain [61] with precondition: [V1>=0] 1131.48/294.62 - Upper bound: 6546*V1+391+98*V1*V1+248*V1*nat(V)+23*V1*nat(V1-1)+23*V1*nat(nat(V)+ -1)+23*V1*nat(2*V1-1)+23*V1*nat(nat(2*V)+ -1)+46*V1*nat(nat(V1+V)+ -1)+62*V1*(2*V1)+62*V1*nat(2*V)+12*V1*(3*V1)+12*V1*(5*V1)+186*V1*nat(V1+V)+12*V1*nat(V1+2*V)+12*V1*nat(V1+4*V)+24*V1*nat(3*V1+2*V)+nat(V)*9277+nat(V)*330*nat(V)+nat(V)*62*nat(V9)+nat(V)*62*nat(V14)+nat(V)*69*nat(V1-1)+nat(V)*69*nat(nat(V)+ -1)+nat(V)*23*nat(nat(V9)+ -1)+nat(V)*23*nat(nat(V14)+ -1)+nat(V)*69*nat(2*V1-1)+nat(V)*69*nat(nat(2*V)+ -1)+nat(V)*23*nat(nat(2*V9)+ -1)+nat(V)*23*nat(nat(2*V14)+ -1)+nat(V)*138*nat(nat(V1+V)+ -1)+nat(V)*46*nat(nat(V9+V14)+ -1)+nat(V)*186*(2*V1)+nat(V)*186*nat(2*V)+nat(V)*62*nat(2*V9)+nat(V)*62*nat(2*V14)+nat(V)*36*nat(3*V)+nat(V)*36*nat(5*V)+nat(V)*434*nat(V1+V)+nat(V)*12*nat(V+2*V9)+nat(V)*12*nat(V+2*V14)+nat(V)*12*nat(V+4*V9)+nat(V)*12*nat(V+4*V14)+nat(V)*124*nat(V9+V14)+nat(V)*12*nat(-V1+V)+nat(V)*36*nat(2*V1+V)+nat(V)*72*nat(2*V1+3*V)+nat(V)*36*nat(4*V1+V)+nat(V)*24*nat(V+2*V9+2*V14)+nat(V9)*1182+nat(V14)*1408+nat(V1-1)*23*nat(V1+V)+nat(nat(V)+ -1)*23*nat(V1+V)+nat(2*V1-1)*23*nat(V1+V)+nat(nat(2*V)+ -1)*23*nat(V1+V)+nat(nat(V1+V)+ -1)*46*nat(V1+V)+nat(nat(V9+V14)+ -1)*46*nat(-V1+V)+2700*V1+124*V1*nat(V1+V)+nat(2*V)*1350+nat(2*V)*62*nat(V1+V)+nat(2*V9)*270+nat(2*V14)*270+nat(V1+V)*3291+nat(V1+V)*160*nat(V1+V)+nat(V1+V)*12*nat(V1+3*V)+nat(V1+V)*12*nat(V1+5*V)+nat(V1+V)*12*nat(3*V1+V)+nat(V1+V)*24*nat(3*V1+3*V)+nat(V1+V)*12*nat(5*V1+V)+(10*V1+10)+nat(V9+V14)*1068+nat(V9+V14)*124*nat(-V1+V)+nat(-V1+V)*164+nat(-V1+V)*24*nat(V+2*V9+2*V14)+nat(V1+V9+V14)*12 1131.48/294.62 - Complexity: n^2 1131.48/294.62 * Chain [60] with precondition: [V1=1,V>=0,V9>=0] 1131.48/294.62 - Upper bound: 96*V9+25+36*V9*nat(-V+V9)+nat(V14)*1032+nat(V14)*62*nat(-V+V9)+nat(V22)*1104+nat(V22)*62*nat(-V+V9)+nat(nat(V14)+ -1)*23*nat(-V+V9)+nat(nat(V22)+ -1)*23*nat(-V+V9)+nat(nat(2*V14)+ -1)*23*nat(-V+V9)+nat(nat(2*V22)+ -1)*23*nat(-V+V9)+nat(nat(V14+V22)+ -1)*46*nat(-V+V9)+nat(2*V14)*264+nat(2*V14)*62*nat(-V+V9)+nat(2*V22)*264+nat(2*V22)*62*nat(-V+V9)+nat(V+V14)*6+nat(V+V22)*6+(60*V+60)+nat(V+2*V14)*6+nat(V+2*V22)*6+nat(V9+2*V14)*12*nat(-V+V9)+nat(V9+2*V22)*12*nat(-V+V9)+nat(V9+4*V14)*12*nat(-V+V9)+nat(V9+4*V22)*12*nat(-V+V9)+nat(V14+V22)*528+nat(V14+V22)*124*nat(-V+V9)+nat(-V+V9)*492+nat(-V+V9)*24*nat(V9+2*V14+2*V22)+nat(V+V14+V22)*12 1131.48/294.62 - Complexity: n^2 1131.48/294.62 * Chain [59] with precondition: [V1=2,V>=0,V9>=0] 1131.48/294.62 - Upper bound: 1 1131.48/294.62 - Complexity: constant 1131.48/294.62 * Chain [58] with precondition: [V=0,V1>=0] 1131.48/294.62 - Upper bound: 1 1131.48/294.62 - Complexity: constant 1131.48/294.62 1131.48/294.62 ### Maximum cost of start(V1,V,V9,V14,V22): nat(V9)*96+24+nat(V14)*1032+nat(2*V14)*264+max([nat(V14)*62*nat(-V+V9)+nat(V9)*36*nat(-V+V9)+nat(V22)*1104+nat(V22)*62*nat(-V+V9)+nat(nat(V14)+ -1)*23*nat(-V+V9)+nat(nat(V22)+ -1)*23*nat(-V+V9)+nat(nat(2*V14)+ -1)*23*nat(-V+V9)+nat(nat(2*V22)+ -1)*23*nat(-V+V9)+nat(nat(V14+V22)+ -1)*46*nat(-V+V9)+nat(2*V14)*62*nat(-V+V9)+nat(2*V22)*264+nat(2*V22)*62*nat(-V+V9)+nat(V+V14)*6+nat(V+V22)*6+nat(V+1)*60+nat(V+2*V14)*6+nat(V+2*V22)*6+nat(V9+2*V14)*12*nat(-V+V9)+nat(V9+2*V22)*12*nat(-V+V9)+nat(V9+4*V14)*12*nat(-V+V9)+nat(V9+4*V22)*12*nat(-V+V9)+nat(V14+V22)*528+nat(V14+V22)*124*nat(-V+V9)+nat(-V+V9)*492+nat(-V+V9)*24*nat(V9+2*V14+2*V22)+nat(V+V14+V22)*12,6546*V1+366+98*V1*V1+248*V1*nat(V)+23*V1*nat(V1-1)+23*V1*nat(nat(V)+ -1)+23*V1*nat(2*V1-1)+23*V1*nat(nat(2*V)+ -1)+46*V1*nat(nat(V1+V)+ -1)+62*V1*(2*V1)+62*V1*nat(2*V)+12*V1*(3*V1)+12*V1*(5*V1)+186*V1*nat(V1+V)+12*V1*nat(V1+2*V)+12*V1*nat(V1+4*V)+24*V1*nat(3*V1+2*V)+nat(V)*9277+nat(V)*330*nat(V)+nat(V)*62*nat(V9)+nat(V)*62*nat(V14)+nat(V)*69*nat(V1-1)+nat(V)*69*nat(nat(V)+ -1)+nat(V)*23*nat(nat(V9)+ -1)+nat(V)*23*nat(nat(V14)+ -1)+nat(V)*69*nat(2*V1-1)+nat(V)*69*nat(nat(2*V)+ -1)+nat(V)*23*nat(nat(2*V9)+ -1)+nat(V)*23*nat(nat(2*V14)+ -1)+nat(V)*138*nat(nat(V1+V)+ -1)+nat(V)*46*nat(nat(V9+V14)+ -1)+nat(V)*186*(2*V1)+nat(V)*186*nat(2*V)+nat(V)*62*nat(2*V9)+nat(V)*62*nat(2*V14)+nat(V)*36*nat(3*V)+nat(V)*36*nat(5*V)+nat(V)*434*nat(V1+V)+nat(V)*12*nat(V+2*V9)+nat(V)*12*nat(V+2*V14)+nat(V)*12*nat(V+4*V9)+nat(V)*12*nat(V+4*V14)+nat(V)*124*nat(V9+V14)+nat(V)*12*nat(-V1+V)+nat(V)*36*nat(2*V1+V)+nat(V)*72*nat(2*V1+3*V)+nat(V)*36*nat(4*V1+V)+nat(V)*24*nat(V+2*V9+2*V14)+nat(V9)*1086+nat(V14)*376+nat(V1-1)*23*nat(V1+V)+nat(nat(V)+ -1)*23*nat(V1+V)+nat(2*V1-1)*23*nat(V1+V)+nat(nat(2*V)+ -1)*23*nat(V1+V)+nat(nat(V1+V)+ -1)*46*nat(V1+V)+nat(nat(V9+V14)+ -1)*46*nat(-V1+V)+2700*V1+124*V1*nat(V1+V)+nat(2*V)*1350+nat(2*V)*62*nat(V1+V)+nat(2*V9)*270+nat(2*V14)*6+nat(V1+V)*3291+nat(V1+V)*160*nat(V1+V)+nat(V1+V)*12*nat(V1+3*V)+nat(V1+V)*12*nat(V1+5*V)+nat(V1+V)*12*nat(3*V1+V)+nat(V1+V)*24*nat(3*V1+3*V)+nat(V1+V)*12*nat(5*V1+V)+(10*V1+10)+nat(V9+V14)*1068+nat(V9+V14)*124*nat(-V1+V)+nat(-V1+V)*164+nat(-V1+V)*24*nat(V+2*V9+2*V14)+nat(V1+V9+V14)*12])+1 1131.48/294.62 Asymptotic class: n^2 1131.48/294.62 * Total analysis performed in 6683 ms. 1131.48/294.62 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (10) 1131.48/294.62 BOUNDS(1, n^2) 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1131.48/294.62 Transformed a relative TRS into a decreasing-loop problem. 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (12) 1131.48/294.62 Obligation: 1131.48/294.62 Analyzing the following TRS for decreasing loops: 1131.48/294.62 1131.48/294.62 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.62 1131.48/294.62 1131.48/294.62 The TRS R consists of the following rules: 1131.48/294.62 1131.48/294.62 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 1131.48/294.62 plus(x, 0) -> x 1131.48/294.62 plus(x, s(y)) -> s(plus(x, y)) 1131.48/294.62 length(nil) -> 0 1131.48/294.62 length(cons(x, y)) -> s(length(y)) 1131.48/294.62 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 1131.48/294.62 ge(x, 0) -> true 1131.48/294.62 ge(0, s(x)) -> false 1131.48/294.62 ge(s(x), s(y)) -> ge(x, y) 1131.48/294.62 if(true, c, l, ys, zs) -> nil 1131.48/294.62 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 1131.48/294.62 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 1131.48/294.62 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 1131.48/294.62 helpc(true, ys, zs) -> ys 1131.48/294.62 helpc(false, ys, zs) -> zs 1131.48/294.62 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 1131.48/294.62 1131.48/294.62 S is empty. 1131.48/294.62 Rewrite Strategy: INNERMOST 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (13) DecreasingLoopProof (LOWER BOUND(ID)) 1131.48/294.62 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1131.48/294.62 1131.48/294.62 The rewrite sequence 1131.48/294.62 1131.48/294.62 plus(x, s(y)) ->^+ s(plus(x, y)) 1131.48/294.62 1131.48/294.62 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1131.48/294.62 1131.48/294.62 The pumping substitution is [y / s(y)]. 1131.48/294.62 1131.48/294.62 The result substitution is [ ]. 1131.48/294.62 1131.48/294.62 1131.48/294.62 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (14) 1131.48/294.62 Complex Obligation (BEST) 1131.48/294.62 1131.48/294.62 ---------------------------------------- 1131.48/294.62 1131.48/294.62 (15) 1131.48/294.62 Obligation: 1131.48/294.62 Proved the lower bound n^1 for the following obligation: 1131.48/294.62 1131.48/294.62 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.62 1131.48/294.62 1131.48/294.62 The TRS R consists of the following rules: 1131.48/294.62 1131.48/294.62 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 1131.48/294.62 plus(x, 0) -> x 1131.48/294.62 plus(x, s(y)) -> s(plus(x, y)) 1131.48/294.62 length(nil) -> 0 1131.48/294.62 length(cons(x, y)) -> s(length(y)) 1131.48/294.62 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 1131.48/294.62 ge(x, 0) -> true 1131.48/294.62 ge(0, s(x)) -> false 1131.48/294.62 ge(s(x), s(y)) -> ge(x, y) 1131.48/294.62 if(true, c, l, ys, zs) -> nil 1131.48/294.62 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 1131.48/294.63 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 1131.48/294.63 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 1131.48/294.63 helpc(true, ys, zs) -> ys 1131.48/294.63 helpc(false, ys, zs) -> zs 1131.48/294.63 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 1131.48/294.63 1131.48/294.63 S is empty. 1131.48/294.63 Rewrite Strategy: INNERMOST 1131.48/294.63 ---------------------------------------- 1131.48/294.63 1131.48/294.63 (16) LowerBoundPropagationProof (FINISHED) 1131.48/294.63 Propagated lower bound. 1131.48/294.63 ---------------------------------------- 1131.48/294.63 1131.48/294.63 (17) 1131.48/294.63 BOUNDS(n^1, INF) 1131.48/294.63 1131.48/294.63 ---------------------------------------- 1131.48/294.63 1131.48/294.63 (18) 1131.48/294.63 Obligation: 1131.48/294.63 Analyzing the following TRS for decreasing loops: 1131.48/294.63 1131.48/294.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.48/294.63 1131.48/294.63 1131.48/294.63 The TRS R consists of the following rules: 1131.48/294.63 1131.48/294.63 app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) 1131.48/294.63 plus(x, 0) -> x 1131.48/294.63 plus(x, s(y)) -> s(plus(x, y)) 1131.48/294.63 length(nil) -> 0 1131.48/294.63 length(cons(x, y)) -> s(length(y)) 1131.48/294.63 helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 1131.48/294.63 ge(x, 0) -> true 1131.48/294.63 ge(0, s(x)) -> false 1131.48/294.63 ge(s(x), s(y)) -> ge(x, y) 1131.48/294.63 if(true, c, l, ys, zs) -> nil 1131.48/294.63 if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) 1131.48/294.63 greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 1131.48/294.63 smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 1131.48/294.63 helpc(true, ys, zs) -> ys 1131.48/294.63 helpc(false, ys, zs) -> zs 1131.48/294.63 helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 1131.48/294.63 1131.48/294.63 S is empty. 1131.48/294.63 Rewrite Strategy: INNERMOST 1131.72/294.68 EOF