4.58/2.01 WORST_CASE(?, O(1)) 4.58/2.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.58/2.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.58/2.02 4.58/2.02 4.58/2.02 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.58/2.02 4.58/2.02 (0) CpxIntTrs 4.58/2.02 (1) Koat Proof [FINISHED, 391 ms] 4.58/2.02 (2) BOUNDS(1, 1) 4.58/2.02 4.58/2.02 4.58/2.02 ---------------------------------------- 4.58/2.02 4.58/2.02 (0) 4.58/2.02 Obligation: 4.58/2.02 Complexity Int TRS consisting of the following rules: 4.58/2.02 start(A, B, C, D, E, F) -> Com_1(lbl91(A, B, 100, D, 1, F)) :|: A >= 0 && A <= 0 && B >= 0 && B <= 0 && C >= D && C <= D && E >= F && E <= F 4.58/2.02 start(A, B, C, D, E, F) -> Com_1(lbl111(A, B, 100, D, 2, F)) :|: 0 >= B + 1 && A >= B && A <= B && C >= D && C <= D && E >= F && E <= F 4.58/2.02 start(A, B, C, D, E, F) -> Com_1(lbl111(A, B, 100, D, 2, F)) :|: B >= 1 && A >= B && A <= B && C >= D && C <= D && E >= F && E <= F 4.58/2.02 lbl91(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: E >= 40 && E <= 40 && C >= 100 && C <= 100 && A >= 0 && A <= 0 && B >= 0 && B <= 0 4.58/2.02 lbl91(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D, 1 + E, F)) :|: 39 >= E && E >= 1 && 40 >= E && A >= 0 && A <= 0 && C >= 100 && C <= 100 && B >= 0 && B <= 0 4.58/2.02 lbl91(A, B, C, D, E, F) -> Com_1(lbl111(A, B, C, D, 2 + E, F)) :|: 0 >= 1 && 39 >= E && E >= 1 && 40 >= E && C >= 100 && C <= 100 && A >= 0 && A <= 0 && B >= 0 && B <= 0 4.58/2.02 lbl111(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: E >= 40 && E >= 2 && 41 >= E && C >= 100 && C <= 100 && A >= B && A <= B 4.58/2.02 lbl111(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D, 1 + E, F)) :|: 39 >= E && E >= 2 && 41 >= E && A >= 0 && A <= 0 && C >= 100 && C <= 100 && B >= 0 && B <= 0 4.58/2.02 lbl111(A, B, C, D, E, F) -> Com_1(lbl111(A, B, C, D, 2 + E, F)) :|: 0 >= B + 1 && 39 >= E && E >= 2 && 41 >= E && C >= 100 && C <= 100 && A >= B && A <= B 4.58/2.02 lbl111(A, B, C, D, E, F) -> Com_1(lbl111(A, B, C, D, 2 + E, F)) :|: B >= 1 && 39 >= E && E >= 2 && 41 >= E && C >= 100 && C <= 100 && A >= B && A <= B 4.58/2.02 start0(A, B, C, D, E, F) -> Com_1(start(B, B, D, D, F, F)) :|: TRUE 4.58/2.02 4.58/2.02 The start-symbols are:[start0_6] 4.58/2.02 4.58/2.02 4.58/2.02 ---------------------------------------- 4.58/2.02 4.58/2.02 (1) Koat Proof (FINISHED) 4.58/2.02 YES(?, 123) 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 Initial complexity problem: 4.58/2.02 4.58/2.02 1: T: 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, 100, ar_3, 1, ar_5)) [ ar_0 = 0 /\ ar_1 = 0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ 0 >= ar_1 + 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ ar_1 >= 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.58/2.02 4.58/2.02 start location: koat_start 4.58/2.02 4.58/2.02 leaf cost: 0 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 Testing for reachability in the complexity graph removes the following transitions from problem 1: 4.58/2.02 4.58/2.02 lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 We thus obtain the following problem: 4.58/2.02 4.58/2.02 2: T: 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ ar_1 >= 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ 0 >= ar_1 + 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, 100, ar_3, 1, ar_5)) [ ar_0 = 0 /\ ar_1 = 0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.58/2.02 4.58/2.02 start location: koat_start 4.58/2.02 4.58/2.02 leaf cost: 0 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 Repeatedly propagating knowledge in problem 2 produces the following problem: 4.58/2.02 4.58/2.02 3: T: 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ ar_1 >= 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ 0 >= ar_1 + 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, 100, ar_3, 1, ar_5)) [ ar_0 = 0 /\ ar_1 = 0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.58/2.02 4.58/2.02 start location: koat_start 4.58/2.02 4.58/2.02 leaf cost: 0 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 A polynomial rank function with 4.58/2.02 4.58/2.02 Pol(lbl111) = 1 4.58/2.02 4.58/2.02 Pol(stop) = 0 4.58/2.02 4.58/2.02 Pol(lbl91) = 1 4.58/2.02 4.58/2.02 Pol(start) = 1 4.58/2.02 4.58/2.02 Pol(start0) = 1 4.58/2.02 4.58/2.02 Pol(koat_start) = 1 4.58/2.02 4.58/2.02 orients all transitions weakly and the transitions 4.58/2.02 4.58/2.02 lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 strictly and produces the following problem: 4.58/2.02 4.58/2.02 4: T: 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ ar_1 >= 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ 0 >= ar_1 + 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, 100, ar_3, 1, ar_5)) [ ar_0 = 0 /\ ar_1 = 0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.58/2.02 4.58/2.02 start location: koat_start 4.58/2.02 4.58/2.02 leaf cost: 0 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 A polynomial rank function with 4.58/2.02 4.58/2.02 Pol(lbl111) = -V_5 + 40 4.58/2.02 4.58/2.02 Pol(stop) = -V_5 + 40 4.58/2.02 4.58/2.02 Pol(lbl91) = -V_5 + 40 4.58/2.02 4.58/2.02 Pol(start) = 39 4.58/2.02 4.58/2.02 Pol(start0) = 39 4.58/2.02 4.58/2.02 Pol(koat_start) = 39 4.58/2.02 4.58/2.02 orients all transitions weakly and the transitions 4.58/2.02 4.58/2.02 lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 strictly and produces the following problem: 4.58/2.02 4.58/2.02 5: T: 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 40 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 = 40 /\ ar_2 = 100 /\ ar_0 = 0 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: 39, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ ar_1 >= 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: 39, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 + 2, ar_5)) [ 0 >= ar_1 + 1 /\ 39 >= ar_4 /\ ar_4 >= 2 /\ 41 >= ar_4 /\ ar_2 = 100 /\ ar_0 = ar_1 ] 4.58/2.02 4.58/2.02 (Comp: 39, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ 39 >= ar_4 /\ ar_4 >= 1 /\ 40 >= ar_4 /\ ar_0 = 0 /\ ar_2 = 100 /\ ar_1 = 0 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ ar_1 >= 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, 100, ar_3, 2, ar_5)) [ 0 >= ar_1 + 1 /\ ar_0 = ar_1 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl91(ar_0, ar_1, 100, ar_3, 1, ar_5)) [ ar_0 = 0 /\ ar_1 = 0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ] 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) 4.58/2.02 4.58/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.58/2.02 4.58/2.02 start location: koat_start 4.58/2.02 4.58/2.02 leaf cost: 0 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 Complexity upper bound 123 4.58/2.02 4.58/2.02 4.58/2.02 4.58/2.02 Time: 0.366 sec (SMT: 0.314 sec) 4.58/2.02 4.58/2.02 4.58/2.02 ---------------------------------------- 4.58/2.02 4.58/2.02 (2) 4.58/2.02 BOUNDS(1, 1) 4.75/2.04 EOF