/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 280 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 start0(A, B, C, D, E, F) -> Com_1(start(B, B, D, D, F, F)) :|: TRUE The start-symbols are:[start0_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 891) Initial complexity problem: 1: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 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 ] 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 ] We thus obtain the following problem: 2: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(lbl111) = 1 Pol(stop) = 0 Pol(lbl91) = 1 Pol(start) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transitions 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 ] 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 ] strictly and produces the following problem: 4: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(lbl111) = -V_5 + 40 Pol(stop) = 3*V_3 - 5*V_5 - 100 Pol(lbl91) = 3*V_3 - 5*V_5 Pol(start) = 295 Pol(start0) = 295 Pol(koat_start) = 295 orients all transitions weakly and the transitions 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 ] 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 ] 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 ] strictly and produces the following problem: 5: T: (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 ] (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 ] (Comp: 295, 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 ] (Comp: 295, 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 ] (Comp: 295, 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 ] (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 ] (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 Complexity upper bound 891 Time: 0.249 sec (SMT: 0.204 sec) ---------------------------------------- (2) BOUNDS(1, 1)