/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 860 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 3201 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, 0, C, 0, E, F, G, 0, I, J)) :|: 0 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= I && H <= I && J >= A && J <= A start(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, 0, C, 0, E, K, G, 1, I, J)) :|: A >= 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= I && H <= I && J >= A && J <= A lbl21(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: A + D + B >= 1 && A + D >= B + 1 && A + B >= D + 1 && A >= D + B + 1 && H >= A && H <= A && J >= A && J <= A lbl21(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D, E, K, G, 1 + H, I, J)) :|: A >= H + 1 && A >= H && H + D + B >= 1 && H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && J >= A && J <= A lbl121(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: A + D + B >= 2 && A + D >= B + 2 && A + B >= D && A >= D + B && H >= A && H <= A && F >= 0 && F <= 0 && J >= A && J <= A lbl121(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D, E, K, G, 1 + H, I, J)) :|: A >= H + 1 && A >= H && H + D + B >= 2 && H + D >= B + 2 && H + B >= D && H >= D + B && F >= 0 && F <= 0 && J >= A && J <= A lbl141(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: A + D + B >= 0 && A + D >= B && A + B >= D + 2 && A >= D + B + 2 && H >= A && H <= A && F >= 1 && F <= 1 && J >= A && J <= A lbl141(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D, E, K, G, 1 + H, I, J)) :|: A >= H + 1 && A >= H && H + D + B >= 0 && H + D >= B && H + B >= D + 2 && H >= D + B + 2 && F >= 1 && F <= 1 && J >= A && J <= A lbl171(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: A + D + B >= 2 && A + D >= B && A + B >= D + 2 && A >= D + B && H >= A && H <= A && F >= 2 && F <= 2 && J >= A && J <= A lbl171(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D, E, K, G, 1 + H, I, J)) :|: A >= H + 1 && A >= H && H + D + B >= 2 && H + D >= B && H + B >= D + 2 && H >= D + B && F >= 2 && F <= 2 && J >= A && J <= A lbl191(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: A + D + B >= 0 && A + D >= B + 2 && A + B >= D && A >= D + B + 2 && H >= A && H <= A && F >= 3 && F <= 3 && J >= A && J <= A lbl191(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D, E, K, G, 1 + H, I, J)) :|: A >= H + 1 && A >= H && H + D + B >= 0 && H + D >= B + 2 && H + B >= D && H >= D + B + 2 && F >= 3 && F <= 3 && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl21(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= F + 1 && H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl21(A, B, C, D, E, F, G, H, I, J)) :|: F >= 4 && H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl121(A, B, C, 1 + D, E, F, G, H, I, J)) :|: H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && F >= 0 && F <= 0 && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl141(A, B, C, D - 1, E, F, G, H, I, J)) :|: H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && F >= 1 && F <= 1 && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl171(A, 1 + B, C, D, E, F, G, H, I, J)) :|: H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && F >= 2 && F <= 2 && J >= A && J <= A lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl191(A, B - 1, C, D, E, F, G, H, I, J)) :|: H + D >= B + 1 && H + B >= D + 1 && H >= D + B + 1 && H + D + B >= 1 && A >= H && F >= 3 && F <= 3 && J >= A && J <= A start0(A, B, C, D, E, F, G, H, I, J) -> Com_1(start(A, C, C, E, E, G, G, I, I, A)) :|: TRUE The start-symbols are:[start0_10] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 44*Ar_0 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, 0, Ar_2, 0, Ar_4, Ar_5, Ar_6, 0, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, 0, Ar_2, 0, Ar_4, Fresh_5, Ar_6, 1, Ar_8, Ar_9)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 1 /\ Ar_0 + Ar_3 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 + Ar_1 + 1 /\ Ar_7 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_3, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_5 + 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_5 >= 4 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl171(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl191(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, 0, Ar_2, 0, Ar_4, Ar_5, Ar_6, 0, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, 0, Ar_2, 0, Ar_4, Fresh_5, Ar_6, 1, Ar_8, Ar_9)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 1 /\ Ar_0 + Ar_3 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 + Ar_1 + 1 /\ Ar_7 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_3, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_5 + 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_5 >= 4 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl171(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl191(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 1 Pol(stop) = 0 Pol(lbl81) = 1 Pol(lbl21) = 1 Pol(lbl121) = 1 Pol(lbl141) = 1 Pol(lbl171) = 1 Pol(lbl191) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transitions lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 1 /\ Ar_0 + Ar_3 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 + Ar_1 + 1 /\ Ar_7 = Ar_0 /\ Ar_9 = Ar_0 ] lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, 0, Ar_2, 0, Ar_4, Ar_5, Ar_6, 0, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, 0, Ar_2, 0, Ar_4, Fresh_5, Ar_6, 1, Ar_8, Ar_9)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 1 /\ Ar_0 + Ar_3 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 + Ar_1 + 1 /\ Ar_7 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_3, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_5 + 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_5 >= 4 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl171(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl191(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 4*V_1 Pol(stop) = -4*V_8 + 4*V_10 Pol(lbl81) = V_2 - V_4 - 3*V_8 + 4*V_10 Pol(lbl21) = V_2 - V_4 - 3*V_8 + 4*V_10 - 1 Pol(lbl121) = V_2 - V_4 - 3*V_8 + 4*V_10 Pol(lbl141) = V_2 - V_4 - 3*V_8 + 4*V_10 - 2 Pol(lbl171) = V_2 - V_4 - 3*V_8 + 4*V_10 - 2 Pol(lbl191) = V_2 - V_4 - 3*V_8 + 4*V_10 Pol(start0) = 4*V_1 Pol(koat_start) = 4*V_1 orients all transitions weakly and the transitions lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_5 >= 4 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_5 + 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl191(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl171(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_9 = Ar_0 ] lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_3, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, 0, Ar_2, 0, Ar_4, Ar_5, Ar_6, 0, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, 0, Ar_2, 0, Ar_4, Fresh_5, Ar_6, 1, Ar_8, Ar_9)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 1 /\ Ar_0 + Ar_3 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 + Ar_1 + 1 /\ Ar_7 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_3, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 2 /\ Ar_0 + Ar_3 >= Ar_1 /\ Ar_0 + Ar_1 >= Ar_3 + 2 /\ Ar_0 >= Ar_3 + Ar_1 /\ Ar_7 = Ar_0 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl171(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_1, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 2 /\ Ar_7 + Ar_3 >= Ar_1 /\ Ar_7 + Ar_1 >= Ar_3 + 2 /\ Ar_7 >= Ar_3 + Ar_1 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 + Ar_3 + Ar_1 >= 0 /\ Ar_0 + Ar_3 >= Ar_1 + 2 /\ Ar_0 + Ar_1 >= Ar_3 /\ Ar_0 >= Ar_3 + Ar_1 + 2 /\ Ar_7 = Ar_0 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl191(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7 + 1, Ar_8, Ar_9)) [ Ar_0 >= Ar_7 + 1 /\ Ar_0 >= Ar_7 /\ Ar_7 + Ar_3 + Ar_1 >= 0 /\ Ar_7 + Ar_3 >= Ar_1 + 2 /\ Ar_7 + Ar_1 >= Ar_3 /\ Ar_7 >= Ar_3 + Ar_1 + 2 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_5 + 1 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_5 >= 4 /\ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 0 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 1 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl171(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 2 /\ Ar_9 = Ar_0 ] (Comp: 4*Ar_0, Cost: 1) lbl81(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(lbl191(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_7 + Ar_3 >= Ar_1 + 1 /\ Ar_7 + Ar_1 >= Ar_3 + 1 /\ Ar_7 >= Ar_3 + Ar_1 + 1 /\ Ar_7 + Ar_3 + Ar_1 >= 1 /\ Ar_0 >= Ar_7 /\ Ar_5 = 3 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 44*Ar_0 + 8 Time: 0.828 sec (SMT: 0.549 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start0 0: start -> stop : B'=0, D'=0, H'=0, [ 0>=A && B==C && D==E && F==G && H==Q && J==A ], cost: 1 1: start -> lbl81 : B'=0, D'=0, F'=free, H'=1, [ A>=1 && B==C && D==E && F==G && H==Q && J==A ], cost: 1 2: lbl21 -> stop : [ D+A+B>=1 && D+A>=1+B && A+B>=1+D && A>=1+D+B && H==A && J==A ], cost: 1 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && A>=H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 4: lbl121 -> stop : [ D+A+B>=2 && D+A>=2+B && A+B>=D && A>=D+B && H==A && F==0 && J==A ], cost: 1 5: lbl121 -> lbl81 : F'=free_2, H'=1+H, [ A>=1+H && A>=H && D+H+B>=2 && D+H>=2+B && H+B>=D && H>=D+B && F==0 && J==A ], cost: 1 6: lbl141 -> stop : [ D+A+B>=0 && D+A>=B && A+B>=2+D && A>=2+D+B && H==A && F==1 && J==A ], cost: 1 7: lbl141 -> lbl81 : F'=free_3, H'=1+H, [ A>=1+H && A>=H && D+H+B>=0 && D+H>=B && H+B>=2+D && H>=2+D+B && F==1 && J==A ], cost: 1 8: lbl171 -> stop : [ D+A+B>=2 && D+A>=B && A+B>=2+D && A>=D+B && H==A && F==2 && J==A ], cost: 1 9: lbl171 -> lbl81 : F'=free_4, H'=1+H, [ A>=1+H && A>=H && D+H+B>=2 && D+H>=B && H+B>=2+D && H>=D+B && F==2 && J==A ], cost: 1 10: lbl191 -> stop : [ D+A+B>=0 && D+A>=2+B && A+B>=D && A>=2+D+B && H==A && F==3 && J==A ], cost: 1 11: lbl191 -> lbl81 : F'=free_5, H'=1+H, [ A>=1+H && A>=H && D+H+B>=0 && D+H>=2+B && H+B>=D && H>=2+D+B && F==3 && J==A ], cost: 1 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 14: lbl81 -> lbl121 : D'=1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==0 && J==A ], cost: 1 15: lbl81 -> lbl141 : D'=-1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==1 && J==A ], cost: 1 16: lbl81 -> lbl171 : B'=1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==2 && J==A ], cost: 1 17: lbl81 -> lbl191 : B'=-1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==3 && J==A ], cost: 1 18: start0 -> start : B'=C, D'=E, F'=G, H'=Q, J'=A, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 18: start0 -> start : B'=C, D'=E, F'=G, H'=Q, J'=A, [], cost: 1 Removed unreachable and leaf rules: Start location: start0 1: start -> lbl81 : B'=0, D'=0, F'=free, H'=1, [ A>=1 && B==C && D==E && F==G && H==Q && J==A ], cost: 1 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && A>=H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 5: lbl121 -> lbl81 : F'=free_2, H'=1+H, [ A>=1+H && A>=H && D+H+B>=2 && D+H>=2+B && H+B>=D && H>=D+B && F==0 && J==A ], cost: 1 7: lbl141 -> lbl81 : F'=free_3, H'=1+H, [ A>=1+H && A>=H && D+H+B>=0 && D+H>=B && H+B>=2+D && H>=2+D+B && F==1 && J==A ], cost: 1 9: lbl171 -> lbl81 : F'=free_4, H'=1+H, [ A>=1+H && A>=H && D+H+B>=2 && D+H>=B && H+B>=2+D && H>=D+B && F==2 && J==A ], cost: 1 11: lbl191 -> lbl81 : F'=free_5, H'=1+H, [ A>=1+H && A>=H && D+H+B>=0 && D+H>=2+B && H+B>=D && H>=2+D+B && F==3 && J==A ], cost: 1 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 14: lbl81 -> lbl121 : D'=1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==0 && J==A ], cost: 1 15: lbl81 -> lbl141 : D'=-1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==1 && J==A ], cost: 1 16: lbl81 -> lbl171 : B'=1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==2 && J==A ], cost: 1 17: lbl81 -> lbl191 : B'=-1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==3 && J==A ], cost: 1 18: start0 -> start : B'=C, D'=E, F'=G, H'=Q, J'=A, [], cost: 1 Simplified all rules, resulting in: Start location: start0 1: start -> lbl81 : B'=0, D'=0, F'=free, H'=1, [ A>=1 && B==C && D==E && F==G && H==Q && J==A ], cost: 1 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 5: lbl121 -> lbl81 : F'=free_2, H'=1+H, [ A>=1+H && D+H+B>=2 && D+H>=2+B && H+B>=D && H>=D+B && F==0 && J==A ], cost: 1 7: lbl141 -> lbl81 : F'=free_3, H'=1+H, [ A>=1+H && D+H+B>=0 && D+H>=B && H+B>=2+D && H>=2+D+B && F==1 && J==A ], cost: 1 9: lbl171 -> lbl81 : F'=free_4, H'=1+H, [ A>=1+H && D+H+B>=2 && D+H>=B && H+B>=2+D && H>=D+B && F==2 && J==A ], cost: 1 11: lbl191 -> lbl81 : F'=free_5, H'=1+H, [ A>=1+H && D+H+B>=0 && D+H>=2+B && H+B>=D && H>=2+D+B && F==3 && J==A ], cost: 1 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 14: lbl81 -> lbl121 : D'=1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==0 && J==A ], cost: 1 15: lbl81 -> lbl141 : D'=-1+D, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==1 && J==A ], cost: 1 16: lbl81 -> lbl171 : B'=1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==2 && J==A ], cost: 1 17: lbl81 -> lbl191 : B'=-1+B, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && F==3 && J==A ], cost: 1 18: start0 -> start : B'=C, D'=E, F'=G, H'=Q, J'=A, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: start0 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 20: lbl81 -> lbl81 : D'=1+D, F'=free_2, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==0 && J==A && A>=1+H ], cost: 2 21: lbl81 -> lbl81 : D'=-1+D, F'=free_3, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==1 && J==A && A>=1+H ], cost: 2 22: lbl81 -> lbl81 : B'=1+B, F'=free_4, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==2 && J==A && A>=1+H ], cost: 2 23: lbl81 -> lbl81 : B'=-1+B, F'=free_5, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==3 && J==A && A>=1+H ], cost: 2 19: start0 -> lbl81 : B'=0, D'=0, F'=free, H'=1, J'=A, [ A>=1 ], cost: 2 Accelerating simple loops of location 6. Accelerating the following rules: 20: lbl81 -> lbl81 : D'=1+D, F'=free_2, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==0 && J==A && A>=1+H ], cost: 2 21: lbl81 -> lbl81 : D'=-1+D, F'=free_3, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==1 && J==A && A>=1+H ], cost: 2 22: lbl81 -> lbl81 : B'=1+B, F'=free_4, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==2 && J==A && A>=1+H ], cost: 2 23: lbl81 -> lbl81 : B'=-1+B, F'=free_5, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==3 && J==A && A>=1+H ], cost: 2 Accelerated rule 20 with metering function A-H (after strengthening guard), yielding the new rule 24. Accelerated rule 21 with metering function A-H (after strengthening guard), yielding the new rule 25. Accelerated rule 22 with metering function A-H (after strengthening guard), yielding the new rule 26. Accelerated rule 23 with metering function A-H (after strengthening guard), yielding the new rule 27. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: start0 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 20: lbl81 -> lbl81 : D'=1+D, F'=free_2, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==0 && J==A && A>=1+H ], cost: 2 21: lbl81 -> lbl81 : D'=-1+D, F'=free_3, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==1 && J==A && A>=1+H ], cost: 2 22: lbl81 -> lbl81 : B'=1+B, F'=free_4, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==2 && J==A && A>=1+H ], cost: 2 23: lbl81 -> lbl81 : B'=-1+B, F'=free_5, H'=1+H, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==3 && J==A && A>=1+H ], cost: 2 24: lbl81 -> lbl81 : D'=D+A-H, F'=free_2, H'=A, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==0 && J==A && A>=1+H && free_2==0 ], cost: 2*A-2*H 25: lbl81 -> lbl81 : D'=D-A+H, F'=free_3, H'=A, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==1 && J==A && A>=1+H && free_3==1 ], cost: 2*A-2*H 26: lbl81 -> lbl81 : B'=A-H+B, F'=free_4, H'=A, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==2 && J==A && A>=1+H && free_4==2 ], cost: 2*A-2*H 27: lbl81 -> lbl81 : B'=-A+H+B, F'=free_5, H'=A, [ D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && F==3 && J==A && A>=1+H && free_5==3 ], cost: 2*A-2*H 19: start0 -> lbl81 : B'=0, D'=0, F'=free, H'=1, J'=A, [ A>=1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: start0 3: lbl21 -> lbl81 : F'=free_1, H'=1+H, [ A>=1+H && D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A ], cost: 1 28: lbl21 -> lbl81 : D'=1+D, F'=free_2, H'=2+H, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: 3 30: lbl21 -> lbl81 : D'=-1+D, F'=free_3, H'=2+H, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: 3 32: lbl21 -> lbl81 : B'=1+B, F'=free_4, H'=2+H, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: 3 34: lbl21 -> lbl81 : B'=-1+B, F'=free_5, H'=2+H, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: 3 36: lbl21 -> lbl81 : D'=-1+D+A-H, F'=0, H'=A, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: -1+2*A-2*H 38: lbl21 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: -1+2*A-2*H 40: lbl21 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: -1+2*A-2*H 42: lbl21 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ D+H+B>=1 && D+H>=1+B && H+B>=1+D && H>=1+D+B && J==A && A>=2+H ], cost: -1+2*A-2*H 12: lbl81 -> lbl21 : [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 13: lbl81 -> lbl21 : [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && A>=H && J==A ], cost: 1 19: start0 -> lbl81 : B'=0, D'=0, F'=free, H'=1, J'=A, [ A>=1 ], cost: 2 29: start0 -> lbl81 : B'=0, D'=1, F'=free_2, H'=2, J'=A, [ A>=2 ], cost: 4 31: start0 -> lbl81 : B'=0, D'=-1, F'=free_3, H'=2, J'=A, [ A>=2 ], cost: 4 33: start0 -> lbl81 : B'=1, D'=0, F'=free_4, H'=2, J'=A, [ A>=2 ], cost: 4 35: start0 -> lbl81 : B'=-1, D'=0, F'=free_5, H'=2, J'=A, [ A>=2 ], cost: 4 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A Eliminated locations (on tree-shaped paths): Start location: start0 44: lbl81 -> lbl81 : F'=free_1, H'=1+H, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=1+H ], cost: 2 45: lbl81 -> lbl81 : D'=1+D, F'=free_2, H'=2+H, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 46: lbl81 -> lbl81 : D'=-1+D, F'=free_3, H'=2+H, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 47: lbl81 -> lbl81 : B'=1+B, F'=free_4, H'=2+H, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 48: lbl81 -> lbl81 : B'=-1+B, F'=free_5, H'=2+H, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 49: lbl81 -> lbl81 : D'=-1+D+A-H, F'=0, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 50: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 51: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 52: lbl81 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 53: lbl81 -> lbl81 : F'=free_1, H'=1+H, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=1+H ], cost: 2 54: lbl81 -> lbl81 : D'=1+D, F'=free_2, H'=2+H, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 55: lbl81 -> lbl81 : D'=-1+D, F'=free_3, H'=2+H, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 56: lbl81 -> lbl81 : B'=1+B, F'=free_4, H'=2+H, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 57: lbl81 -> lbl81 : B'=-1+B, F'=free_5, H'=2+H, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 4 58: lbl81 -> lbl81 : D'=-1+D+A-H, F'=0, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 59: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 60: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 61: lbl81 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 19: start0 -> lbl81 : B'=0, D'=0, F'=free, H'=1, J'=A, [ A>=1 ], cost: 2 29: start0 -> lbl81 : B'=0, D'=1, F'=free_2, H'=2, J'=A, [ A>=2 ], cost: 4 31: start0 -> lbl81 : B'=0, D'=-1, F'=free_3, H'=2, J'=A, [ A>=2 ], cost: 4 33: start0 -> lbl81 : B'=1, D'=0, F'=free_4, H'=2, J'=A, [ A>=2 ], cost: 4 35: start0 -> lbl81 : B'=-1, D'=0, F'=free_5, H'=2, J'=A, [ A>=2 ], cost: 4 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A Applied pruning (of leafs and parallel rules): Start location: start0 50: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 51: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 59: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 60: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 61: lbl81 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 33: start0 -> lbl81 : B'=1, D'=0, F'=free_4, H'=2, J'=A, [ A>=2 ], cost: 4 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A Accelerating simple loops of location 6. Accelerating the following rules: 50: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 51: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 59: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 60: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 61: lbl81 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H Found no metering function for rule 50. Found no metering function for rule 51. Found no metering function for rule 59. Found no metering function for rule 60. Found no metering function for rule 61. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: start0 50: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 51: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ 0>=1+F && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 59: lbl81 -> lbl81 : D'=1+D-A+H, F'=1, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 60: lbl81 -> lbl81 : B'=-1+A-H+B, F'=2, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 61: lbl81 -> lbl81 : B'=1-A+H+B, F'=3, H'=A, [ F>=4 && D+H>=1+B && H+B>=1+D && H>=1+D+B && D+H+B>=1 && J==A && A>=2+H ], cost: 2*A-2*H 33: start0 -> lbl81 : B'=1, D'=0, F'=free_4, H'=2, J'=A, [ A>=2 ], cost: 4 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A Chained accelerated rules (with incoming rules): Start location: start0 33: start0 -> lbl81 : B'=1, D'=0, F'=free_4, H'=2, J'=A, [ A>=2 ], cost: 4 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A 62: start0 -> lbl81 : B'=1, D'=3-A, F'=1, H'=A, J'=A, [ A>=4 ], cost: 2*A 63: start0 -> lbl81 : B'=-2+A, D'=0, F'=2, H'=A, J'=A, [ A>=4 ], cost: 2*A 64: start0 -> lbl81 : B'=1, D'=3-A, F'=1, H'=A, J'=A, [ A>=4 ], cost: 2*A 65: start0 -> lbl81 : B'=-2+A, D'=0, F'=2, H'=A, J'=A, [ A>=4 ], cost: 2*A 66: start0 -> lbl81 : B'=4-A, D'=0, F'=3, H'=A, J'=A, [ A>=4 ], cost: 2*A Removed unreachable locations (and leaf rules with constant cost): Start location: start0 37: start0 -> lbl81 : B'=0, D'=-1+A, F'=0, H'=A, J'=A, [ A>=2 ], cost: 2*A 39: start0 -> lbl81 : B'=0, D'=1-A, F'=1, H'=A, J'=A, [ A>=2 ], cost: 2*A 41: start0 -> lbl81 : B'=-1+A, D'=0, F'=2, H'=A, J'=A, [ A>=2 ], cost: 2*A 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A 62: start0 -> lbl81 : B'=1, D'=3-A, F'=1, H'=A, J'=A, [ A>=4 ], cost: 2*A 63: start0 -> lbl81 : B'=-2+A, D'=0, F'=2, H'=A, J'=A, [ A>=4 ], cost: 2*A 64: start0 -> lbl81 : B'=1, D'=3-A, F'=1, H'=A, J'=A, [ A>=4 ], cost: 2*A 65: start0 -> lbl81 : B'=-2+A, D'=0, F'=2, H'=A, J'=A, [ A>=4 ], cost: 2*A 66: start0 -> lbl81 : B'=4-A, D'=0, F'=3, H'=A, J'=A, [ A>=4 ], cost: 2*A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start0 43: start0 -> lbl81 : B'=1-A, D'=0, F'=3, H'=A, J'=A, [ A>=2 ], cost: 2*A 66: start0 -> lbl81 : B'=4-A, D'=0, F'=3, H'=A, J'=A, [ A>=4 ], cost: 2*A Computing asymptotic complexity for rule 43 Solved the limit problem by the following transformations: Created initial limit problem: -1+A (+/+!), 2*A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n} resulting limit problem: [solved] Solution: A / n Resulting cost 2*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2*n Rule cost: 2*A Rule guard: [ A>=2 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)