17.63/8.30 WORST_CASE(Omega(n^1), O(n^1)) 17.63/8.31 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 17.63/8.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.63/8.31 17.63/8.31 17.63/8.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 17.63/8.31 17.63/8.31 (0) CpxIntTrs 17.63/8.31 (1) Koat Proof [FINISHED, 496 ms] 17.63/8.31 (2) BOUNDS(1, n^1) 17.63/8.31 (3) Loat Proof [FINISHED, 6441 ms] 17.63/8.31 (4) BOUNDS(n^1, INF) 17.63/8.31 17.63/8.31 17.63/8.31 ---------------------------------------- 17.63/8.31 17.63/8.31 (0) 17.63/8.31 Obligation: 17.63/8.31 Complexity Int TRS consisting of the following rules: 17.63/8.31 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 2 17.63/8.31 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f9(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= B + 1 17.63/8.31 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f9(A, B, C, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 + S && A >= D 17.63/8.31 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f9(A, B, S, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: S >= C && A >= D 17.63/8.31 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f26(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 17.63/8.31 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f32(A, B, C, D + 1, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R)) :|: A >= D 17.63/8.31 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f32(A, B, C, D + 1, E, F, G, S, S * S, J + S * S, K, L, M, N, O, P, Q, R)) :|: 0 >= S + 1 && A >= D 17.63/8.31 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f32(A, B, C, D + 1, E, F, G, S, S * S, J + S * S, K, L, M, N, O, P, Q, R)) :|: S >= 1 && A >= D 17.63/8.31 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= K 17.63/8.31 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D + 1, E, F, G, H, I, J + S * T, K, L, M, N, O, P, Q, R)) :|: A >= D 17.63/8.31 f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f62(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 17.63/8.31 f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K + 1, L, M, N, O, P, Q, R)) :|: D >= 1 + A 17.63/8.31 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f62(A, B, C, D, E, F, G, H, I, J, K, S, M, N, O, P, Q, R)) :|: J >= T * U && T * U + T >= J + 1 && T >= S && J >= U * V && U * V + V >= J + 1 && S >= V && D >= 1 + A 17.63/8.31 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f5(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: K >= 1 + A 17.63/8.31 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, S, T, T, P, Q, R)) :|: D >= 1 + A 17.63/8.31 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, -(S), T, S, R)) :|: D >= 1 + A 17.63/8.31 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: D >= 1 + A 17.63/8.31 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f5(A, B + 1, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, 0)) :|: D >= 1 + A && C >= 0 && C <= 0 17.63/8.31 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= C + 1 && D >= 1 + A 17.63/8.31 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 && D >= 1 + A 17.63/8.31 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A && 0 >= S + 1 17.63/8.31 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A && S >= 1 17.63/8.31 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A 17.63/8.31 17.63/8.31 The start-symbols are:[f2_18] 17.63/8.31 17.63/8.31 17.63/8.31 ---------------------------------------- 17.63/8.31 17.63/8.31 (1) Koat Proof (FINISHED) 17.63/8.31 YES(?, 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 39) 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Initial complexity problem: 17.63/8.31 17.63/8.31 1: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0, 0, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, s^2, ar_9 + s^2, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, s^2, ar_9 + s^2, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + s*t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, s, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, s, t, t, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, -s, t, s, ar_17)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, 0)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (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, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_9, ar_10]. 17.63/8.31 17.63/8.31 We thus obtain the following problem: 17.63/8.31 17.63/8.31 2: T: 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s^2, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s^2, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Testing for reachability in the complexity graph removes the following transitions from problem 2: 17.63/8.31 17.63/8.31 f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s^2, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s^2, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 We thus obtain the following problem: 17.63/8.31 17.63/8.31 3: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Repeatedly propagating knowledge in problem 3 produces the following problem: 17.63/8.31 17.63/8.31 4: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 A polynomial rank function with 17.63/8.31 17.63/8.31 Pol(f62) = 1 17.63/8.31 17.63/8.31 Pol(f52) = 1 17.63/8.31 17.63/8.31 Pol(f55) = 1 17.63/8.31 17.63/8.31 Pol(f5) = 1 17.63/8.31 17.63/8.31 Pol(f32) = 1 17.63/8.31 17.63/8.31 Pol(f26) = 1 17.63/8.31 17.63/8.31 Pol(f9) = 1 17.63/8.31 17.63/8.31 Pol(f1) = 0 17.63/8.31 17.63/8.31 Pol(f2) = 1 17.63/8.31 17.63/8.31 Pol(koat_start) = 1 17.63/8.31 17.63/8.31 orients all transitions weakly and the transitions 17.63/8.31 17.63/8.31 f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 strictly and produces the following problem: 17.63/8.31 17.63/8.31 5: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 A polynomial rank function with 17.63/8.31 17.63/8.31 Pol(f62) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f52) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f55) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f5) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f32) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f26) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f9) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(f1) = V_1 - V_4 17.63/8.31 17.63/8.31 Pol(f2) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 Pol(koat_start) = V_1 - V_4 + 1 17.63/8.31 17.63/8.31 orients all transitions weakly and the transitions 17.63/8.31 17.63/8.31 f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 strictly and produces the following problem: 17.63/8.31 17.63/8.31 6: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Repeatedly propagating knowledge in problem 6 produces the following problem: 17.63/8.31 17.63/8.31 7: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 A polynomial rank function with 17.63/8.31 17.63/8.31 Pol(f9) = 0 17.63/8.31 17.63/8.31 Pol(f5) = 0 17.63/8.31 17.63/8.31 Pol(f62) = 1 17.63/8.31 17.63/8.31 Pol(f52) = 1 17.63/8.31 17.63/8.31 Pol(f55) = 1 17.63/8.31 17.63/8.31 and size complexities 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-1) = ar_1 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-2) = ar_2 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-3) = ar_3 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-4) = ar_9 17.63/8.31 17.63/8.31 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ]", 0-5) = ar_10 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-1) = ar_1 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-2) = ar_2 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-3) = ar_3 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-4) = ar_9 17.63/8.31 17.63/8.31 S("f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ]", 0-5) = ar_10 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-2) = 0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\\ t*u + t >= ar_9 + 1 /\\ t >= s /\\ ar_9 >= u*v /\\ u*v + v >= ar_9 + 1 /\\ s >= v /\\ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ]", 0-5) = ? 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 17.63/8.31 17.63/8.31 S("f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-5) = ? 17.63/8.31 17.63/8.31 orients the transitions 17.63/8.31 17.63/8.31 f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 weakly and the transition 17.63/8.31 17.63/8.31 f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 strictly and produces the following problem: 17.63/8.31 17.63/8.31 8: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 A polynomial rank function with 17.63/8.31 17.63/8.31 Pol(f62) = V_1 - V_6 17.63/8.31 17.63/8.31 Pol(f52) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(f55) = V_1 - V_6 17.63/8.31 17.63/8.31 Pol(f5) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(f32) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(f26) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(f9) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(f1) = V_1 - V_6 17.63/8.31 17.63/8.31 Pol(f2) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 Pol(koat_start) = V_1 - V_6 + 1 17.63/8.31 17.63/8.31 orients all transitions weakly and the transition 17.63/8.31 17.63/8.31 f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 strictly and produces the following problem: 17.63/8.31 17.63/8.31 9: T: 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Repeatedly propagating knowledge in problem 9 produces the following problem: 17.63/8.31 17.63/8.31 10: T: 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 A polynomial rank function with 17.63/8.31 17.63/8.31 Pol(f62) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f52) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f55) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f5) = V_1 - V_2 17.63/8.31 17.63/8.31 Pol(f32) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f26) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f9) = V_1 - V_2 - 1 17.63/8.31 17.63/8.31 Pol(f1) = V_1 - V_2 17.63/8.31 17.63/8.31 Pol(f2) = V_1 - V_2 17.63/8.31 17.63/8.31 Pol(koat_start) = V_1 - V_2 17.63/8.31 17.63/8.31 orients all transitions weakly and the transition 17.63/8.31 17.63/8.31 f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 strictly and produces the following problem: 17.63/8.31 17.63/8.31 11: T: 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Repeatedly propagating knowledge in problem 11 produces the following problem: 17.63/8.31 17.63/8.31 12: T: 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_9 + s*t, ar_10)) [ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_9 >= t*u /\ t*u + t >= ar_9 + 1 /\ t >= s /\ ar_9 >= u*v /\ u*v + v >= ar_9 + 1 /\ s >= v /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= ar_10 ] 17.63/8.31 17.63/8.31 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_9, ar_10)) [ ar_10 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_9, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_9, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 17.63/8.31 17.63/8.31 (Comp: 3*ar_0 + ar_1 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 17.63/8.31 17.63/8.31 (Comp: ar_0 + ar_1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_9, ar_10)) [ ar_0 >= ar_1 + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_1 >= ar_0 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ ar_0 >= 2 ] 17.63/8.31 17.63/8.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_9, ar_10)) [ 0 <= 0 ] 17.63/8.31 17.63/8.31 start location: koat_start 17.63/8.31 17.63/8.31 leaf cost: 0 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Complexity upper bound 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 39 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Time: 0.455 sec (SMT: 0.322 sec) 17.63/8.31 17.63/8.31 17.63/8.31 ---------------------------------------- 17.63/8.31 17.63/8.31 (2) 17.63/8.31 BOUNDS(1, n^1) 17.63/8.31 17.63/8.31 ---------------------------------------- 17.63/8.31 17.63/8.31 (3) Loat Proof (FINISHED) 17.63/8.31 17.63/8.31 17.63/8.31 ### Pre-processing the ITS problem ### 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Initial linear ITS problem 17.63/8.31 17.63/8.31 Start location: f2 17.63/8.31 17.63/8.31 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.31 17.63/8.31 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 17.63/8.31 17.63/8.31 20: f5 -> f1 : [ B>=A && 0>=1+free_14 ], cost: 1 17.63/8.31 17.63/8.31 21: f5 -> f1 : [ B>=A && free_15>=1 ], cost: 1 17.63/8.31 17.63/8.31 22: f5 -> f1 : [ B>=A ], cost: 1 17.63/8.31 17.63/8.31 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 17.63/8.31 17.63/8.31 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17.63/8.31 17.63/8.31 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 17.63/8.31 17.63/8.31 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 16: f26 -> f32 : [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_2^2, J'=J+free_2^2, [ 0>=1+free_2 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 7: f32 -> f32 : D'=1+D, H'=free_3, Q'=free_3^2, J'=free_3^2+J, [ free_3>=1 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 14: f32 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 15: f32 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 8: f52 -> f55 : [ A>=K ], cost: 1 17.63/8.31 17.63/8.31 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.31 17.63/8.31 9: f55 -> f55 : D'=1+D, J'=J+free_5*free_4, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 12: f55 -> f62 : L'=free_7, [ J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Removed unreachable and leaf rules: 17.63/8.31 17.63/8.31 Start location: f2 17.63/8.31 17.63/8.31 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.31 17.63/8.31 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 17.63/8.31 17.63/8.31 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 17.63/8.31 17.63/8.31 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17.63/8.31 17.63/8.31 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 17.63/8.31 17.63/8.31 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 16: f26 -> f32 : [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_2^2, J'=J+free_2^2, [ 0>=1+free_2 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 7: f32 -> f32 : D'=1+D, H'=free_3, Q'=free_3^2, J'=free_3^2+J, [ free_3>=1 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 14: f32 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 15: f32 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 8: f52 -> f55 : [ A>=K ], cost: 1 17.63/8.31 17.63/8.31 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.31 17.63/8.31 9: f55 -> f55 : D'=1+D, J'=J+free_5*free_4, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 12: f55 -> f62 : L'=free_7, [ J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 ### Simplification by acceleration and chaining ### 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerating simple loops of location 2. 17.63/8.31 17.63/8.31 Accelerating the following rules: 17.63/8.31 17.63/8.31 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 17.63/8.31 17.63/8.31 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated rule 2 with metering function 1-D+A, yielding the new rule 23. 17.63/8.31 17.63/8.31 Accelerated rule 3 with metering function 1-D+A, yielding the new rule 24. 17.63/8.31 17.63/8.31 Removing the simple loops: 2 3. 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerating simple loops of location 3. 17.63/8.31 17.63/8.31 Accelerating the following rules: 17.63/8.31 17.63/8.31 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated rule 4 with metering function 1-D+A, yielding the new rule 25. 17.63/8.31 17.63/8.31 Removing the simple loops: 4. 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerating simple loops of location 4. 17.63/8.31 17.63/8.31 Accelerating the following rules: 17.63/8.31 17.63/8.31 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_2^2, J'=J+free_2^2, [ 0>=1+free_2 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 7: f32 -> f32 : D'=1+D, H'=free_3, Q'=free_3^2, J'=free_3^2+J, [ free_3>=1 && A>=D ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated rule 5 with metering function 1-D+A, yielding the new rule 26. 17.63/8.31 17.63/8.31 Accelerated rule 6 with metering function 1-D+A, yielding the new rule 27. 17.63/8.31 17.63/8.31 Accelerated rule 7 with metering function 1-D+A, yielding the new rule 28. 17.63/8.31 17.63/8.31 Removing the simple loops: 5 6 7. 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerating simple loops of location 6. 17.63/8.31 17.63/8.31 Accelerating the following rules: 17.63/8.31 17.63/8.31 9: f55 -> f55 : D'=1+D, J'=J+free_5*free_4, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated rule 9 with metering function 1-D+A, yielding the new rule 29. 17.63/8.31 17.63/8.31 Removing the simple loops: 9. 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerating simple loops of location 7. 17.63/8.31 17.63/8.31 Accelerating the following rules: 17.63/8.31 17.63/8.31 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated rule 10 with metering function 1-D+A, yielding the new rule 30. 17.63/8.31 17.63/8.31 Removing the simple loops: 10. 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Accelerated all simple loops using metering functions (where possible): 17.63/8.31 17.63/8.31 Start location: f2 17.63/8.31 17.63/8.31 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.31 17.63/8.31 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 17.63/8.31 17.63/8.31 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 17.63/8.31 17.63/8.31 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 23: f9 -> f9 : D'=1+A, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 24: f9 -> f9 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 16: f26 -> f32 : [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 25: f26 -> f26 : D'=1+A, [ A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 14: f32 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 15: f32 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 26: f32 -> f32 : D'=1+A, H'=0, Q'=0, [ A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 27: f32 -> f32 : D'=1+A, H'=free_2, Q'=free_2^2, J'=J-free_2^2*(-1+D-A), [ 0>=1+free_2 && A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 28: f32 -> f32 : D'=1+A, H'=free_3, Q'=free_3^2, J'=-(-1+D-A)*free_3^2+J, [ free_3>=1 && A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 8: f52 -> f55 : [ A>=K ], cost: 1 17.63/8.31 17.63/8.31 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.31 17.63/8.31 12: f55 -> f62 : L'=free_7, [ J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 29: f55 -> f55 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, [ A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 30: f62 -> f62 : D'=1+A, [ A>=D ], cost: 1-D+A 17.63/8.31 17.63/8.31 17.63/8.31 17.63/8.31 Chained accelerated rules (with incoming rules): 17.63/8.31 17.63/8.31 Start location: f2 17.63/8.31 17.63/8.31 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.31 17.63/8.31 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 17.63/8.31 17.63/8.31 31: f5 -> f9 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.31 17.63/8.31 32: f5 -> f9 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.31 17.63/8.31 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 17.63/8.31 17.63/8.31 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 16: f26 -> f32 : [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 14: f32 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 15: f32 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 1 17.63/8.31 17.63/8.31 8: f52 -> f55 : [ A>=K ], cost: 1 17.63/8.31 17.63/8.31 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.31 17.63/8.31 33: f52 -> f55 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, [ A>=K && A>=D ], cost: 2-D+A 17.63/8.31 17.63/8.31 12: f55 -> f62 : L'=free_7, [ J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Eliminated locations (on linear paths): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 17.63/8.32 17.63/8.32 31: f5 -> f9 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 32: f5 -> f9 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 17.63/8.32 17.63/8.32 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 16: f26 -> f32 : [ D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 14: f32 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 15: f32 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 1 17.63/8.32 17.63/8.32 8: f52 -> f55 : [ A>=K ], cost: 1 17.63/8.32 17.63/8.32 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.32 17.63/8.32 33: f52 -> f55 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, [ A>=K && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 34: f55 -> f52 : K'=1+K, L'=free_7, [ J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Eliminated locations (on tree-shaped paths): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 35: f5 -> f5 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 36: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 37: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, R'=0, [ A>=1+B && A>=D && free_1==0 ], cost: 3-D+A 17.63/8.32 17.63/8.32 38: f5 -> f26 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 41: f26 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 42: f26 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.32 17.63/8.32 43: f52 -> f52 : K'=1+K, L'=free_7, [ A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 3 17.63/8.32 17.63/8.32 44: f52 -> f52 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, K'=1+K, L'=free_7, [ A>=K && A>=D && -free_5*(-1+D-A)*free_4+J>=free_8*free_9 && free_8+free_8*free_9>=1-free_5*(-1+D-A)*free_4+J && free_8>=free_7 && -free_5*(-1+D-A)*free_4+J>=free_6*free_9 && free_6*free_9+free_6>=1-free_5*(-1+D-A)*free_4+J && free_7>=free_6 ], cost: 4-D+A 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerating simple loops of location 1. 17.63/8.32 17.63/8.32 Simplified some of the simple loops (and removed duplicate rules). 17.63/8.32 17.63/8.32 Accelerating the following rules: 17.63/8.32 17.63/8.32 35: f5 -> f5 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 36: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 37: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerated rule 35 with metering function A-B, yielding the new rule 45. 17.63/8.32 17.63/8.32 Found no metering function for rule 36. 17.63/8.32 17.63/8.32 Found no metering function for rule 37. 17.63/8.32 17.63/8.32 Removing the simple loops: 35. 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerating simple loops of location 5. 17.63/8.32 17.63/8.32 Accelerating the following rules: 17.63/8.32 17.63/8.32 43: f52 -> f52 : K'=1+K, L'=free_7, [ A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 3 17.63/8.32 17.63/8.32 44: f52 -> f52 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, K'=1+K, L'=free_7, [ A>=K && A>=D && -free_5*(-1+D-A)*free_4+J>=free_8*free_9 && free_8+free_8*free_9>=1-free_5*(-1+D-A)*free_4+J && free_8>=free_7 && -free_5*(-1+D-A)*free_4+J>=free_6*free_9 && free_6*free_9+free_6>=1-free_5*(-1+D-A)*free_4+J && free_7>=free_6 ], cost: 4-D+A 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerated rule 43 with metering function 1+A-K, yielding the new rule 46. 17.63/8.32 17.63/8.32 Found no metering function for rule 44 (rule is too complicated). 17.63/8.32 17.63/8.32 Removing the simple loops: 43. 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerated all simple loops using metering functions (where possible): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 36: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 37: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 38: f5 -> f26 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 45: f5 -> f5 : B'=A, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2*A-2*B 17.63/8.32 17.63/8.32 41: f26 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 42: f26 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.32 17.63/8.32 44: f52 -> f52 : D'=1+A, J'=-free_5*(-1+D-A)*free_4+J, K'=1+K, L'=free_7, [ A>=K && A>=D && -free_5*(-1+D-A)*free_4+J>=free_8*free_9 && free_8+free_8*free_9>=1-free_5*(-1+D-A)*free_4+J && free_8>=free_7 && -free_5*(-1+D-A)*free_4+J>=free_6*free_9 && free_6*free_9+free_6>=1-free_5*(-1+D-A)*free_4+J && free_7>=free_6 ], cost: 4-D+A 17.63/8.32 17.63/8.32 46: f52 -> f52 : K'=1+A, L'=free_7, [ A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && D>=1+A ], cost: 3+3*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Chained accelerated rules (with incoming rules): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 38: f5 -> f26 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 41: f26 -> f52 : M'=free_10, N'=free_11, O'=free_11, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 42: f26 -> f52 : O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A ], cost: 2 17.63/8.32 17.63/8.32 53: f26 -> f52 : K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ D>=1+A && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 5+3*A-3*K 17.63/8.32 17.63/8.32 54: f26 -> f52 : K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ D>=1+A && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 5+3*A-3*K 17.63/8.32 17.63/8.32 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.32 17.63/8.32 48: f52 -> f5 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 50: f52 -> f5 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 52: f52 -> f5 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Eliminated locations (on tree-shaped paths): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 55: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 56: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 57: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 58: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 17.63/8.32 17.63/8.32 48: f52 -> f5 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 50: f52 -> f5 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 52: f52 -> f5 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Eliminated locations (on tree-shaped paths): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 59: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 17.63/8.32 17.63/8.32 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 61: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 17.63/8.32 17.63/8.32 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 63: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 64: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 7-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 65: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 66: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 7-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 67: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 69: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Applied pruning (of leafs and parallel rules): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 63: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 64: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 7-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 65: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerating simple loops of location 1. 17.63/8.32 17.63/8.32 Accelerating the following rules: 17.63/8.32 17.63/8.32 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 63: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 64: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 7-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 65: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Found no metering function for rule 60. 17.63/8.32 17.63/8.32 Found no metering function for rule 62. 17.63/8.32 17.63/8.32 Found no metering function for rule 63. 17.63/8.32 17.63/8.32 Found no metering function for rule 64. 17.63/8.32 17.63/8.32 Found no metering function for rule 65. 17.63/8.32 17.63/8.32 Removing the simple loops:. 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Accelerated all simple loops using metering functions (where possible): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 17.63/8.32 17.63/8.32 63: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 64: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 7-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 65: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Chained accelerated rules (with incoming rules): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 0: f2 -> f5 : [ A>=2 ], cost: 1 17.63/8.32 17.63/8.32 47: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 49: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 71: f2 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 17.63/8.32 17.63/8.32 72: f2 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_12, P'=free_13, Q_1'=free_12, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 17.63/8.32 17.63/8.32 73: f2 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 74: f2 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_10, N'=free_11, O'=free_11, R'=0, [ A>=2 && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 8-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 75: f2 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_12, P'=free_13, Q_1'=free_12, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17.63/8.32 17.63/8.32 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 17.63/8.32 17.63/8.32 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 8-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Eliminated locations (on tree-shaped paths): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 76: f2 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 17.63/8.32 17.63/8.32 79: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 83: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 17.63/8.32 17.63/8.32 84: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 17.63/8.32 17.63/8.32 85: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 86: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 8-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 87: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Applied pruning (of leafs and parallel rules): 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 76: f2 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 17.63/8.32 17.63/8.32 79: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 9-D+4*A-3*K 17.63/8.32 17.63/8.32 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 86: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 8-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 87: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 ### Computing asymptotic complexity ### 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Fully simplified ITS problem 17.63/8.32 17.63/8.32 Start location: f2 17.63/8.32 17.63/8.32 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 17.63/8.32 17.63/8.32 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 17.63/8.32 17.63/8.32 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 17.63/8.32 17.63/8.32 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 17.63/8.32 17.63/8.32 86: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 && A>=2+B ], cost: 8-D+6*A-3*K-2*B 17.63/8.32 17.63/8.32 87: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K && J>=free_8*free_9 && free_8+free_8*free_9>=1+J && free_8>=free_7 && J>=free_6*free_9 && free_6*free_9+free_6>=1+J && free_7>=free_6 ], cost: 10-D+4*A-3*K 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Computing asymptotic complexity for rule 77 17.63/8.32 17.63/8.32 Solved the limit problem by the following transformations: 17.63/8.32 17.63/8.32 Created initial limit problem: 17.63/8.32 17.63/8.32 1+free_1 (+/+!), -1+A (+/+!), 3-D+A (+), 1-D+A (+/+!), A-B (+/+!) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (C) using substitution {A==2} 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (C) using substitution {A==1+B} 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (C) using substitution {free_1==0} 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (C) using substitution {A==D} 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (B), deleting 1 (+/+!) 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 3-D (+/+!), 2-B (+/+!), 5-D (+) [not solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 removing all constraints (solved by SMT) 17.63/8.32 17.63/8.32 resulting limit problem: [solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 applying transformation rule (C) using substitution {D==-n,B==0} 17.63/8.32 17.63/8.32 resulting limit problem: 17.63/8.32 17.63/8.32 [solved] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Solution: 17.63/8.32 17.63/8.32 D / -n 17.63/8.32 17.63/8.32 A / 2 17.63/8.32 17.63/8.32 free_1 / 0 17.63/8.32 17.63/8.32 B / 0 17.63/8.32 17.63/8.32 Resulting cost 5+n has complexity: Poly(n^1) 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Found new complexity Poly(n^1). 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 Obtained the following overall complexity (w.r.t. the length of the input n): 17.63/8.32 17.63/8.32 Complexity: Poly(n^1) 17.63/8.32 17.63/8.32 Cpx degree: 1 17.63/8.32 17.63/8.32 Solved cost: 5+n 17.63/8.32 17.63/8.32 Rule cost: 3-D+A 17.63/8.32 17.63/8.32 Rule guard: [ A>=2 && A>=1+B && free_1>=0 && A>=D ] 17.63/8.32 17.63/8.32 17.63/8.32 17.63/8.32 WORST_CASE(Omega(n^1),?) 17.63/8.32 17.63/8.32 17.63/8.32 ---------------------------------------- 17.63/8.32 17.63/8.32 (4) 17.63/8.32 BOUNDS(n^1, INF) 17.74/8.34 EOF