16.20/7.55 WORST_CASE(Omega(n^1), O(n^1)) 16.20/7.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 16.20/7.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.20/7.56 16.20/7.56 16.20/7.56 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 16.20/7.56 16.20/7.56 (0) CpxIntTrs 16.20/7.56 (1) Koat Proof [FINISHED, 398 ms] 16.20/7.56 (2) BOUNDS(1, n^1) 16.20/7.56 (3) Loat Proof [FINISHED, 5746 ms] 16.20/7.56 (4) BOUNDS(n^1, INF) 16.20/7.56 16.20/7.56 16.20/7.56 ---------------------------------------- 16.20/7.56 16.20/7.56 (0) 16.20/7.56 Obligation: 16.20/7.56 Complexity Int TRS consisting of the following rules: 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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, T, J + T, K, L, M, N, O, P, Q, R)) :|: 0 >= S + 1 && A >= D 16.20/7.56 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, T, J + T, K, L, M, N, O, P, Q, R)) :|: S >= 1 && A >= D 16.20/7.56 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 16.20/7.56 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, S, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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)) :|: D >= 1 + A 16.20/7.56 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 16.20/7.56 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)) :|: U >= 0 && D >= 1 + A 16.20/7.56 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)) :|: 0 >= U + 1 && D >= 1 + A 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 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 16.20/7.56 16.20/7.56 The start-symbols are:[f2_18] 16.20/7.56 16.20/7.56 16.20/7.56 ---------------------------------------- 16.20/7.56 16.20/7.56 (1) Koat Proof (FINISHED) 16.20/7.56 YES(?, 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 39) 16.20/7.56 16.20/7.56 16.20/7.56 16.20/7.56 Initial complexity problem: 16.20/7.56 16.20/7.56 1: T: 16.20/7.56 16.20/7.56 (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 ] 16.20/7.56 16.20/7.56 (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 ] 16.20/7.56 16.20/7.56 (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 ] 16.20/7.56 16.20/7.56 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (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, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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, s, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (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)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 (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 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_10]. 16.20/7.57 16.20/7.57 We thus obtain the following problem: 16.20/7.57 16.20/7.57 2: T: 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Testing for reachability in the complexity graph removes the following transitions from problem 2: 16.20/7.57 16.20/7.57 f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 We thus obtain the following problem: 16.20/7.57 16.20/7.57 3: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Repeatedly propagating knowledge in problem 3 produces the following problem: 16.20/7.57 16.20/7.57 4: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 A polynomial rank function with 16.20/7.57 16.20/7.57 Pol(f62) = 1 16.20/7.57 16.20/7.57 Pol(f52) = 1 16.20/7.57 16.20/7.57 Pol(f55) = 1 16.20/7.57 16.20/7.57 Pol(f5) = 1 16.20/7.57 16.20/7.57 Pol(f32) = 1 16.20/7.57 16.20/7.57 Pol(f26) = 1 16.20/7.57 16.20/7.57 Pol(f9) = 1 16.20/7.57 16.20/7.57 Pol(f1) = 0 16.20/7.57 16.20/7.57 Pol(f2) = 1 16.20/7.57 16.20/7.57 Pol(koat_start) = 1 16.20/7.57 16.20/7.57 orients all transitions weakly and the transitions 16.20/7.57 16.20/7.57 f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 strictly and produces the following problem: 16.20/7.57 16.20/7.57 5: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 A polynomial rank function with 16.20/7.57 16.20/7.57 Pol(f62) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f52) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f55) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f5) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f32) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f26) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f9) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(f1) = V_1 - V_4 16.20/7.57 16.20/7.57 Pol(f2) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 Pol(koat_start) = V_1 - V_4 + 1 16.20/7.57 16.20/7.57 orients all transitions weakly and the transitions 16.20/7.57 16.20/7.57 f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 strictly and produces the following problem: 16.20/7.57 16.20/7.57 6: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Repeatedly propagating knowledge in problem 6 produces the following problem: 16.20/7.57 16.20/7.57 7: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 A polynomial rank function with 16.20/7.57 16.20/7.57 Pol(f9) = 0 16.20/7.57 16.20/7.57 Pol(f5) = 0 16.20/7.57 16.20/7.57 Pol(f62) = 1 16.20/7.57 16.20/7.57 Pol(f52) = 1 16.20/7.57 16.20/7.57 Pol(f55) = 1 16.20/7.57 16.20/7.57 and size complexities 16.20/7.57 16.20/7.57 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-1) = ar_1 16.20/7.57 16.20/7.57 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-2) = ar_2 16.20/7.57 16.20/7.57 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-3) = ar_3 16.20/7.57 16.20/7.57 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-4) = ar_10 16.20/7.57 16.20/7.57 S("f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-1) = ar_1 16.20/7.57 16.20/7.57 S("f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-2) = ar_2 16.20/7.57 16.20/7.57 S("f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-3) = ar_3 16.20/7.57 16.20/7.57 S("f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-4) = ar_10 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ s >= 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-2) = 0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-4) = ? 16.20/7.57 16.20/7.57 S("f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.20/7.57 16.20/7.57 S("f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.20/7.57 16.20/7.57 S("f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.20/7.57 16.20/7.57 S("f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.20/7.57 16.20/7.57 S("f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.20/7.57 16.20/7.57 orients the transitions 16.20/7.57 16.20/7.57 f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 weakly and the transition 16.20/7.57 16.20/7.57 f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 strictly and produces the following problem: 16.20/7.57 16.20/7.57 8: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 A polynomial rank function with 16.20/7.57 16.20/7.57 Pol(f62) = V_1 - V_5 16.20/7.57 16.20/7.57 Pol(f52) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(f55) = V_1 - V_5 16.20/7.57 16.20/7.57 Pol(f5) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(f32) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(f26) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(f9) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(f1) = V_1 - V_5 16.20/7.57 16.20/7.57 Pol(f2) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 Pol(koat_start) = V_1 - V_5 + 1 16.20/7.57 16.20/7.57 orients all transitions weakly and the transition 16.20/7.57 16.20/7.57 f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 strictly and produces the following problem: 16.20/7.57 16.20/7.57 9: T: 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Repeatedly propagating knowledge in problem 9 produces the following problem: 16.20/7.57 16.20/7.57 10: T: 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 A polynomial rank function with 16.20/7.57 16.20/7.57 Pol(f62) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f52) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f55) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f5) = V_1 - V_2 16.20/7.57 16.20/7.57 Pol(f32) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f26) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f9) = V_1 - V_2 - 1 16.20/7.57 16.20/7.57 Pol(f1) = V_1 - V_2 16.20/7.57 16.20/7.57 Pol(f2) = V_1 - V_2 16.20/7.57 16.20/7.57 Pol(koat_start) = V_1 - V_2 16.20/7.57 16.20/7.57 orients all transitions weakly and the transition 16.20/7.57 16.20/7.57 f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 strictly and produces the following problem: 16.20/7.57 16.20/7.57 11: T: 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Repeatedly propagating knowledge in problem 11 produces the following problem: 16.20/7.57 16.20/7.57 12: T: 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_10 + 1, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.57 16.20/7.57 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f52(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ u >= 0 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f52(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f32(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_3 + 1, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.57 16.20/7.57 (Comp: 3*ar_0 + ar_1 + 2*ar_3 + 2, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.57 16.20/7.57 (Comp: ar_0 + ar_1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ s >= 1 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.57 16.20/7.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.57 16.20/7.57 start location: koat_start 16.20/7.57 16.20/7.57 leaf cost: 0 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Complexity upper bound 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 39 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Time: 0.400 sec (SMT: 0.297 sec) 16.20/7.57 16.20/7.57 16.20/7.57 ---------------------------------------- 16.20/7.57 16.20/7.57 (2) 16.20/7.57 BOUNDS(1, n^1) 16.20/7.57 16.20/7.57 ---------------------------------------- 16.20/7.57 16.20/7.57 (3) Loat Proof (FINISHED) 16.20/7.57 16.20/7.57 16.20/7.57 ### Pre-processing the ITS problem ### 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Initial linear ITS problem 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 20: f5 -> f1 : [ B>=A && 0>=1+free_14 ], cost: 1 16.20/7.57 16.20/7.57 21: f5 -> f1 : [ B>=A && free_15>=1 ], cost: 1 16.20/7.57 16.20/7.57 22: f5 -> f1 : [ B>=A ], cost: 1 16.20/7.57 16.20/7.57 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.20/7.57 16.20/7.57 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 7: f32 -> f32 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ free_10>=0 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ 0>=1+free_13 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 12: f55 -> f62 : L'=free_7, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Removed unreachable and leaf rules: 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.20/7.57 16.20/7.57 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 7: f32 -> f32 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ free_10>=0 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ 0>=1+free_13 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 12: f55 -> f62 : L'=free_7, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Simplified all rules, resulting in: 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.20/7.57 16.20/7.57 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 7: f32 -> f32 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 12: f55 -> f62 : L'=free_7, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 ### Simplification by acceleration and chaining ### 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 2. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 2: f9 -> f9 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.20/7.57 16.20/7.57 3: f9 -> f9 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 2 with metering function 1-D+A, yielding the new rule 23. 16.20/7.57 16.20/7.57 Accelerated rule 3 with metering function 1-D+A, yielding the new rule 24. 16.20/7.57 16.20/7.57 Removing the simple loops: 2 3. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 3. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 4: f26 -> f26 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 4 with metering function 1-D+A, yielding the new rule 25. 16.20/7.57 16.20/7.57 Removing the simple loops: 4. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 4. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 5: f32 -> f32 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 6: f32 -> f32 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 7: f32 -> f32 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 5 with metering function 1-D+A, yielding the new rule 26. 16.20/7.57 16.20/7.57 Accelerated rule 6 with metering function 1-D+A, yielding the new rule 27. 16.20/7.57 16.20/7.57 Accelerated rule 7 with metering function 1-D+A, yielding the new rule 28. 16.20/7.57 16.20/7.57 Removing the simple loops: 5 6 7. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 6. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 9 with metering function 1-D+A, yielding the new rule 29. 16.20/7.57 16.20/7.57 Removing the simple loops: 9. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 7. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 10: f62 -> f62 : D'=1+D, [ A>=D ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 10 with metering function 1-D+A, yielding the new rule 30. 16.20/7.57 16.20/7.57 Removing the simple loops: 10. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated all simple loops using metering functions (where possible): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 23: f9 -> f9 : D'=1+A, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 25: f26 -> f26 : D'=1+A, [ A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 26: f32 -> f32 : D'=1+A, H'=0, Q'=0, [ A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 27: f32 -> f32 : D'=1+A, H'=free_2, Q'=free_3, J'=-free_3*(-1+D-A)+J, [ 0>=1+free_2 && A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 28: f32 -> f32 : D'=1+A, H'=free_4, Q'=free_5, J'=J-(-1+D-A)*free_5, [ free_4>=1 && A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 12: f55 -> f62 : L'=free_7, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 29: f55 -> f55 : D'=1+A, J'=free_6, [ A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 30: f62 -> f62 : D'=1+A, [ A>=D ], cost: 1-D+A 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Chained accelerated rules (with incoming rules): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 33: f52 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 12: f55 -> f62 : L'=free_7, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 11: f62 -> f52 : K'=1+K, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Eliminated locations (on linear paths): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 1: f5 -> f9 : C'=0, [ A>=1+B ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 17: f9 -> f5 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.20/7.57 16.20/7.57 18: f9 -> f26 : [ 0>=1+C && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 19: f9 -> f26 : [ C>=1 && D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 16: f26 -> f32 : [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 14: f32 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 15: f32 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 1 16.20/7.57 16.20/7.57 8: f52 -> f55 : [ A>=K ], cost: 1 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 33: f52 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 34: f55 -> f52 : K'=1+K, L'=free_7, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Eliminated locations (on tree-shaped paths): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 35: f5 -> f5 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 41: f26 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 42: f26 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 43: f52 -> f52 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 16.20/7.57 16.20/7.57 44: f52 -> f52 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 1. 16.20/7.57 16.20/7.57 Simplified some of the simple loops (and removed duplicate rules). 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 35: f5 -> f5 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 35 with metering function A-B, yielding the new rule 45. 16.20/7.57 16.20/7.57 Found no metering function for rule 36. 16.20/7.57 16.20/7.57 Found no metering function for rule 37. 16.20/7.57 16.20/7.57 Removing the simple loops: 35. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 5. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 43: f52 -> f52 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 16.20/7.57 16.20/7.57 44: f52 -> f52 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated rule 43 with metering function 1+A-K, yielding the new rule 46. 16.20/7.57 16.20/7.57 Found no metering function for rule 44. 16.20/7.57 16.20/7.57 Removing the simple loops: 43. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated all simple loops using metering functions (where possible): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 45: f5 -> f5 : B'=A, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2*A-2*B 16.20/7.57 16.20/7.57 41: f26 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 42: f26 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 44: f52 -> f52 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 46: f52 -> f52 : K'=1+A, L'=free_7, [ A>=K && D>=1+A ], cost: 3+3*A-3*K 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Chained accelerated rules (with incoming rules): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 41: f26 -> f52 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 42: f26 -> f52 : O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A ], cost: 2 16.20/7.57 16.20/7.57 53: f26 -> f52 : K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 16.20/7.57 16.20/7.57 54: f26 -> f52 : K'=1+A, L'=free_7, O'=-free_11, P'=free_12, Q_1'=free_11, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 52: f52 -> f5 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Eliminated locations (on tree-shaped paths): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 55: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 56: f5 -> f52 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 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_11, P'=free_12, Q_1'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 13: f52 -> f5 : B'=1+B, [ K>=1+A ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 52: f52 -> f5 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Eliminated locations (on tree-shaped paths): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 59: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.20/7.57 16.20/7.57 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 61: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.20/7.57 16.20/7.57 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 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_11, P'=free_12, Q_1'=free_11, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 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_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 67: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 69: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Applied pruning (of leafs and parallel rules): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 59: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.20/7.57 16.20/7.57 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerating simple loops of location 1. 16.20/7.57 16.20/7.57 Accelerating the following rules: 16.20/7.57 16.20/7.57 59: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.20/7.57 16.20/7.57 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Found no metering function for rule 59. 16.20/7.57 16.20/7.57 Found no metering function for rule 60. 16.20/7.57 16.20/7.57 Found no metering function for rule 62. 16.20/7.57 16.20/7.57 Found no metering function for rule 63. 16.20/7.57 16.20/7.57 Found no metering function for rule 64. 16.20/7.57 16.20/7.57 Removing the simple loops:. 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Accelerated all simple loops using metering functions (where possible): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 59: f5 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.20/7.57 16.20/7.57 60: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 62: f5 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 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_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Chained accelerated rules (with incoming rules): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 0: f2 -> f5 : [ A>=2 ], cost: 1 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 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 16.20/7.57 16.20/7.57 51: f2 -> f5 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 71: f2 -> f5 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 16.20/7.57 16.20/7.57 72: f2 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.20/7.57 16.20/7.57 73: f2 -> f5 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_11, P'=free_12, Q_1'=free_11, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.20/7.57 16.20/7.57 74: 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_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.20/7.57 16.20/7.57 75: 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_8, N'=free_9, O'=free_9, R'=0, [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 39: f5 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 40: f5 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.20/7.57 16.20/7.57 68: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.20/7.57 16.20/7.57 70: f5 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Eliminated locations (on tree-shaped paths): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 76: f2 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.20/7.57 16.20/7.57 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.20/7.57 16.20/7.57 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.20/7.57 16.20/7.57 79: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 83: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 16.20/7.57 16.20/7.57 84: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.20/7.57 16.20/7.57 85: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.20/7.57 16.20/7.57 86: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.20/7.57 16.20/7.57 87: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Applied pruning (of leafs and parallel rules): 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 76: f2 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.20/7.57 16.20/7.57 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.20/7.57 16.20/7.57 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.20/7.57 16.20/7.57 79: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.20/7.57 16.20/7.57 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 86: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.20/7.57 16.20/7.57 87: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 ### Computing asymptotic complexity ### 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Fully simplified ITS problem 16.20/7.57 16.20/7.57 Start location: f2 16.20/7.57 16.20/7.57 77: f2 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.20/7.57 16.20/7.57 78: f2 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.20/7.57 16.20/7.57 80: f2 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 81: f2 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.20/7.57 16.20/7.57 82: f2 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.20/7.57 16.20/7.57 86: f2 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.20/7.57 16.20/7.57 87: f2 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Computing asymptotic complexity for rule 77 16.20/7.57 16.20/7.57 Solved the limit problem by the following transformations: 16.20/7.57 16.20/7.57 Created initial limit problem: 16.20/7.57 16.20/7.57 -1+A (+/+!), 1+free_1 (+/+!), 3-D+A (+), 1-D+A (+/+!), A-B (+/+!) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (C) using substitution {A==2} 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (C) using substitution {A==1+B} 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (C) using substitution {free_1==0} 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (C) using substitution {A==D} 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (B), deleting 1 (+/+!) 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 3-D (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 removing all constraints (solved by SMT) 16.20/7.57 16.20/7.57 resulting limit problem: [solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 applying transformation rule (C) using substitution {D==-n,B==0} 16.20/7.57 16.20/7.57 resulting limit problem: 16.20/7.57 16.20/7.57 [solved] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Solution: 16.20/7.57 16.20/7.57 free_1 / 0 16.20/7.57 16.20/7.57 D / -n 16.20/7.57 16.20/7.57 A / 2 16.20/7.57 16.20/7.57 B / 0 16.20/7.57 16.20/7.57 Resulting cost 5+n has complexity: Poly(n^1) 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Found new complexity Poly(n^1). 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 Obtained the following overall complexity (w.r.t. the length of the input n): 16.20/7.57 16.20/7.57 Complexity: Poly(n^1) 16.20/7.57 16.20/7.57 Cpx degree: 1 16.20/7.57 16.20/7.57 Solved cost: 5+n 16.20/7.57 16.20/7.57 Rule cost: 3-D+A 16.20/7.57 16.20/7.57 Rule guard: [ A>=2 && A>=1+B && free_1>=0 && A>=D ] 16.20/7.57 16.20/7.57 16.20/7.57 16.20/7.57 WORST_CASE(Omega(n^1),?) 16.20/7.57 16.20/7.57 16.20/7.57 ---------------------------------------- 16.20/7.57 16.20/7.57 (4) 16.20/7.57 BOUNDS(n^1, INF) 16.25/8.87 EOF