29.77/14.01 WORST_CASE(Omega(n^1), O(n^1)) 29.77/14.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 29.77/14.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.77/14.03 29.77/14.03 29.77/14.03 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 29.77/14.03 29.77/14.03 (0) CpxIntTrs 29.77/14.03 (1) Koat Proof [FINISHED, 885 ms] 29.77/14.03 (2) BOUNDS(1, n^1) 29.77/14.03 (3) Loat Proof [FINISHED, 12.2 s] 29.77/14.03 (4) BOUNDS(n^1, INF) 29.77/14.03 29.77/14.03 29.77/14.03 ---------------------------------------- 29.77/14.03 29.77/14.03 (0) 29.77/14.03 Obligation: 29.77/14.03 Complexity Int TRS consisting of the following rules: 29.77/14.03 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f16(1, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 1 && A <= 1 29.77/14.03 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: H >= I 29.77/14.03 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f18(A, B, C, D, E, F, G, H, I, J, K + 1, L + 2, M, N, O, P, Q, R, S, T, U, V, W)) :|: J >= K 29.77/14.03 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= A 29.77/14.03 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 2 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, I, J, K, L, H - I + 2, 1, 0, P, Q, R, S, T, U, V, W)) :|: 0 >= I && H >= I 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, I, J, K, L, H - I + 2, 1, 0, P, Q, R, S, T, U, V, W)) :|: I >= 2 && H >= I 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, 1, J, K, L, 1, 1, 0, P, Q, R, S, T, U, V, W)) :|: H >= 1 && I >= 1 && I <= 1 29.77/14.03 f35(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: P >= 2 * X && 3 * X >= P + 1 && X + 1 >= Q 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= Q && J >= K 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: Q >= 2 && J >= K 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, X, M, N, O, P, 1, Y, Z, A1, B1, V, W)) :|: 0 >= K && J >= K && Q >= 1 && Q <= 1 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, X, M, N, O, P, 1, Y, Z, A1, B1, V, W)) :|: J >= K && K >= 2 && Q >= 1 && Q <= 1 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, 2, 1, M, N, O, P, 1, X, Y, Z, A1, V, W)) :|: J >= 1 && K >= 1 && K <= 1 && Q >= 1 && Q <= 1 29.77/14.03 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, J - K + 2, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: 0 >= K 29.77/14.03 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, J - K + 2, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: K >= 2 29.77/14.03 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, 2, 1, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: K >= 1 && K <= 1 29.77/14.03 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, N, F, G, H, I, J, K, L, M, X, Y, P, Q + 1, R, S, T, U, V, W + 2)) :|: K >= 1 + J 29.77/14.03 f35(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: P >= 2 * X && 3 * X >= P + 1 && Q >= 2 + X 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= 2 + A && I >= 1 + H 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 0 && I >= 1 + H 29.77/14.03 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(-(1), B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= 1 + H && A + 1 >= 0 && A + 1 <= 0 29.77/14.03 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f16(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: K >= 1 + J 29.77/14.03 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= 1 + H 29.77/14.03 29.77/14.03 The start-symbols are:[f0_23] 29.77/14.03 29.77/14.03 29.77/14.03 ---------------------------------------- 29.77/14.03 29.77/14.03 (1) Koat Proof (FINISHED) 29.77/14.03 YES(?, 8*ar_7 + 8*ar_8 + 13*ar_9 + 25*ar_10 + 3*ar_15 + 3*ar_16 + 59) 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Initial complexity problem: 29.77/14.03 29.77/14.03 1: T: 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f16(1, x, y, z, a1, b1, c1, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f18(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_18, ar_19, ar_20, ar_21, ar_22)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f18(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 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(ar_0, x, y, z, a1, b1, c1, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(ar_0, x, y, z, a1, b1, c1, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f35(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_7 - ar_8 + 2, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f35(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_7 - ar_8 + 2, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, 1, ar_9, ar_10, ar_11, 1, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(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_18, ar_19, ar_20, ar_21, ar_22)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> 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, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> 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, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, x, ar_12, ar_13, ar_14, ar_15, 1, y, z, a1, b1, ar_21, ar_22)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, x, ar_12, ar_13, ar_14, ar_15, 1, y, z, a1, b1, ar_21, ar_22)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, 2, 1, ar_12, ar_13, ar_14, ar_15, 1, x, y, z, a1, ar_21, ar_22)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_9 - ar_10 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_9 - ar_10 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, 2, 1, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_13, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, x, y, ar_15, ar_16 + 1, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22 + 2)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 + 1, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f76(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_18, ar_19, ar_20, ar_21, ar_22)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f76(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_18, ar_19, ar_20, ar_21, ar_22)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f76(-1, 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_18, ar_19, ar_20, ar_21, ar_22)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 + 1, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(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_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(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_18, ar_19, ar_20, ar_21, ar_22)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f0(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_18, ar_19, ar_20, ar_21, ar_22)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16]. 29.77/14.03 29.77/14.03 We thus obtain the following problem: 29.77/14.03 29.77/14.03 2: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Repeatedly propagating knowledge in problem 2 produces the following problem: 29.77/14.03 29.77/14.03 3: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 A polynomial rank function with 29.77/14.03 29.77/14.03 Pol(koat_start) = 2 29.77/14.03 29.77/14.03 Pol(f0) = 2 29.77/14.03 29.77/14.03 Pol(f16) = 2 29.77/14.03 29.77/14.03 Pol(f28) = 1 29.77/14.03 29.77/14.03 Pol(f18) = 2 29.77/14.03 29.77/14.03 Pol(f76) = 0 29.77/14.03 29.77/14.03 Pol(f35) = 1 29.77/14.03 29.77/14.03 Pol(f37) = 1 29.77/14.03 29.77/14.03 Pol(f52) = 1 29.77/14.03 29.77/14.03 orients all transitions weakly and the transitions 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 strictly and produces the following problem: 29.77/14.03 29.77/14.03 4: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 A polynomial rank function with 29.77/14.03 29.77/14.03 Pol(koat_start) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f0) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f16) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f28) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f18) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f76) = -V_5 29.77/14.03 29.77/14.03 Pol(f35) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f37) = -V_5 + 2 29.77/14.03 29.77/14.03 Pol(f52) = -V_5 + 2 29.77/14.03 29.77/14.03 orients all transitions weakly and the transitions 29.77/14.03 29.77/14.03 f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 strictly and produces the following problem: 29.77/14.03 29.77/14.03 5: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 A polynomial rank function with 29.77/14.03 29.77/14.03 Pol(koat_start) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f0) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f16) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f28) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f18) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f76) = V_4 - V_5 29.77/14.03 29.77/14.03 Pol(f35) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f37) = V_4 - V_5 + 1 29.77/14.03 29.77/14.03 Pol(f52) = V_4 - V_5 29.77/14.03 29.77/14.03 orients all transitions weakly and the transitions 29.77/14.03 29.77/14.03 f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 strictly and produces the following problem: 29.77/14.03 29.77/14.03 6: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Repeatedly propagating knowledge in problem 6 produces the following problem: 29.77/14.03 29.77/14.03 7: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: 2*ar_9 + 2*ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 A polynomial rank function with 29.77/14.03 29.77/14.03 Pol(koat_start) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f0) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f16) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f28) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f18) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f76) = V_6 - V_7 29.77/14.03 29.77/14.03 Pol(f35) = V_6 - V_7 + 1 29.77/14.03 29.77/14.03 Pol(f37) = V_6 - V_7 29.77/14.03 29.77/14.03 Pol(f52) = V_6 - V_7 29.77/14.03 29.77/14.03 orients all transitions weakly and the transition 29.77/14.03 29.77/14.03 f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 strictly and produces the following problem: 29.77/14.03 29.77/14.03 8: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: 2*ar_9 + 2*ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 1, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Repeatedly propagating knowledge in problem 8 produces the following problem: 29.77/14.03 29.77/14.03 9: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 7*ar_10 + 3*ar_9 + 12, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: 2*ar_9 + 2*ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 1, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 A polynomial rank function with 29.77/14.03 29.77/14.03 Pol(koat_start) = V_2 - V_3 + 1 29.77/14.03 29.77/14.03 Pol(f0) = V_2 - V_3 + 1 29.77/14.03 29.77/14.03 Pol(f16) = V_2 - V_3 + 1 29.77/14.03 29.77/14.03 Pol(f28) = V_2 - V_3 + 1 29.77/14.03 29.77/14.03 Pol(f18) = V_2 - V_3 29.77/14.03 29.77/14.03 Pol(f76) = V_2 - V_3 29.77/14.03 29.77/14.03 Pol(f35) = V_2 - V_3 29.77/14.03 29.77/14.03 Pol(f37) = V_2 - V_3 29.77/14.03 29.77/14.03 Pol(f52) = V_2 - V_3 29.77/14.03 29.77/14.03 orients all transitions weakly and the transitions 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 strictly and produces the following problem: 29.77/14.03 29.77/14.03 10: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ?, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 7*ar_10 + 3*ar_9 + 12, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: 2*ar_9 + 2*ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 1, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Repeatedly propagating knowledge in problem 10 produces the following problem: 29.77/14.03 29.77/14.03 11: T: 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 <= 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + ar_9 + ar_10 + 2, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(-1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= ar_7 + 1 /\ ar_0 + 1 = 0 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 0 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 2, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f76(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 + 2 /\ ar_8 >= ar_7 + 1 ] 29.77/14.03 29.77/14.03 (Comp: 3*ar_7 + 3*ar_8 + ar_15 + ar_16 + 7*ar_10 + 3*ar_9 + 15, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8 + 1, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ ar_16 >= x + 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 7*ar_10 + 3*ar_9 + 12, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16 + 1)) [ ar_10 >= ar_9 + 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, ar_16)) [ ar_10 = 1 ] 29.77/14.03 29.77/14.03 (Comp: 2*ar_9 + 2*ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_10 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ 0 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, 2, ar_15, 1)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_10 + 2, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, 1)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_16 >= 2 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f52(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_15 + ar_16 + 1, Cost: 1) f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f37(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, 1, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= 1 /\ ar_8 = 1 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f35(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 >= 2 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f28(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ 0 >= ar_0 ] 29.77/14.03 29.77/14.03 (Comp: ar_9 + ar_10 + 1, Cost: 1) f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10 + 1, ar_15, ar_16)) [ ar_9 >= ar_10 ] 29.77/14.03 29.77/14.03 (Comp: ar_7 + ar_8 + 1, Cost: 1) f16(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f18(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_7 >= ar_8 ] 29.77/14.03 29.77/14.03 (Comp: 1, Cost: 1) f0(ar_0, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16) -> Com_1(f16(1, ar_7, ar_8, ar_9, ar_10, ar_15, ar_16)) [ ar_0 = 1 ] 29.77/14.03 29.77/14.03 start location: koat_start 29.77/14.03 29.77/14.03 leaf cost: 0 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Complexity upper bound 8*ar_7 + 8*ar_8 + 13*ar_9 + 25*ar_10 + 3*ar_15 + 3*ar_16 + 59 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Time: 0.867 sec (SMT: 0.536 sec) 29.77/14.03 29.77/14.03 29.77/14.03 ---------------------------------------- 29.77/14.03 29.77/14.03 (2) 29.77/14.03 BOUNDS(1, n^1) 29.77/14.03 29.77/14.03 ---------------------------------------- 29.77/14.03 29.77/14.03 (3) Loat Proof (FINISHED) 29.77/14.03 29.77/14.03 29.77/14.03 ### Pre-processing the ITS problem ### 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Initial linear ITS problem 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 1: f16 -> f18 : [ H>=Q ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 2: f18 -> f18 : K'=1+K, L'=2+L, [ J>=K ], cost: 1 29.77/14.03 29.77/14.03 22: f18 -> f16 : Q'=1+Q, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 19: f28 -> f76 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, E'=H, F'=Q, G'=J, H'=K, Q'=L, J'=M, K'=N, L'=O, M'=P, N'=Q_1, O'=R, P'=S, Q_1'=T, R'=U, S'=V, T'=W, [ 0>=2+A && Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 20: f28 -> f76 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, E'=H, F'=Q, G'=J, H'=K, Q'=L, J'=M, K'=N, L'=O, M'=P, N'=Q_1, O'=R, P'=S, Q_1'=T, R'=U, S'=V, T'=W, [ A>=0 && Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 21: f28 -> f76 : A'=-1, A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, E'=H, F'=Q, G'=J, H'=K, Q'=L, J'=M, K'=N, L'=O, M'=P, N'=Q_1, O'=R, P'=S, Q_1'=T, R'=U, S'=V, T'=W, [ Q>=1+H && 1+A==0 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 9: f37 -> f52 : [ 0>=Q_1 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 10: f37 -> f52 : [ Q_1>=2 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 11: f37 -> f37 : K'=1+K, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ 0>=K && J>=K && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 12: f37 -> f37 : K'=1+K, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ J>=K && K>=2 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 13: f37 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ J>=1 && K==1 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 14: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=K ], cost: 1 29.77/14.03 29.77/14.03 15: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ K>=2 ], cost: 1 29.77/14.03 29.77/14.03 16: f52 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ K==1 ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Removed unreachable and leaf rules: 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 1: f16 -> f18 : [ H>=Q ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 2: f18 -> f18 : K'=1+K, L'=2+L, [ J>=K ], cost: 1 29.77/14.03 29.77/14.03 22: f18 -> f16 : Q'=1+Q, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 9: f37 -> f52 : [ 0>=Q_1 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 10: f37 -> f52 : [ Q_1>=2 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 11: f37 -> f37 : K'=1+K, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ 0>=K && J>=K && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 12: f37 -> f37 : K'=1+K, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ J>=K && K>=2 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 13: f37 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ J>=1 && K==1 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 14: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=K ], cost: 1 29.77/14.03 29.77/14.03 15: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ K>=2 ], cost: 1 29.77/14.03 29.77/14.03 16: f52 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ K==1 ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 ### Simplification by acceleration and chaining ### 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 2. 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 2: f18 -> f18 : K'=1+K, L'=2+L, [ J>=K ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 2 with metering function 1+J-K, yielding the new rule 24. 29.77/14.03 29.77/14.03 Removing the simple loops: 2. 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 5. 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 11: f37 -> f37 : K'=1+K, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ 0>=K && J>=K && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 12: f37 -> f37 : K'=1+K, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ J>=K && K>=2 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 13: f37 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ J>=1 && K==1 && Q_1==1 ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 11 with backward acceleration, yielding the new rule 25. 29.77/14.03 29.77/14.03 Accelerated rule 11 with backward acceleration, yielding the new rule 26. 29.77/14.03 29.77/14.03 Accelerated rule 12 with metering function 1+J-K, yielding the new rule 27. 29.77/14.03 29.77/14.03 Accelerated rule 13 with metering function 2-K, yielding the new rule 28. 29.77/14.03 29.77/14.03 Removing the simple loops: 11 12 13. 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated all simple loops using metering functions (where possible): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 1: f16 -> f18 : [ H>=Q ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 22: f18 -> f16 : Q'=1+Q, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 24: f18 -> f18 : K'=1+J, L'=2+2*J-2*K+L, [ J>=K ], cost: 1+J-K 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 9: f37 -> f52 : [ 0>=Q_1 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 10: f37 -> f52 : [ Q_1>=2 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 25: f37 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 1-K 29.77/14.03 29.77/14.03 26: f37 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 1+J-K 29.77/14.03 29.77/14.03 27: f37 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ J>=K && K>=2 && Q_1==1 ], cost: 1+J-K 29.77/14.03 29.77/14.03 28: f37 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ J>=1 && K==1 && Q_1==1 ], cost: 2-K 29.77/14.03 29.77/14.03 14: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=K ], cost: 1 29.77/14.03 29.77/14.03 15: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ K>=2 ], cost: 1 29.77/14.03 29.77/14.03 16: f52 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ K==1 ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Chained accelerated rules (with incoming rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 1: f16 -> f18 : [ H>=Q ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 29: f16 -> f18 : K'=1+J, L'=2+2*J-2*K+L, [ H>=Q && J>=K ], cost: 2+J-K 29.77/14.03 29.77/14.03 22: f18 -> f16 : Q'=1+Q, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 30: f35 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 2-K 29.77/14.03 29.77/14.03 32: f35 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 2+J-K 29.77/14.03 29.77/14.03 34: f35 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 2+J-K 29.77/14.03 29.77/14.03 37: f35 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 ], cost: 3-K 29.77/14.03 29.77/14.03 9: f37 -> f52 : [ 0>=Q_1 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 10: f37 -> f52 : [ Q_1>=2 && J>=K ], cost: 1 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 14: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=K ], cost: 1 29.77/14.03 29.77/14.03 15: f52 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ K>=2 ], cost: 1 29.77/14.03 29.77/14.03 16: f52 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ K==1 ], cost: 1 29.77/14.03 29.77/14.03 31: f52 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, V'=free_35, [ 0>=1+K && J>=1+K && Q_1==1 && J>=0 ], cost: 1-K 29.77/14.03 29.77/14.03 33: f52 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, V'=free_35, [ 0>=1+K && J>=1+K && Q_1==1 && 0>=J ], cost: 1+J-K 29.77/14.03 29.77/14.03 35: f52 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, V'=free_40, [ K>=2 && J>=1+K && Q_1==1 ], cost: 1+J-K 29.77/14.03 29.77/14.03 36: f52 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, V'=free_45, [ K==1 && J>=2 && Q_1==1 ], cost: J 29.77/14.03 29.77/14.03 38: f52 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, V'=free_35, [ J>=1 && 1+K==1 && Q_1==1 ], cost: 2-K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Eliminated locations (on tree-shaped paths): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 39: f16 -> f16 : Q'=1+Q, [ H>=Q && K>=1+J ], cost: 2 29.77/14.03 29.77/14.03 40: f16 -> f16 : Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ H>=Q && J>=K ], cost: 3+J-K 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 30: f35 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 2-K 29.77/14.03 29.77/14.03 32: f35 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 2+J-K 29.77/14.03 29.77/14.03 34: f35 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 2+J-K 29.77/14.03 29.77/14.03 37: f35 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 ], cost: 3-K 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 41: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=Q_1 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 42: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ 0>=Q_1 && J>=K && K>=2 ], cost: 2 29.77/14.03 29.77/14.03 43: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ 0>=Q_1 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 44: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ Q_1>=2 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 45: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ Q_1>=2 && J>=K && K>=2 ], cost: 2 29.77/14.03 29.77/14.03 46: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ Q_1>=2 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Applied pruning (of leafs and parallel rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 39: f16 -> f16 : Q'=1+Q, [ H>=Q && K>=1+J ], cost: 2 29.77/14.03 29.77/14.03 40: f16 -> f16 : Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ H>=Q && J>=K ], cost: 3+J-K 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 30: f35 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 2-K 29.77/14.03 29.77/14.03 32: f35 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 2+J-K 29.77/14.03 29.77/14.03 34: f35 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 2+J-K 29.77/14.03 29.77/14.03 37: f35 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 ], cost: 3-K 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 41: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=Q_1 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 42: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ 0>=Q_1 && J>=K && K>=2 ], cost: 2 29.77/14.03 29.77/14.03 43: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ 0>=Q_1 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 44: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ Q_1>=2 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 46: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ Q_1>=2 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 1. 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 39: f16 -> f16 : Q'=1+Q, [ H>=Q && K>=1+J ], cost: 2 29.77/14.03 29.77/14.03 40: f16 -> f16 : Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ H>=Q && J>=K ], cost: 3+J-K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 39 with metering function 1-Q+H, yielding the new rule 47. 29.77/14.03 29.77/14.03 Found no metering function for rule 40. 29.77/14.03 29.77/14.03 Removing the simple loops: 39. 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 5. 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 41: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=Q_1 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 42: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ 0>=Q_1 && J>=K && K>=2 ], cost: 2 29.77/14.03 29.77/14.03 43: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ 0>=Q_1 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 44: f37 -> f37 : K'=1+K, L'=2+J-K, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ Q_1>=2 && J>=K && 0>=K ], cost: 2 29.77/14.03 29.77/14.03 46: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ Q_1>=2 && J>=K && K==1 ], cost: 2 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 41 with backward acceleration, yielding the new rule 48. 29.77/14.03 29.77/14.03 Accelerated rule 41 with backward acceleration, yielding the new rule 49. 29.77/14.03 29.77/14.03 Accelerated rule 42 with metering function 1+J-K, yielding the new rule 50. 29.77/14.03 29.77/14.03 Accelerated rule 43 with metering function 1-K, yielding the new rule 51. 29.77/14.03 29.77/14.03 Accelerated rule 44 with backward acceleration, yielding the new rule 52. 29.77/14.03 29.77/14.03 Accelerated rule 44 with backward acceleration, yielding the new rule 53. 29.77/14.03 29.77/14.03 Accelerated rule 46 with metering function 1-K, yielding the new rule 54. 29.77/14.03 29.77/14.03 Removing the simple loops: 41 42 43 44 46. 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated all simple loops using metering functions (where possible): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 40: f16 -> f16 : Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ H>=Q && J>=K ], cost: 3+J-K 29.77/14.03 29.77/14.03 47: f16 -> f16 : Q'=1+H, [ H>=Q && K>=1+J ], cost: 2-2*Q+2*H 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 30: f35 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 2-K 29.77/14.03 29.77/14.03 32: f35 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 2+J-K 29.77/14.03 29.77/14.03 34: f35 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 2+J-K 29.77/14.03 29.77/14.03 37: f35 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 ], cost: 3-K 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 48: f37 -> f37 : K'=1+J, L'=2, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 2+2*J-2*K 29.77/14.03 29.77/14.03 49: f37 -> f37 : K'=1, L'=2+J, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ 0>=Q_1 && J>=K && 0>=K && J>=0 ], cost: 2-2*K 29.77/14.03 29.77/14.03 50: f37 -> f37 : K'=1+J, L'=2, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ 0>=Q_1 && J>=K && K>=2 ], cost: 2+2*J-2*K 29.77/14.03 29.77/14.03 51: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ 0>=Q_1 && J>=K && K==1 && 1-K>=1 ], cost: 2-2*K 29.77/14.03 29.77/14.03 52: f37 -> f37 : K'=1+J, L'=2, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 2+2*J-2*K 29.77/14.03 29.77/14.03 53: f37 -> f37 : K'=1, L'=2+J, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ Q_1>=2 && J>=K && 0>=K && J>=0 ], cost: 2-2*K 29.77/14.03 29.77/14.03 54: f37 -> f37 : K'=2, L'=1, R'=free_46, S'=free_43, T'=free_44, U'=free_47, V'=free_45, [ Q_1>=2 && J>=K && K==1 && 1-K>=1 ], cost: 2-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Chained accelerated rules (with incoming rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 0: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 ], cost: 1 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 55: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K ], cost: 4+J-K 29.77/14.03 29.77/14.03 56: f0 -> f16 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 3-2*Q+2*H 29.77/14.03 29.77/14.03 23: f16 -> f28 : [ Q>=1+H ], cost: 1 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 8: f35 -> f37 : [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 30: f35 -> f37 : K'=1, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 ], cost: 2-K 29.77/14.03 29.77/14.03 32: f35 -> f37 : K'=1+J, L'=free_22, Q_1'=1, R'=free_19, S'=free_20, T'=free_23, U'=free_21, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 2+J-K 29.77/14.03 29.77/14.03 34: f35 -> f37 : K'=1+J, L'=free_27, Q_1'=1, R'=free_24, S'=free_25, T'=free_28, U'=free_26, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 2+J-K 29.77/14.03 29.77/14.03 37: f35 -> f37 : K'=2, L'=1, Q_1'=1, R'=free_31, S'=free_29, T'=free_30, U'=free_32, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 ], cost: 3-K 29.77/14.03 29.77/14.03 57: f35 -> f37 : K'=1+J, L'=2, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 3+2*J-2*K 29.77/14.03 29.77/14.03 58: f35 -> f37 : K'=1, L'=2+J, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && J>=0 ], cost: 3-2*K 29.77/14.03 29.77/14.03 59: f35 -> f37 : K'=1+J, L'=2, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && K>=2 ], cost: 3+2*J-2*K 29.77/14.03 29.77/14.03 60: f35 -> f37 : K'=1+J, L'=2, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 3+2*J-2*K 29.77/14.03 29.77/14.03 61: f35 -> f37 : K'=1, L'=2+J, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && J>=0 ], cost: 3-2*K 29.77/14.03 29.77/14.03 17: f37 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ K>=1+J ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Eliminated locations (on tree-shaped paths): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 65: f35 -> f35 : E'=N, N'=free_49, O'=free_48, Q_1'=1+Q_1, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && K>=1+J ], cost: 2 29.77/14.03 29.77/14.03 66: f35 -> f35 : E'=N, K'=1, L'=free_22, N'=free_49, O'=free_48, Q_1'=2, R'=free_19, S'=free_20, T'=free_23, U'=free_21, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 && 1>=1+J ], cost: 3-K 29.77/14.03 29.77/14.03 67: f35 -> f35 : E'=N, K'=1+J, L'=free_22, N'=free_49, O'=free_48, Q_1'=2, R'=free_19, S'=free_20, T'=free_23, U'=free_21, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && 0>=J ], cost: 3+J-K 29.77/14.03 29.77/14.03 68: f35 -> f35 : E'=N, K'=1+J, L'=free_27, N'=free_49, O'=free_48, Q_1'=2, R'=free_24, S'=free_25, T'=free_28, U'=free_26, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 3+J-K 29.77/14.03 29.77/14.03 69: f35 -> f35 : E'=N, K'=2, L'=1, N'=free_49, O'=free_48, Q_1'=2, R'=free_31, S'=free_29, T'=free_30, U'=free_32, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=1 && K==1 && Q_1==1 && 2>=1+J ], cost: 4-K 29.77/14.03 29.77/14.03 70: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 71: f35 -> f35 : E'=N, K'=1, L'=2+J, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && J>=0 && 1>=1+J ], cost: 4-2*K 29.77/14.03 29.77/14.03 72: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_41, S'=free_38, T'=free_39, U'=free_42, V'=free_40, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && K>=2 ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 73: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 74: f35 -> f35 : E'=N, K'=1, L'=2+J, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && J>=0 && 1>=1+J ], cost: 4-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Applied pruning (of leafs and parallel rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 66: f35 -> f35 : E'=N, K'=1, L'=free_22, N'=free_49, O'=free_48, Q_1'=2, R'=free_19, S'=free_20, T'=free_23, U'=free_21, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && J>=0 && 1>=1+J ], cost: 3-K 29.77/14.03 29.77/14.03 68: f35 -> f35 : E'=N, K'=1+J, L'=free_27, N'=free_49, O'=free_48, Q_1'=2, R'=free_24, S'=free_25, T'=free_28, U'=free_26, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 3+J-K 29.77/14.03 29.77/14.03 70: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 73: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 74: f35 -> f35 : E'=N, K'=1, L'=2+J, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && J>=0 && 1>=1+J ], cost: 4-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 4. 29.77/14.03 29.77/14.03 Simplified some of the simple loops (and removed duplicate rules). 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 66: f35 -> f35 : E'=N, K'=1, L'=free_22, N'=free_49, O'=free_48, Q_1'=2, R'=free_19, S'=free_20, T'=free_23, U'=free_21, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && -J==0 ], cost: 3-K 29.77/14.03 29.77/14.03 68: f35 -> f35 : E'=N, K'=1+J, L'=free_27, N'=free_49, O'=free_48, Q_1'=2, R'=free_24, S'=free_25, T'=free_28, U'=free_26, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 ], cost: 3+J-K 29.77/14.03 29.77/14.03 70: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 73: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 74: f35 -> f35 : E'=N, K'=1, L'=2+J, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && -J==0 ], cost: 4-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 66 with metering function 1-J-Q_1, yielding the new rule 75. 29.77/14.03 29.77/14.03 Accelerated rule 68 with metering function 1-Q_1, yielding the new rule 76. 29.77/14.03 29.77/14.03 Found no metering function for rule 70. 29.77/14.03 29.77/14.03 Found no metering function for rule 73. 29.77/14.03 29.77/14.03 Accelerated rule 74 with metering function -J, yielding the new rule 77. 29.77/14.03 29.77/14.03 Removing the simple loops: 66 68 74. 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated all simple loops using metering functions (where possible): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 70: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 73: f35 -> f35 : E'=N, K'=1+J, L'=2, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 4+2*J-2*K 29.77/14.03 29.77/14.03 75: f35 -> f35 : E'=free_49, K'=1, L'=free_22, N'=free_49, O'=free_48, Q_1'=2, R'=free_19, S'=free_20, T'=free_23, U'=free_21, W'=2-2*J+W-2*Q_1, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=K && J>=K && Q_1==1 && -J==0 && 1-J-Q_1>=1 ], cost: 2-2*J-2*Q_1 29.77/14.03 29.77/14.03 76: f35 -> f35 : E'=free_49, K'=1+J, L'=free_27, N'=free_49, O'=free_48, Q_1'=2, R'=free_24, S'=free_25, T'=free_28, U'=free_26, W'=2+W-2*Q_1, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && J>=K && K>=2 && Q_1==1 && 1-Q_1>=1 ], cost: 2-2*Q_1 29.77/14.03 29.77/14.03 77: f35 -> f35 : E'=free_49, K'=1, L'=2+J, N'=free_49, O'=free_48, Q_1'=-J+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=-2*J+W, [ P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && -J==0 && -J>=1 ], cost: -2*J 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Chained accelerated rules (with incoming rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 5: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 6: f28 -> f35 : M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q ], cost: 1 29.77/14.03 29.77/14.03 7: f28 -> f35 : Q'=1, M'=1, N'=1, O'=0, [ H>=1 && Q==1 ], cost: 1 29.77/14.03 29.77/14.03 78: f28 -> f35 : E'=1, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 79: f28 -> f35 : E'=1, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 80: f28 -> f35 : E'=1, Q'=1, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 81: f28 -> f35 : E'=1, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 82: f28 -> f35 : E'=1, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 83: f28 -> f35 : E'=1, Q'=1, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 18: f35 -> f28 : Q'=1+Q, [ P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 1 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Eliminated locations (on tree-shaped paths): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 84: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 85: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 86: f28 -> f28 : Q'=2, M'=1, N'=1, O'=0, [ H>=1 && Q==1 && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 87: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 88: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 89: f28 -> f28 : E'=1, Q'=2, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 90: f28 -> [13] : [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 91: f28 -> [13] : [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 92: f28 -> [13] : [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Applied pruning (of leafs and parallel rules): 29.77/14.03 29.77/14.03 Start location: f0 29.77/14.03 29.77/14.03 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.03 29.77/14.03 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.03 29.77/14.03 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.03 29.77/14.03 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.03 29.77/14.03 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.03 29.77/14.03 84: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 85: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 87: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 88: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 89: f28 -> f28 : E'=1, Q'=2, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 90: f28 -> [13] : [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 91: f28 -> [13] : [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 92: f28 -> [13] : [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerating simple loops of location 3. 29.77/14.03 29.77/14.03 Accelerating the following rules: 29.77/14.03 29.77/14.03 84: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 85: f28 -> f28 : Q'=1+Q, M'=2-Q+H, N'=1, O'=0, [ Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2 29.77/14.03 29.77/14.03 87: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 88: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 89: f28 -> f28 : E'=1, Q'=2, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.03 29.77/14.03 29.77/14.03 29.77/14.03 Accelerated rule 84 with backward acceleration, yielding the new rule 93. 29.77/14.03 29.77/14.03 Accelerated rule 84 with backward acceleration, yielding the new rule 94. 29.77/14.03 29.77/14.03 Accelerated rule 85 with metering function 1-Q+H, yielding the new rule 95. 29.77/14.03 29.77/14.03 Found no metering function for rule 87. 29.77/14.03 29.77/14.03 Found no metering function for rule 88. 29.77/14.03 29.77/14.03 Accelerated rule 89 with metering function 1-Q, yielding the new rule 96. 29.77/14.03 29.77/14.03 Removing the simple loops: 84 85 89. 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Accelerated all simple loops using metering functions (where possible): 29.77/14.04 29.77/14.04 Start location: f0 29.77/14.04 29.77/14.04 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.04 29.77/14.04 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.04 29.77/14.04 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.04 29.77/14.04 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.04 29.77/14.04 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.04 29.77/14.04 87: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 88: f28 -> f28 : E'=1, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 90: f28 -> [13] : [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 91: f28 -> [13] : [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 92: f28 -> [13] : [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 93: f28 -> f28 : Q'=1, M'=2+H, N'=1, O'=0, [ 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 2-2*Q 29.77/14.04 29.77/14.04 94: f28 -> f28 : Q'=1+H, M'=2, N'=1, O'=0, [ 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 2-2*Q+2*H 29.77/14.04 29.77/14.04 95: f28 -> f28 : Q'=1+H, M'=2, N'=1, O'=0, [ Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 2-2*Q+2*H 29.77/14.04 29.77/14.04 96: f28 -> f28 : E'=1, Q'=2, K'=1+J, L'=2, M'=1, N'=free_49, O'=free_48, Q_1'=1-Q+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2-2*Q+W, [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 && 1-Q>=1 ], cost: 4-4*Q 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Chained accelerated rules (with incoming rules): 29.77/14.04 29.77/14.04 Start location: f0 29.77/14.04 29.77/14.04 3: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A ], cost: 1 29.77/14.04 29.77/14.04 4: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 ], cost: 1 29.77/14.04 29.77/14.04 62: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, [ A==1 && Q>=1+H ], cost: 2 29.77/14.04 29.77/14.04 63: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+Q, K'=1+J, L'=2+2*J-2*K+L, [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.04 29.77/14.04 64: f0 -> f28 : A'=1, B'=free_4, C'=free, D'=free_2, E'=free_5, F'=free_3, G'=free_1, Q'=1+H, [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.04 29.77/14.04 97: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=1, F'=free_9, G'=free_7, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 98: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=1, F'=free_15, G'=free_13, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ A>=2 && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 99: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=1, F'=free_9, G'=free_7, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ 0>=A && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 100: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=1, F'=free_15, G'=free_13, Q'=1+Q, K'=1+J, L'=2, M'=2-Q+H, N'=free_49, O'=free_48, Q_1'=1+Q_1, R'=free_36, S'=free_33, T'=free_34, U'=free_37, V'=free_35, W'=2+W, [ A>=2 && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 101: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, Q'=1, M'=2+H, N'=1, O'=0, [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 102: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, Q'=1, M'=2+H, N'=1, O'=0, [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 103: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, Q'=1+H, M'=2, N'=1, O'=0, [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 104: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, Q'=1+H, M'=2, N'=1, O'=0, [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 105: f0 -> f28 : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, Q'=1+H, M'=2, N'=1, O'=0, [ 0>=A && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 106: f0 -> f28 : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, Q'=1+H, M'=2, N'=1, O'=0, [ A>=2 && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 90: f28 -> [13] : [ 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 91: f28 -> [13] : [ Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 92: f28 -> [13] : [ H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 5+2*J-2*K 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Eliminated locations (on tree-shaped paths): 29.77/14.04 29.77/14.04 Start location: f0 29.77/14.04 29.77/14.04 107: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 108: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 109: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 110: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 111: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 112: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 113: f0 -> [15] : [ A==1 && H>=Q && J>=K && 1+Q>=1+H ], cost: 5+J-K 29.77/14.04 29.77/14.04 114: f0 -> [15] : [ A==1 && H>=Q && K>=1+J ], cost: 4-2*Q+2*H 29.77/14.04 29.77/14.04 115: f0 -> [15] : [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 116: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 117: f0 -> [15] : [ 0>=A && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 118: f0 -> [15] : [ A>=2 && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && Q_1>=2 && J>=K && 0>=K && 0>=J && P>=2*free_50 && 3*free_50>=1+P && 1+Q_1>=2+free_50 ], cost: 7+2*J-2*K 29.77/14.04 29.77/14.04 119: f0 -> [15] : [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 120: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 121: f0 -> [15] : [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 122: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 123: f0 -> [15] : [ 0>=A && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 124: f0 -> [15] : [ A>=2 && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Applied pruning (of leafs and parallel rules): 29.77/14.04 29.77/14.04 Start location: f0 29.77/14.04 29.77/14.04 107: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 108: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 109: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 110: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 112: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 119: f0 -> [15] : [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 120: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 122: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 123: f0 -> [15] : [ 0>=A && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 124: f0 -> [15] : [ A>=2 && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 ### Computing asymptotic complexity ### 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Fully simplified ITS problem 29.77/14.04 29.77/14.04 Start location: f0 29.77/14.04 29.77/14.04 107: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 108: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && Q>=2 && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 109: f0 -> [13] : B'=free_10, C'=free_6, D'=free_8, E'=free_11, F'=free_9, G'=free_7, [ 0>=A && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 110: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 112: f0 -> [13] : B'=free_16, C'=free_12, D'=free_14, E'=free_17, F'=free_15, G'=free_13, [ A>=2 && H>=1 && Q==1 && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ], cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 119: f0 -> [15] : [ 0>=A && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 120: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && H>=0 ], cost: 3-2*Q 29.77/14.04 29.77/14.04 122: f0 -> [15] : [ A>=2 && 0>=Q && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 && 0>=H ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 123: f0 -> [15] : [ 0>=A && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 124: f0 -> [15] : [ A>=2 && Q>=2 && H>=Q && P>=2*free_50 && 3*free_50>=1+P && Q_1>=2+free_50 ], cost: 3-2*Q+2*H 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Computing asymptotic complexity for rule 107 29.77/14.04 29.77/14.04 Solved the limit problem by the following transformations: 29.77/14.04 29.77/14.04 Created initial limit problem: 29.77/14.04 29.77/14.04 1-K (+/+!), 1-Q+H (+/+!), 1-A (+/+!), 1-Q (+/+!), 1+J-K (+/+!), 1-Q_1 (+/+!), 2+free_18-Q_1 (+/+!), 1+P-2*free_18 (+/+!), -P+3*free_18 (+/+!), 1-J (+/+!), 6+2*J-2*K (+) [not solved] 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 removing all constraints (solved by SMT) 29.77/14.04 29.77/14.04 resulting limit problem: [solved] 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 applying transformation rule (C) using substitution {Q==0,P==2,J==-n,free_18==1,Q_1==0,A==-n,K==-2*n,H==0} 29.77/14.04 29.77/14.04 resulting limit problem: 29.77/14.04 29.77/14.04 [solved] 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Solution: 29.77/14.04 29.77/14.04 Q / 0 29.77/14.04 29.77/14.04 P / 2 29.77/14.04 29.77/14.04 J / -n 29.77/14.04 29.77/14.04 free_18 / 1 29.77/14.04 29.77/14.04 Q_1 / 0 29.77/14.04 29.77/14.04 A / -n 29.77/14.04 29.77/14.04 K / -2*n 29.77/14.04 29.77/14.04 H / 0 29.77/14.04 29.77/14.04 Resulting cost 6+2*n has complexity: Poly(n^1) 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Found new complexity Poly(n^1). 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 Obtained the following overall complexity (w.r.t. the length of the input n): 29.77/14.04 29.77/14.04 Complexity: Poly(n^1) 29.77/14.04 29.77/14.04 Cpx degree: 1 29.77/14.04 29.77/14.04 Solved cost: 6+2*n 29.77/14.04 29.77/14.04 Rule cost: 6+2*J-2*K 29.77/14.04 29.77/14.04 Rule guard: [ 0>=A && 0>=Q && H>=Q && P>=2*free_18 && 3*free_18>=1+P && 1+free_18>=Q_1 && 0>=Q_1 && J>=K && 0>=K && 0>=J ] 29.77/14.04 29.77/14.04 29.77/14.04 29.77/14.04 WORST_CASE(Omega(n^1),?) 29.77/14.04 29.77/14.04 29.77/14.04 ---------------------------------------- 29.77/14.04 29.77/14.04 (4) 29.77/14.04 BOUNDS(n^1, INF) 29.88/14.77 EOF