/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 521 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 2004 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f1(A, 1 + B, D, B1, Y, Z, A1, C1, D1, E1, D, F1, B, N, O, P, Q, R, S, T, U, V, W, X)) :|: A >= B + 1 && B >= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: B1 >= N + 1 && O >= 0 && A1 >= 2 && Z >= A1 && Y >= B1 + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: B1 >= N + 1 && O >= 0 && A1 >= 2 && Z >= A1 && B1 >= Y + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: N >= B1 + 1 && O >= 0 && A1 >= 2 && Z >= A1 && Y >= B1 + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: N >= B1 + 1 && O >= 0 && A1 >= 2 && Z >= A1 && B1 >= Y + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(E1, D1, F1, D, E, F, G, H, G1, J, K, L, M, C1, O, B1, Y, Z, A1, H1, U, V, W, X)) :|: O >= 0 && E1 >= 2 && D1 >= E1 && 0 >= F1 + 1 && P >= N && P <= N f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(E1, D1, F1, D, E, F, G, H, G1, J, K, L, M, C1, O, B1, Y, Z, A1, H1, U, V, W, X)) :|: O >= 0 && E1 >= 2 && D1 >= E1 && F1 >= 1 && P >= N && P <= N f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: C1 >= N + 1 && U >= 0 && A1 >= 2 && Z >= A1 && Y >= C1 + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: C1 >= N + 1 && U >= 0 && A1 >= 2 && Z >= A1 && C1 >= Y + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: N >= C1 + 1 && U >= 0 && A1 >= 2 && Z >= A1 && Y >= C1 + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: N >= C1 + 1 && U >= 0 && A1 >= 2 && Z >= A1 && C1 >= Y + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(D1, B, C, D, E, F, G, H, E1, J, K, L, M, C1, O, B1, Y, Z, A1, F1, U, V, W, X)) :|: D1 >= 2 && U >= 0 && P >= N && P <= N f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && C >= 1 && 0 >= C + 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && C >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && 0 >= C + 1 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(D1, 0, 0, D, E, F, G, H, E1, J, K, L, M, C1, O, B1, Y, Z, A1, F1, U, V, W, X)) :|: 0 >= D1 && 0 >= A f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f1(A, 2, Y, C1, Z, A1, B1, D1, E1, F1, Y, L, M, N, O, P, Q, R, S, T, U, V, W, G1)) :|: A >= 2 The start-symbols are:[f3_24] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, Ar_0 + 4*Ar_20 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Fresh_77, Fresh_78, Fresh_79, Fresh_80, Fresh_81, Fresh_82, Ar_3, Fresh_83, Ar_1, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_73, Fresh_74, Fresh_75, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_75, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_75, 0, Fresh_75, Ar_13, Ar_20, Ar_21, Ar_22, Ar_23)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_73 >= 2 /\ Fresh_74 >= Fresh_73 /\ Fresh_75 >= B1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_70, Fresh_71, Fresh_72, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_72, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_72, 0, Fresh_72, Ar_13, Ar_20, Ar_21, Ar_22, Ar_23)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_70 >= 2 /\ Fresh_71 >= Fresh_70 /\ B1 >= Fresh_72 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_67, Fresh_68, Fresh_69, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_69, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_69, 0, Fresh_69, Ar_13, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_67 >= 2 /\ Fresh_68 >= Fresh_67 /\ Fresh_69 >= B1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_64, Fresh_65, Fresh_66, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_66, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_66, 0, Fresh_66, Ar_13, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_64 >= 2 /\ Fresh_65 >= Fresh_64 /\ B1 >= Fresh_66 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f4(Fresh_54, Fresh_55, Fresh_56, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_57, Ar_9, Ar_10, Ar_11, Ar_12, Fresh_58, Ar_14, Fresh_59, Fresh_60, Fresh_61, Fresh_62, Fresh_63, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_14 >= 0 /\ Fresh_54 >= 2 /\ Fresh_55 >= Fresh_54 /\ 0 >= Fresh_56 + 1 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f4(Fresh_44, Fresh_45, Fresh_46, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_47, Ar_9, Ar_10, Ar_11, Ar_12, Fresh_48, Ar_14, Fresh_49, Fresh_50, Fresh_51, Fresh_52, Fresh_53, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_14 >= 0 /\ Fresh_44 >= 2 /\ Fresh_45 >= Fresh_44 /\ Fresh_46 >= 1 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f10(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_23) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_42, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_42, 0, Fresh_42, Ar_13, Ar_20 - 1, Fresh_43, Ar_20 - 1, Ar_23)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(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_23) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_38, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_38, 0, Fresh_38, Ar_13, Ar_20 - 1, Fresh_39, Ar_20 - 1, Ar_23)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(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_23) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_34, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_34, 0, Fresh_34, Ar_13, Ar_20 - 1, Fresh_35, Ar_20 - 1, Ar_23)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(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_23) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Fresh_30, Ar_11, Ar_12, Ar_13, Ar_14, 0, Fresh_30, 0, Fresh_30, Ar_13, Ar_20 - 1, Fresh_31, Ar_20 - 1, Ar_23)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(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_23) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_21, Ar_9, Ar_10, Ar_11, Ar_12, Fresh_22, Ar_14, Fresh_23, Fresh_24, Fresh_25, Fresh_26, Fresh_27, Ar_20, Ar_21, Ar_22, Ar_23)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_19, Ar_20 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_2, Ar_11, Ar_12, Ar_2, Ar_20, 0, Ar_2, 0, Ar_2, Ar_2, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_19 /\ Fresh_19 >= 2 /\ Ar_2 >= 1 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_2, Ar_11, Ar_12, Ar_2, Ar_20, 0, Ar_2, 0, Ar_2, Ar_2, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Ar_23) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_2, Ar_11, Ar_12, Ar_2, Ar_20, 0, Ar_2, 0, Ar_2, Ar_2, Ar_20, Ar_21, Ar_22, Ar_23)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f3(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_23) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_10, Ar_9, Ar_10, Ar_11, Ar_12, Fresh_11, Ar_14, Fresh_12, Fresh_13, Fresh_14, Fresh_15, Fresh_16, Ar_20, Ar_21, Ar_22, Ar_23)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f3(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_23) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Fresh_2, Fresh_3, Fresh_4, Fresh_5, Fresh_6, Fresh_7, Fresh_0, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22, Fresh_8)) [ Ar_0 >= 2 ] (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, Ar_23) -> Com_1(f3(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_23)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_14, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Ar_14, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_19, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_19 /\ Fresh_19 >= 2 /\ Ar_2 >= 1 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Ar_14, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_44, Fresh_45, Fresh_46, Ar_3, Fresh_48, Ar_14, Fresh_49, Ar_20)) [ Ar_14 >= 0 /\ Fresh_44 >= 2 /\ Fresh_45 >= Fresh_44 /\ Fresh_46 >= 1 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_54, Fresh_55, Fresh_56, Ar_3, Fresh_58, Ar_14, Fresh_59, Ar_20)) [ Ar_14 >= 0 /\ Fresh_54 >= 2 /\ Fresh_55 >= Fresh_54 /\ 0 >= Fresh_56 + 1 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_64, Fresh_65, Fresh_66, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_64 >= 2 /\ Fresh_65 >= Fresh_64 /\ B1 >= Fresh_66 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_67, Fresh_68, Fresh_69, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_67 >= 2 /\ Fresh_68 >= Fresh_67 /\ Fresh_69 >= B1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_70, Fresh_71, Fresh_72, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_70 >= 2 /\ Fresh_71 >= Fresh_70 /\ B1 >= Fresh_72 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_73, Fresh_74, Fresh_75, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_73 >= 2 /\ Fresh_74 >= Fresh_73 /\ Fresh_75 >= B1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_14, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_19, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_19 /\ Fresh_19 >= 2 /\ Ar_2 >= 1 /\ 0 >= Ar_2 + 1 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_44, Fresh_45, Fresh_46, Ar_3, Fresh_48, Ar_14, Fresh_49, Ar_20)) [ Ar_14 >= 0 /\ Fresh_44 >= 2 /\ Fresh_45 >= Fresh_44 /\ Fresh_46 >= 1 /\ Ar_15 = Ar_13 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_54, Fresh_55, Fresh_56, Ar_3, Fresh_58, Ar_14, Fresh_59, Ar_20)) [ Ar_14 >= 0 /\ Fresh_54 >= 2 /\ Fresh_55 >= Fresh_54 /\ 0 >= Fresh_56 + 1 /\ Ar_15 = Ar_13 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_64, Fresh_65, Fresh_66, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_64 >= 2 /\ Fresh_65 >= Fresh_64 /\ B1 >= Fresh_66 + 1 /\ Ar_15 = 0 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_67, Fresh_68, Fresh_69, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ Ar_13 >= B1 + 1 /\ Ar_14 >= 0 /\ Fresh_67 >= 2 /\ Fresh_68 >= Fresh_67 /\ Fresh_69 >= B1 + 1 /\ Ar_15 = 0 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_70, Fresh_71, Fresh_72, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_70 >= 2 /\ Fresh_71 >= Fresh_70 /\ B1 >= Fresh_72 + 1 /\ Ar_15 = 0 ] f9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_73, Fresh_74, Fresh_75, Ar_3, Ar_13, Ar_14, 0, Ar_20)) [ B1 >= Ar_13 + 1 /\ Ar_14 >= 0 /\ Fresh_73 >= 2 /\ Fresh_74 >= Fresh_73 /\ Fresh_75 >= B1 + 1 /\ Ar_15 = 0 ] We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Ar_14, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, Ar_14, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_14, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, Ar_20, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Ar_14, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_14, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_14, Ar_15, Ar_20)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f3) = 2 Pol(f1) = 2 Pol(f4) = 0 Pol(f10) = 1 orients all transitions weakly and the transitions f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_7 + 1 Pol(f3) = V_7 + 1 Pol(f1) = V_7 + 1 Pol(f4) = V_7 Pol(f10) = V_7 + 1 orients all transitions weakly and the transitions f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f1) = V_1 - V_2 and size complexities S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-3) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-5) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\\ Ar_20 >= 0 /\\ Ar_15 = Ar_13 ]", 0-6) = Ar_20 + 4 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-3) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-5) = 0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_40 >= 2 /\\ Fresh_41 >= Fresh_40 /\\ Fresh_42 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-6) = Ar_20 + 4 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-3) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-5) = 0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\\ Ar_20 >= 0 /\\ Fresh_36 >= 2 /\\ Fresh_37 >= Fresh_36 /\\ C1 >= Fresh_38 + 1 /\\ Ar_15 = 0 ]", 0-6) = Ar_20 + 4 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-3) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-5) = 0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_32 >= 2 /\\ Fresh_33 >= Fresh_32 /\\ Fresh_34 >= C1 + 1 /\\ Ar_15 = 0 ]", 0-6) = Ar_20 + 4 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-3) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-5) = 0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\\ Ar_20 >= 0 /\\ Fresh_28 >= 2 /\\ Fresh_29 >= Fresh_28 /\\ C1 >= Fresh_30 + 1 /\\ Ar_15 = 0 ]", 0-6) = Ar_20 + 4 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-1) = Ar_0 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-2) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-3) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-4) = Ar_13 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-5) = Ar_15 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 ]", 0-6) = Ar_20 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-0) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-1) = Ar_20 + 1 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-2) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-3) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-4) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-5) = 0 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_18 /\\ Fresh_18 >= 2 /\\ Ar_2 >= 1 ]", 0-6) = Ar_20 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-0) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-1) = Ar_20 + 1 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-2) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-3) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-4) = ? S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-5) = 0 S("f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ Z >= Fresh_17 /\\ Fresh_17 >= 2 /\\ 0 >= Ar_2 + 1 ]", 0-6) = Ar_20 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-0) = ? S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-1) = 0 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-2) = 0 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-3) = Ar_3 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-4) = ? S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-5) = ? S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\\ 0 >= Ar_0 ]", 0-6) = Ar_20 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-1) = 2 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-2) = ? S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-3) = ? S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-4) = Ar_13 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-5) = Ar_15 S("f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ]", 0-6) = Ar_20 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-4) = Ar_13 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-5) = Ar_15 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ]", 0-6) = Ar_20 orients the transitions f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] weakly and the transition f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, 2, Fresh_0, Fresh_1, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_9, 0, 0, Ar_3, Fresh_11, Fresh_12, Ar_20)) [ 0 >= Fresh_9 /\ 0 >= Ar_0 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_17, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_17 /\ Fresh_17 >= 2 /\ 0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_18, Ar_20 + 1, Ar_2, Ar_3, Ar_2, 0, Ar_20)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Z >= Fresh_18 /\ Fresh_18 >= 2 /\ Ar_2 >= 1 ] (Comp: Ar_0 + 2, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_76, Ar_13, Ar_15, Ar_20)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_28, Fresh_29, Fresh_30, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_28 >= 2 /\ Fresh_29 >= Fresh_28 /\ C1 >= Fresh_30 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_32, Fresh_33, Fresh_34, Ar_3, Ar_13, 0, Ar_20 - 1)) [ Ar_13 >= C1 + 1 /\ Ar_20 >= 0 /\ Fresh_32 >= 2 /\ Fresh_33 >= Fresh_32 /\ Fresh_34 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_36, Fresh_37, Fresh_38, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_36 >= 2 /\ Fresh_37 >= Fresh_36 /\ C1 >= Fresh_38 + 1 /\ Ar_15 = 0 ] (Comp: Ar_20 + 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f10(Fresh_40, Fresh_41, Fresh_42, Ar_3, Ar_13, 0, Ar_20 - 1)) [ C1 >= Ar_13 + 1 /\ Ar_20 >= 0 /\ Fresh_40 >= 2 /\ Fresh_41 >= Fresh_40 /\ Fresh_42 >= C1 + 1 /\ Ar_15 = 0 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_13, Ar_15, Ar_20) -> Com_1(f4(Fresh_20, Ar_1, Ar_2, Ar_3, Fresh_22, Fresh_23, Ar_20)) [ Fresh_20 >= 2 /\ Ar_20 >= 0 /\ Ar_15 = Ar_13 ] start location: koat_start leaf cost: 0 Complexity upper bound Ar_0 + 4*Ar_20 + 14 Time: 0.516 sec (SMT: 0.406 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f3 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 12: f1 -> f10 : A'=free_72, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_73>=free_72 && free_72>=2 && C>=1 && 0>=1+C ], cost: 1 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_75>=free_74 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_77>=free_76 && free_76>=2 && 0>=1+C ], cost: 1 1: f9 -> f10 : A'=free_8, B'=free_10, C'=free_11, K'=free_11, P'=0, Q_1'=free_11, R'=0, S'=free_11, T'=N, [ free_9>=1+N && O>=0 && free_8>=2 && free_10>=free_8 && free_11>=1+free_9 && P==0 ], cost: 1 2: f9 -> f10 : A'=free_12, B'=free_14, C'=free_15, K'=free_15, P'=0, Q_1'=free_15, R'=0, S'=free_15, T'=N, [ free_13>=1+N && O>=0 && free_12>=2 && free_14>=free_12 && free_13>=1+free_15 && P==0 ], cost: 1 3: f9 -> f10 : A'=free_16, B'=free_18, C'=free_19, K'=free_19, P'=0, Q_1'=free_19, R'=0, S'=free_19, T'=N, [ N>=1+free_17 && O>=0 && free_16>=2 && free_18>=free_16 && free_19>=1+free_17 && P==0 ], cost: 1 4: f9 -> f10 : A'=free_20, B'=free_22, C'=free_23, K'=free_23, P'=0, Q_1'=free_23, R'=0, S'=free_23, T'=N, [ N>=1+free_21 && O>=0 && free_20>=2 && free_22>=free_20 && free_21>=1+free_23 && P==0 ], cost: 1 5: f9 -> f4 : A'=free_27, A1'=free_31, B'=free_32, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_28, E1'=J, F'=K, F1'=L, G'=M, G1'=free_24, H'=O, H1'=free_30, Q'=free_26, J'=free_33, K'=free_29, L'=free_25, M'=U, N'=V, O'=W, P'=X, [ O>=0 && free_27>=2 && free_31>=free_27 && 0>=1+free_32 && P==N ], cost: 1 6: f9 -> f4 : A'=free_37, A1'=free_41, B'=free_42, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_38, E1'=J, F'=K, F1'=L, G'=M, G1'=free_34, H'=O, H1'=free_40, Q'=free_36, J'=free_43, K'=free_39, L'=free_35, M'=U, N'=V, O'=W, P'=X, [ O>=0 && free_37>=2 && free_41>=free_37 && free_42>=1 && P==N ], cost: 1 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ free_44>=1+N && U>=0 && free_45>=2 && free_47>=free_45 && free_48>=1+free_44 && P==0 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ free_49>=1+N && U>=0 && free_50>=2 && free_52>=free_50 && free_49>=1+free_53 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ N>=1+free_54 && U>=0 && free_55>=2 && free_57>=free_55 && free_58>=1+free_54 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ N>=1+free_59 && U>=0 && free_60>=2 && free_62>=free_60 && free_59>=1+free_63 && P==0 ], cost: 1 11: f10 -> f4 : A'=free_66, A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_69, E1'=J, F'=K, F1'=L, G'=M, G1'=free_70, H'=O, H1'=free_67, Q'=free_64, J'=free_68, K'=free_65, L'=free_71, M'=U, N'=V, O'=W, P'=X, [ free_66>=2 && U>=0 && P==N ], cost: 1 15: f3 -> f4 : A'=free_80, A1'=0, B'=0, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_83, E1'=J, F'=K, F1'=L, G'=M, G1'=free_84, H'=O, H1'=free_81, Q'=free_78, J'=free_82, K'=free_79, L'=free_85, M'=U, N'=V, O'=W, P'=X, [ 0>=free_80 && 0>=A ], cost: 1 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 15: f3 -> f4 : A'=free_80, A1'=0, B'=0, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_83, E1'=J, F'=K, F1'=L, G'=M, G1'=free_84, H'=O, H1'=free_81, Q'=free_78, J'=free_82, K'=free_79, L'=free_85, M'=U, N'=V, O'=W, P'=X, [ 0>=free_80 && 0>=A ], cost: 1 Removed unreachable and leaf rules: Start location: f3 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 12: f1 -> f10 : A'=free_72, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_73>=free_72 && free_72>=2 && C>=1 && 0>=1+C ], cost: 1 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_75>=free_74 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_77>=free_76 && free_76>=2 && 0>=1+C ], cost: 1 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ free_44>=1+N && U>=0 && free_45>=2 && free_47>=free_45 && free_48>=1+free_44 && P==0 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ free_49>=1+N && U>=0 && free_50>=2 && free_52>=free_50 && free_49>=1+free_53 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ N>=1+free_54 && U>=0 && free_55>=2 && free_57>=free_55 && free_58>=1+free_54 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ N>=1+free_59 && U>=0 && free_60>=2 && free_62>=free_60 && free_59>=1+free_63 && P==0 ], cost: 1 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 Removed rules with unsatisfiable guard: Start location: f3 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_75>=free_74 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_77>=free_76 && free_76>=2 && 0>=1+C ], cost: 1 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ free_44>=1+N && U>=0 && free_45>=2 && free_47>=free_45 && free_48>=1+free_44 && P==0 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ free_49>=1+N && U>=0 && free_50>=2 && free_52>=free_50 && free_49>=1+free_53 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ N>=1+free_54 && U>=0 && free_55>=2 && free_57>=free_55 && free_58>=1+free_54 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ N>=1+free_59 && U>=0 && free_60>=2 && free_62>=free_60 && free_59>=1+free_63 && P==0 ], cost: 1 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 Removed unreachable and leaf rules: Start location: f3 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_75>=free_74 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_77>=free_76 && free_76>=2 && 0>=1+C ], cost: 1 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ free_44>=1+N && U>=0 && free_45>=2 && free_47>=free_45 && free_48>=1+free_44 && P==0 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ free_49>=1+N && U>=0 && free_50>=2 && free_52>=free_50 && free_49>=1+free_53 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ N>=1+free_54 && U>=0 && free_55>=2 && free_57>=free_55 && free_58>=1+free_54 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ N>=1+free_59 && U>=0 && free_60>=2 && free_62>=free_60 && free_59>=1+free_63 && P==0 ], cost: 1 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 Simplified all rules, resulting in: Start location: f3 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_76>=2 && 0>=1+C ], cost: 1 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ U>=0 && free_45>=2 && free_47>=free_45 && P==0 && 1+N<=-1+free_48 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ U>=0 && free_50>=2 && free_52>=free_50 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ U>=0 && free_55>=2 && free_57>=free_55 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ U>=0 && free_60>=2 && free_62>=free_60 && P==0 && 1+free_63<=-1+N ], cost: 1 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: f1 -> f1 : B'=1+B, C'=D, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=D, L'=free_7, M'=B, [ A>=1+B && B>=0 ], cost: 1 Accelerated rule 0 with metering function -B+A, yielding the new rule 17. Removing the simple loops: 0. Accelerating simple loops of location 2. Accelerating the following rules: 7: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1+U, V'=free_46, W'=-1+U, [ U>=0 && free_45>=2 && free_47>=free_45 && P==0 && 1+N<=-1+free_48 ], cost: 1 8: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1+U, V'=free_51, W'=-1+U, [ U>=0 && free_50>=2 && free_52>=free_50 && P==0 ], cost: 1 9: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1+U, V'=free_56, W'=-1+U, [ U>=0 && free_55>=2 && free_57>=free_55 && P==0 ], cost: 1 10: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1+U, V'=free_61, W'=-1+U, [ U>=0 && free_60>=2 && free_62>=free_60 && P==0 && 1+free_63<=-1+N ], cost: 1 Accelerated rule 7 with metering function 1+U, yielding the new rule 18. Accelerated rule 8 with metering function 1+U, yielding the new rule 19. Accelerated rule 9 with metering function 1+U, yielding the new rule 20. Accelerated rule 10 with metering function 1+U, yielding the new rule 21. Removing the simple loops: 7 8 9 10. Accelerated all simple loops using metering functions (where possible): Start location: f3 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_76>=2 && 0>=1+C ], cost: 1 17: f1 -> f1 : B'=A, C'=free_2, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_2, L'=free_7, M'=-1+A, [ A>=1+B && B>=0 ], cost: -B+A 18: f10 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=N, U'=-1, V'=free_46, W'=-1, [ U>=0 && free_45>=2 && free_47>=free_45 && P==0 && 1+N<=-1+free_48 ], cost: 1+U 19: f10 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=N, U'=-1, V'=free_51, W'=-1, [ U>=0 && free_50>=2 && free_52>=free_50 && P==0 ], cost: 1+U 20: f10 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=N, U'=-1, V'=free_56, W'=-1, [ U>=0 && free_55>=2 && free_57>=free_55 && P==0 ], cost: 1+U 21: f10 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=N, U'=-1, V'=free_61, W'=-1, [ U>=0 && free_60>=2 && free_62>=free_60 && P==0 && 1+free_63<=-1+N ], cost: 1+U 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f3 13: f1 -> f10 : A'=free_74, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_74>=2 && C>=1 ], cost: 1 14: f1 -> f10 : A'=free_76, B'=1+U, K'=C, N'=C, O'=U, P'=0, Q_1'=C, R'=0, S'=C, T'=C, [ B>=A && B>=0 && free_76>=2 && 0>=1+C ], cost: 1 23: f1 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, N'=C, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=C, U'=-1, V'=free_46, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+C<=-1+free_48 ], cost: 2+U 24: f1 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, N'=C, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=C, U'=-1, V'=free_46, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_45>=2 && free_47>=free_45 && 1+C<=-1+free_48 ], cost: 2+U 25: f1 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, N'=C, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=C, U'=-1, V'=free_51, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 2+U 26: f1 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, N'=C, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=C, U'=-1, V'=free_51, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 2+U 27: f1 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, N'=C, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=C, U'=-1, V'=free_56, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 2+U 28: f1 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, N'=C, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=C, U'=-1, V'=free_56, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 2+U 29: f1 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, N'=C, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=C, U'=-1, V'=free_61, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+C ], cost: 2+U 30: f1 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, N'=C, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=C, U'=-1, V'=free_61, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+C ], cost: 2+U 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 22: f3 -> f1 : B'=A, C'=free_2, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_2, L'=free_7, M'=-1+A, X'=free_90, [ A>=3 ], cost: -1+A Removed unreachable locations (and leaf rules with constant cost): Start location: f3 23: f1 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, N'=C, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=C, U'=-1, V'=free_46, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+C<=-1+free_48 ], cost: 2+U 24: f1 -> f10 : A'=free_45, B'=free_47, C'=free_48, K'=free_48, N'=C, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=C, U'=-1, V'=free_46, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_45>=2 && free_47>=free_45 && 1+C<=-1+free_48 ], cost: 2+U 25: f1 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, N'=C, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=C, U'=-1, V'=free_51, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 2+U 26: f1 -> f10 : A'=free_50, B'=free_52, C'=free_53, K'=free_53, N'=C, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=C, U'=-1, V'=free_51, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 2+U 27: f1 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, N'=C, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=C, U'=-1, V'=free_56, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 2+U 28: f1 -> f10 : A'=free_55, B'=free_57, C'=free_58, K'=free_58, N'=C, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=C, U'=-1, V'=free_56, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 2+U 29: f1 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, N'=C, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=C, U'=-1, V'=free_61, W'=-1, [ B>=A && B>=0 && C>=1 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+C ], cost: 2+U 30: f1 -> f10 : A'=free_60, B'=free_62, C'=free_63, K'=free_63, N'=C, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=C, U'=-1, V'=free_61, W'=-1, [ B>=A && B>=0 && 0>=1+C && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+C ], cost: 2+U 16: f3 -> f1 : B'=2, C'=free_88, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_88, X'=free_90, [ A>=2 ], cost: 1 22: f3 -> f1 : B'=A, C'=free_2, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_2, L'=free_7, M'=-1+A, X'=free_90, [ A>=3 ], cost: -1+A Eliminated locations (on tree-shaped paths): Start location: f3 31: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_48, N'=free_88, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_88, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_88<=-1+free_48 ], cost: 3+U 32: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_48, N'=free_88, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_88, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_88<=-1+free_48 ], cost: 3+U 33: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_53, N'=free_88, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_88, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 3+U 34: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_53, N'=free_88, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_88, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 3+U 35: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_58, N'=free_88, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_88, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 3+U 36: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_58, N'=free_88, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_88, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 3+U 37: f3 -> f10 : A'=free_60, B'=free_62, C'=free_63, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_63, N'=free_88, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=free_88, U'=-1, V'=free_61, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+free_88 ], cost: 3+U 38: f3 -> f10 : A'=free_60, B'=free_62, C'=free_63, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_63, N'=free_88, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=free_88, U'=-1, V'=free_61, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+free_88 ], cost: 3+U 39: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_48, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_2, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_2<=-1+free_48 ], cost: 1+U+A 40: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_48, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_2, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_2<=-1+free_48 ], cost: 1+U+A 41: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_53, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_2, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 1+U+A 42: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_53, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_2, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 1+U+A 43: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_58, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_2, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 1+U+A 44: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_58, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_2, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 1+U+A 45: f3 -> f10 : A'=free_60, B'=free_62, C'=free_63, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_63, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=free_2, U'=-1, V'=free_61, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+free_2 ], cost: 1+U+A 46: f3 -> f10 : A'=free_60, B'=free_62, C'=free_63, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_63, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_63, R'=0, S'=free_63, T'=free_2, U'=-1, V'=free_61, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_60>=2 && free_62>=free_60 && 1+free_63<=-1+free_2 ], cost: 1+U+A Applied pruning (of leafs and parallel rules): Start location: f3 31: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_48, N'=free_88, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_88, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_88<=-1+free_48 ], cost: 3+U 34: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_53, N'=free_88, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_88, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 3+U 39: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_48, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_2, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_2<=-1+free_48 ], cost: 1+U+A 41: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_53, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_2, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 1+U+A 44: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_58, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_2, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 1+U+A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f3 31: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_48, N'=free_88, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_88, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_88<=-1+free_48 ], cost: 3+U 34: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_92, E'=free_93, F'=free_89, G'=free_86, H'=free_91, Q'=free_87, J'=free_94, K'=free_53, N'=free_88, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_88, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=2 && 2>=A && 0>=1+free_88 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 3+U 39: f3 -> f10 : A'=free_45, B'=free_47, C'=free_48, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_48, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_48, R'=0, S'=free_48, T'=free_2, U'=-1, V'=free_46, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_2<=-1+free_48 ], cost: 1+U+A 41: f3 -> f10 : A'=free_50, B'=free_52, C'=free_53, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_53, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_53, R'=0, S'=free_53, T'=free_2, U'=-1, V'=free_51, W'=-1, X'=free_90, [ A>=3 && free_2>=1 && U>=0 && free_50>=2 && free_52>=free_50 ], cost: 1+U+A 44: f3 -> f10 : A'=free_55, B'=free_57, C'=free_58, D'=free_2, E'=free_5, F'=free_6, G'=free_3, H'=free, Q'=free_4, J'=free_1, K'=free_58, L'=free_7, M'=-1+A, N'=free_2, O'=U, P'=0, Q_1'=free_58, R'=0, S'=free_58, T'=free_2, U'=-1, V'=free_56, W'=-1, X'=free_90, [ A>=3 && 0>=1+free_2 && U>=0 && free_55>=2 && free_57>=free_55 ], cost: 1+U+A Computing asymptotic complexity for rule 31 Solved the limit problem by the following transformations: Created initial limit problem: -1+free_45 (+/+!), 3+U (+), -1-free_88+free_48 (+/+!), free_88 (+/+!), -1+A (+/+!), 1+free_47-free_45 (+/+!), 1+U (+/+!), 3-A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {U==n,free_88==1,A==2,free_47==n,free_48==n,free_45==n} resulting limit problem: [solved] Solution: U / n free_88 / 1 A / 2 free_47 / n free_48 / n free_45 / n Resulting cost 3+n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 3+n Rule cost: 3+U Rule guard: [ A>=2 && 2>=A && free_88>=1 && U>=0 && free_45>=2 && free_47>=free_45 && 1+free_88<=-1+free_48 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)