/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 2064 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && 0 >= D1 + 1 && 0 >= E1 + 1 && 0 >= B + 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && 0 >= D1 + 1 && 0 >= E1 + 1 && B >= 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && 0 >= D1 + 1 && E1 >= 1 && 0 >= B + 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && 0 >= D1 + 1 && E1 >= 1 && B >= 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && D1 >= 1 && 0 >= E1 + 1 && 0 >= B + 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && D1 >= 1 && 0 >= E1 + 1 && B >= 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && D1 >= 1 && E1 >= 1 && 0 >= B + 1 f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f12(A, B, C1, E1, B, G, G, A, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: A >= 0 && C1 >= 2 && D1 >= 1 && E1 >= 1 && B >= 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, Y, Z, A1, B1) -> Com_1(f1(A, B, C, D, E, F, G, H, I, 1 + J, L, C1, L, E1, J, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1)) :|: I >= J + 1 && J >= 0 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f1(A, B, C1, D, E, F, G, H, C1, 2, D1, F1, D1, N, O, E1, D1, G1, 2, T, U, V, W, X, Y, Z, A1, B1)) :|: C1 >= 2 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1) -> Com_1(f9(A, 0, C1, 0, E, F, G, H, N1, L1, O1, R1, Q1, N, O, M1, P1, R, S, E1, D1, F1, G1, K1, S1, T1, U1, B1)) :|: 0 >= H1 && 0 >= I1 && 0 >= C1 && 0 >= J1 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, Y, Z, A1, B1) -> Com_1(f12(A, K, C1, E1, E, F, G, H, G1, F1, K1, N1, M1, N, O, P, L1, R, S, T, U, V, W, X, O1, P1, A1, D1)) :|: J >= I && J >= 0 && Q1 >= 2 && F1 >= Q1 && F1 >= 0 && D1 >= C1 && C1 >= 2 && 0 >= K + 1 && 0 >= E1 + 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, Y, Z, A1, B1) -> Com_1(f12(A, K, C1, E1, E, F, G, H, G1, F1, K1, N1, M1, N, O, P, L1, R, S, T, U, V, W, X, O1, P1, A1, D1)) :|: J >= I && J >= 0 && Q1 >= 2 && F1 >= Q1 && F1 >= 0 && D1 >= C1 && C1 >= 2 && 0 >= K + 1 && E1 >= 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, Y, Z, A1, B1) -> Com_1(f12(A, K, C1, E1, E, F, G, H, G1, F1, K1, N1, M1, N, O, P, L1, R, S, T, U, V, W, X, O1, P1, A1, D1)) :|: J >= I && J >= 0 && Q1 >= 2 && F1 >= Q1 && F1 >= 0 && D1 >= C1 && C1 >= 2 && K >= 1 && 0 >= E1 + 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, Y, Z, A1, B1) -> Com_1(f12(A, K, C1, E1, E, F, G, H, G1, F1, K1, N1, M1, N, O, P, L1, R, S, T, U, V, W, X, O1, P1, A1, D1)) :|: J >= I && J >= 0 && Q1 >= 2 && F1 >= Q1 && F1 >= 0 && D1 >= C1 && C1 >= 2 && K >= 1 && E1 >= 1 The start-symbols are:[f8_28] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f8 0: f12 -> f12 : C'=free, D'=free_1, E'=B, F'=G, H'=A, [ A>=0 && free>=2 && 0>=1+free_2 && 0>=1+free_1 && 0>=1+B ], cost: 1 1: f12 -> f12 : C'=free_3, D'=free_4, E'=B, F'=G, H'=A, [ A>=0 && free_3>=2 && 0>=1+free_5 && 0>=1+free_4 && B>=1 ], cost: 1 2: f12 -> f12 : C'=free_6, D'=free_7, E'=B, F'=G, H'=A, [ A>=0 && free_6>=2 && 0>=1+free_8 && free_7>=1 && 0>=1+B ], cost: 1 3: f12 -> f12 : C'=free_9, D'=free_10, E'=B, F'=G, H'=A, [ A>=0 && free_9>=2 && 0>=1+free_11 && free_10>=1 && B>=1 ], cost: 1 4: f12 -> f12 : C'=free_12, D'=free_13, E'=B, F'=G, H'=A, [ A>=0 && free_12>=2 && free_14>=1 && 0>=1+free_13 && 0>=1+B ], cost: 1 5: f12 -> f12 : C'=free_15, D'=free_16, E'=B, F'=G, H'=A, [ A>=0 && free_15>=2 && free_17>=1 && 0>=1+free_16 && B>=1 ], cost: 1 6: f12 -> f12 : C'=free_18, D'=free_19, E'=B, F'=G, H'=A, [ A>=0 && free_18>=2 && free_20>=1 && free_19>=1 && 0>=1+B ], cost: 1 7: f12 -> f12 : C'=free_21, D'=free_22, E'=B, F'=G, H'=A, [ A>=0 && free_21>=2 && free_23>=1 && free_22>=1 && B>=1 ], cost: 1 8: f1 -> f1 : J'=1+J, K'=L, L'=free_24, M'=L, N'=free_25, O'=J, [ Q>=1+J && J>=0 ], cost: 1 11: f1 -> f12 : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_58>=2 && free_60>=free_58 && free_60>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 ], cost: 1 12: f1 -> f12 : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_70>=2 && free_72>=free_70 && free_72>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 ], cost: 1 13: f1 -> f12 : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_82>=2 && free_84>=free_82 && free_84>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 ], cost: 1 14: f1 -> f12 : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_94>=2 && free_96>=free_94 && free_96>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 ], cost: 1 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 10: f8 -> f9 : A1'=0, B'=free_31, B1'=0, C'=E, C1'=F, D'=G, D1'=H, E'=free_36, E1'=free_43, F'=free_47, F1'=free_40, G'=free_49, G1'=N, H'=O, H1'=free_42, Q'=free_35, Q1'=R, J'=S, J1'=free_46, K'=free_39, K1'=free_32, L'=free_44, L1'=free_37, M'=free_48, M1'=free_41, N'=free_34, N1'=B1, [ 0>=free_33 && 0>=free_45 && 0>=free_31 && 0>=free_38 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 Removed unreachable and leaf rules: Start location: f8 0: f12 -> f12 : C'=free, D'=free_1, E'=B, F'=G, H'=A, [ A>=0 && free>=2 && 0>=1+free_2 && 0>=1+free_1 && 0>=1+B ], cost: 1 1: f12 -> f12 : C'=free_3, D'=free_4, E'=B, F'=G, H'=A, [ A>=0 && free_3>=2 && 0>=1+free_5 && 0>=1+free_4 && B>=1 ], cost: 1 2: f12 -> f12 : C'=free_6, D'=free_7, E'=B, F'=G, H'=A, [ A>=0 && free_6>=2 && 0>=1+free_8 && free_7>=1 && 0>=1+B ], cost: 1 3: f12 -> f12 : C'=free_9, D'=free_10, E'=B, F'=G, H'=A, [ A>=0 && free_9>=2 && 0>=1+free_11 && free_10>=1 && B>=1 ], cost: 1 4: f12 -> f12 : C'=free_12, D'=free_13, E'=B, F'=G, H'=A, [ A>=0 && free_12>=2 && free_14>=1 && 0>=1+free_13 && 0>=1+B ], cost: 1 5: f12 -> f12 : C'=free_15, D'=free_16, E'=B, F'=G, H'=A, [ A>=0 && free_15>=2 && free_17>=1 && 0>=1+free_16 && B>=1 ], cost: 1 6: f12 -> f12 : C'=free_18, D'=free_19, E'=B, F'=G, H'=A, [ A>=0 && free_18>=2 && free_20>=1 && free_19>=1 && 0>=1+B ], cost: 1 7: f12 -> f12 : C'=free_21, D'=free_22, E'=B, F'=G, H'=A, [ A>=0 && free_21>=2 && free_23>=1 && free_22>=1 && B>=1 ], cost: 1 8: f1 -> f1 : J'=1+J, K'=L, L'=free_24, M'=L, N'=free_25, O'=J, [ Q>=1+J && J>=0 ], cost: 1 11: f1 -> f12 : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_58>=2 && free_60>=free_58 && free_60>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 ], cost: 1 12: f1 -> f12 : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_70>=2 && free_72>=free_70 && free_72>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 ], cost: 1 13: f1 -> f12 : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_82>=2 && free_84>=free_82 && free_84>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 ], cost: 1 14: f1 -> f12 : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_94>=2 && free_96>=free_94 && free_96>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 ], cost: 1 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 Simplified all rules, resulting in: Start location: f8 0: f12 -> f12 : C'=free, D'=free_1, E'=B, F'=G, H'=A, [ A>=0 && free>=2 && 0>=1+free_1 && 0>=1+B ], cost: 1 1: f12 -> f12 : C'=free_3, D'=free_4, E'=B, F'=G, H'=A, [ A>=0 && free_3>=2 && 0>=1+free_4 && B>=1 ], cost: 1 2: f12 -> f12 : C'=free_6, D'=free_7, E'=B, F'=G, H'=A, [ A>=0 && free_6>=2 && free_7>=1 && 0>=1+B ], cost: 1 3: f12 -> f12 : C'=free_9, D'=free_10, E'=B, F'=G, H'=A, [ A>=0 && free_9>=2 && free_10>=1 && B>=1 ], cost: 1 4: f12 -> f12 : C'=free_12, D'=free_13, E'=B, F'=G, H'=A, [ A>=0 && free_12>=2 && 0>=1+free_13 && 0>=1+B ], cost: 1 5: f12 -> f12 : C'=free_15, D'=free_16, E'=B, F'=G, H'=A, [ A>=0 && free_15>=2 && 0>=1+free_16 && B>=1 ], cost: 1 6: f12 -> f12 : C'=free_18, D'=free_19, E'=B, F'=G, H'=A, [ A>=0 && free_18>=2 && free_19>=1 && 0>=1+B ], cost: 1 7: f12 -> f12 : C'=free_21, D'=free_22, E'=B, F'=G, H'=A, [ A>=0 && free_21>=2 && free_22>=1 && B>=1 ], cost: 1 8: f1 -> f1 : J'=1+J, K'=L, L'=free_24, M'=L, N'=free_25, O'=J, [ Q>=1+J && J>=0 ], cost: 1 11: f1 -> f12 : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 ], cost: 1 12: f1 -> f12 : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 ], cost: 1 13: f1 -> f12 : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 ], cost: 1 14: f1 -> f12 : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 ], cost: 1 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: f12 -> f12 : C'=free, D'=free_1, E'=B, F'=G, H'=A, [ A>=0 && free>=2 && 0>=1+free_1 && 0>=1+B ], cost: 1 1: f12 -> f12 : C'=free_3, D'=free_4, E'=B, F'=G, H'=A, [ A>=0 && free_3>=2 && 0>=1+free_4 && B>=1 ], cost: 1 2: f12 -> f12 : C'=free_6, D'=free_7, E'=B, F'=G, H'=A, [ A>=0 && free_6>=2 && free_7>=1 && 0>=1+B ], cost: 1 3: f12 -> f12 : C'=free_9, D'=free_10, E'=B, F'=G, H'=A, [ A>=0 && free_9>=2 && free_10>=1 && B>=1 ], cost: 1 4: f12 -> f12 : C'=free_12, D'=free_13, E'=B, F'=G, H'=A, [ A>=0 && free_12>=2 && 0>=1+free_13 && 0>=1+B ], cost: 1 5: f12 -> f12 : C'=free_15, D'=free_16, E'=B, F'=G, H'=A, [ A>=0 && free_15>=2 && 0>=1+free_16 && B>=1 ], cost: 1 6: f12 -> f12 : C'=free_18, D'=free_19, E'=B, F'=G, H'=A, [ A>=0 && free_18>=2 && free_19>=1 && 0>=1+B ], cost: 1 7: f12 -> f12 : C'=free_21, D'=free_22, E'=B, F'=G, H'=A, [ A>=0 && free_21>=2 && free_22>=1 && B>=1 ], cost: 1 Accelerated rule 0 with NONTERM, yielding the new rule 15. Accelerated rule 1 with NONTERM, yielding the new rule 16. Accelerated rule 2 with NONTERM, yielding the new rule 17. Accelerated rule 3 with NONTERM, yielding the new rule 18. Accelerated rule 4 with NONTERM, yielding the new rule 19. Accelerated rule 5 with NONTERM, yielding the new rule 20. Accelerated rule 6 with NONTERM, yielding the new rule 21. Accelerated rule 7 with NONTERM, yielding the new rule 22. Removing the simple loops: 0 1 2 3 4 5 6 7. Accelerating simple loops of location 1. Accelerating the following rules: 8: f1 -> f1 : J'=1+J, K'=L, L'=free_24, M'=L, N'=free_25, O'=J, [ Q>=1+J && J>=0 ], cost: 1 Accelerated rule 8 with metering function -J+Q, yielding the new rule 23. Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: f8 15: f12 -> [4] : [ A>=0 && free>=2 && 0>=1+free_1 && 0>=1+B ], cost: NONTERM 16: f12 -> [4] : [ A>=0 && free_3>=2 && 0>=1+free_4 && B>=1 ], cost: NONTERM 17: f12 -> [4] : [ A>=0 && free_6>=2 && free_7>=1 && 0>=1+B ], cost: NONTERM 18: f12 -> [4] : [ A>=0 && free_9>=2 && free_10>=1 && B>=1 ], cost: NONTERM 19: f12 -> [4] : [ A>=0 && free_12>=2 && 0>=1+free_13 && 0>=1+B ], cost: NONTERM 20: f12 -> [4] : [ A>=0 && free_15>=2 && 0>=1+free_16 && B>=1 ], cost: NONTERM 21: f12 -> [4] : [ A>=0 && free_18>=2 && free_19>=1 && 0>=1+B ], cost: NONTERM 22: f12 -> [4] : [ A>=0 && free_21>=2 && free_22>=1 && B>=1 ], cost: NONTERM 11: f1 -> f12 : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 ], cost: 1 12: f1 -> f12 : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 ], cost: 1 13: f1 -> f12 : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 ], cost: 1 14: f1 -> f12 : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 ], cost: 1 23: f1 -> f1 : J'=Q, K'=free_24, L'=free_24, M'=free_24, N'=free_25, O'=-1+Q, [ Q>=1+J && J>=0 ], cost: -J+Q 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f8 11: f1 -> f12 : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 ], cost: 1 12: f1 -> f12 : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 ], cost: 1 13: f1 -> f12 : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 ], cost: 1 14: f1 -> f12 : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 ], cost: 1 24: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 25: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 26: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 27: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 28: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 29: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 30: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 31: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 32: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 33: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 34: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 35: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 36: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 37: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 38: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 39: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 40: f8 -> f1 : C'=free_26, Q'=free_26, J'=free_26, K'=free_24, L'=free_24, M'=free_24, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=3 ], cost: -1+free_26 Removed unreachable locations (and leaf rules with constant cost): Start location: f8 24: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 25: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 26: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 27: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 28: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 29: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 30: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 31: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 32: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 33: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 34: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 35: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 36: f1 -> [4] : B'=K, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, Q_1'=free_52, Y'=free_59, Z'=free_54, [ J>=Q && J>=0 && free_51>=free_50 && free_50>=2 && 0>=1+K && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 37: f1 -> [4] : B'=K, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, Q_1'=free_64, Y'=free_71, Z'=free_66, [ J>=Q && J>=0 && free_63>=free_62 && free_62>=2 && 0>=1+K && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 38: f1 -> [4] : B'=K, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, Q_1'=free_76, Y'=free_83, Z'=free_78, [ J>=Q && J>=0 && free_75>=free_74 && free_74>=2 && K>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 39: f1 -> [4] : B'=K, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, Q_1'=free_88, Y'=free_95, Z'=free_90, [ J>=Q && J>=0 && free_87>=free_86 && free_86>=2 && K>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 9: f8 -> f1 : C'=free_26, Q'=free_26, J'=2, K'=free_27, L'=free_29, M'=free_27, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=2 ], cost: 1 40: f8 -> f1 : C'=free_26, Q'=free_26, J'=free_26, K'=free_24, L'=free_24, M'=free_24, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_27, R'=free_28, S'=2, [ free_26>=3 ], cost: -1+free_26 Eliminated locations (on tree-shaped paths): Start location: f8 41: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 42: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 43: f8 -> [4] : B'=free_27, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=2 && 2>=free_26 && free_75>=free_74 && free_74>=2 && free_27>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 44: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 45: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 46: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 47: f8 -> [4] : B'=free_27, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=2 && 2>=free_26 && free_75>=free_74 && free_74>=2 && free_27>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 48: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 49: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 50: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 51: f8 -> [4] : B'=free_27, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=2 && 2>=free_26 && free_75>=free_74 && free_74>=2 && free_27>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 52: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 53: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 54: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 55: f8 -> [4] : B'=free_27, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=2 && 2>=free_26 && free_75>=free_74 && free_74>=2 && free_27>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 56: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 57: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 58: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 59: f8 -> [4] : B'=free_24, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=3 && free_75>=free_74 && free_74>=2 && free_24>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 60: f8 -> [4] : B'=free_24, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=3 && free_87>=free_86 && free_86>=2 && free_24>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 61: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 62: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 63: f8 -> [4] : B'=free_24, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=3 && free_75>=free_74 && free_74>=2 && free_24>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 64: f8 -> [4] : B'=free_24, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=3 && free_87>=free_86 && free_86>=2 && free_24>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 65: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 66: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 67: f8 -> [4] : B'=free_24, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=3 && free_75>=free_74 && free_74>=2 && free_24>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 68: f8 -> [4] : B'=free_24, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=3 && free_87>=free_86 && free_86>=2 && free_24>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 69: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 70: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 71: f8 -> [4] : B'=free_24, B1'=free_75, C'=free_74, D'=free_77, Q'=free_81, J'=free_84, K'=free_79, L'=free_85, M'=free_80, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_76, R'=free_28, S'=2, Y'=free_83, Z'=free_78, [ free_26>=3 && free_75>=free_74 && free_74>=2 && free_24>=1 && 0>=1+free_77 && 2<=free_84 && A>=0 ], cost: NONTERM 72: f8 -> [4] : B'=free_24, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=3 && free_87>=free_86 && free_86>=2 && free_24>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM Applied pruning (of leafs and parallel rules): Start location: f8 53: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 54: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 56: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 69: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 70: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f8 53: f8 -> [4] : B'=free_27, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 54: f8 -> [4] : B'=free_27, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=2 && 2>=free_26 && free_63>=free_62 && free_62>=2 && 0>=1+free_27 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM 56: f8 -> [4] : B'=free_27, B1'=free_87, C'=free_86, D'=free_89, Q'=free_93, J'=free_96, K'=free_91, L'=free_97, M'=free_92, P'=free_30, Q_1'=free_88, R'=free_28, S'=2, Y'=free_95, Z'=free_90, [ free_26>=2 && 2>=free_26 && free_87>=free_86 && free_86>=2 && free_27>=1 && free_89>=1 && 2<=free_96 && A>=0 ], cost: NONTERM 69: f8 -> [4] : B'=free_24, B1'=free_51, C'=free_50, D'=free_53, Q'=free_57, J'=free_60, K'=free_55, L'=free_61, M'=free_56, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_52, R'=free_28, S'=2, Y'=free_59, Z'=free_54, [ free_26>=3 && free_51>=free_50 && free_50>=2 && 0>=1+free_24 && 0>=1+free_53 && 2<=free_60 && A>=0 ], cost: NONTERM 70: f8 -> [4] : B'=free_24, B1'=free_63, C'=free_62, D'=free_65, Q'=free_69, J'=free_72, K'=free_67, L'=free_73, M'=free_68, N'=free_25, O'=-1+free_26, P'=free_30, Q_1'=free_64, R'=free_28, S'=2, Y'=free_71, Z'=free_66, [ free_26>=3 && free_63>=free_62 && free_62>=2 && 0>=1+free_24 && free_65>=1 && 2<=free_72 && A>=0 ], cost: NONTERM Computing asymptotic complexity for rule 53 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ free_26>=2 && 2>=free_26 && free_51>=free_50 && free_50>=2 && 0>=1+free_27 && 0>=1+free_53 && 2<=free_60 && A>=0 ] NO ---------------------------------------- (2) BOUNDS(INF, INF)