/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).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, 696 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f11(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, C1, D1, E1, F1, G1, H1) -> Com_1(f11(A, 1 + B, D, I1, D, J1, B, I, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: A >= B + 1 && B >= 0 f2(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, C1, D1, E1, F1, G1, H1) -> Com_1(f2(A, B, C, D, E, F, G, H, I, J, I1, J1, J, J1, J, Q, Q, I, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 1 && I1 >= 2 f2(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, C1, D1, E1, F1, G1, H1) -> Com_1(f2(A, B, C, D, E, F, G, H, I, J, I1, J1, J, J1, J, Q, Q, I, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 1 && I1 >= 2 f5(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, C1, D1, E1, F1, G1, H1) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, 1, I1, J, I1, J, P, Q, R, I, U, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 1 f5(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, C1, D1, E1, F1, G1, H1) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, 1, I1, J, I1, J, P, Q, R, I, U, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 1 f0(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, C1, D1, E1, F1, G1, H1) -> Com_1(f11(J1, 2, K1, L1, K1, F, G, H, I, J, J1, L, M, N, O, P, Q, R, S, T, U, I1, K1, M1, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J1 >= 2 f0(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, C1, D1, E1, F1, G1, H1) -> Com_1(f1(K1, M1, L1, U1, T1, F, G, H, I, P1, J1, V1, W1, N, X1, P, Q, R, S, T, U, I1, S1, X, D2, Q1, R1, Y1, Z1, A2, B2, C2, E2, H1)) :|: 0 >= N1 && 0 >= J1 && 0 >= O1 && Y >= 0 && Y <= 0 f0(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, C1, D1, E1, F1, G1, H1) -> Com_1(f5(J1, L1, K1, S1, R1, F, G, H, I, J, 1, T1, J, T1, J, P, Q, R, S, T, U, I1, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 1 f0(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, C1, D1, E1, F1, G1, H1) -> Com_1(f5(J1, L1, K1, S1, R1, F, G, H, I, J, 1, T1, J, T1, J, P, Q, R, S, T, U, I1, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 1 f11(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, C1, D1, E1, F1, G1, H1) -> Com_1(f2(J1, L1, K1, S1, R1, F, G, H, I, J, I1, T1, J, T1, J, P, Q, R, S, T, U, V, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: U1 >= 2 && H1 >= U1 && V1 >= 2 && H1 >= V1 && B >= A && B >= 0 && I1 >= 2 && 0 >= J + 1 && H1 >= 0 f11(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, C1, D1, E1, F1, G1, H1) -> Com_1(f2(J1, L1, K1, S1, R1, F, G, H, I, J, I1, T1, J, T1, J, P, Q, R, S, T, U, V, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: U1 >= 2 && H1 >= U1 && V1 >= 2 && H1 >= V1 && B >= A && B >= 0 && I1 >= 2 && J >= 1 && H1 >= 0 The start-symbols are:[f0_34] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f0 0: f11 -> f11 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 9: f11 -> f2 : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ free_64>=2 && H1>=free_64 && free_61>=2 && H1>=free_61 && B>=A && B>=0 && free_59>=2 && 0>=1+J && H1>=0 ], cost: 1 10: f11 -> f2 : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ free_76>=2 && H1>=free_76 && free_73>=2 && H1>=free_73 && B>=A && B>=0 && free_71>=2 && J>=1 && H1>=0 ], cost: 1 1: f2 -> f2 : K'=free_2, L'=free_3, M'=J, N'=free_3, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_2>=2 ], cost: 1 2: f2 -> f2 : K'=free_4, L'=free_5, M'=J, N'=free_5, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_4>=2 ], cost: 1 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 6: f0 -> f1 : A'=free_20, A1'=free_33, A2'=free_24, B'=free_17, B1'=free_28, B2'=F, C'=G, C1'=H, C2'=Q, D'=free_19, D1'=free_13, D2'=free_31, E'=free_23, E1'=N, E2'=free_15, F'=P, F1'=Q_1, G'=R, G1'=S, H'=T, H1'=U, Q'=free_27, Q1'=free_21, J'=X, J1'=free_34, K'=free_25, K1'=free_18, L'=free_29, L1'=free_16, M'=free_14, M1'=free_35, N'=free_32, N1'=free_30, O'=H1, [ 0>=free_22 && 0>=free_13 && 0>=free_26 && Y==0 ], cost: 1 7: f0 -> f5 : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 Removed unreachable and leaf rules: Start location: f0 0: f11 -> f11 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 9: f11 -> f2 : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ free_64>=2 && H1>=free_64 && free_61>=2 && H1>=free_61 && B>=A && B>=0 && free_59>=2 && 0>=1+J && H1>=0 ], cost: 1 10: f11 -> f2 : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ free_76>=2 && H1>=free_76 && free_73>=2 && H1>=free_73 && B>=A && B>=0 && free_71>=2 && J>=1 && H1>=0 ], cost: 1 1: f2 -> f2 : K'=free_2, L'=free_3, M'=J, N'=free_3, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_2>=2 ], cost: 1 2: f2 -> f2 : K'=free_4, L'=free_5, M'=J, N'=free_5, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_4>=2 ], cost: 1 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 7: f0 -> f5 : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: 1 Simplified all rules, resulting in: Start location: f0 0: f11 -> f11 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 9: f11 -> f2 : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ B>=A && B>=0 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: 1 10: f11 -> f2 : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ B>=A && B>=0 && free_71>=2 && J>=1 && 2<=H1 ], cost: 1 1: f2 -> f2 : K'=free_2, L'=free_3, M'=J, N'=free_3, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_2>=2 ], cost: 1 2: f2 -> f2 : K'=free_4, L'=free_5, M'=J, N'=free_5, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_4>=2 ], cost: 1 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 7: f0 -> f5 : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: f11 -> f11 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 Accelerated rule 0 with metering function -B+A, yielding the new rule 11. Removing the simple loops: 0. Accelerating simple loops of location 1. Accelerating the following rules: 1: f2 -> f2 : K'=free_2, L'=free_3, M'=J, N'=free_3, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_2>=2 ], cost: 1 2: f2 -> f2 : K'=free_4, L'=free_5, M'=J, N'=free_5, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_4>=2 ], cost: 1 Accelerated rule 1 with NONTERM, yielding the new rule 12. Accelerated rule 2 with NONTERM, yielding the new rule 13. Removing the simple loops: 1 2. Accelerating simple loops of location 2. Accelerating the following rules: 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 Accelerated rule 3 with NONTERM, yielding the new rule 14. Accelerated rule 4 with NONTERM, yielding the new rule 15. Removing the simple loops: 3 4. Accelerated all simple loops using metering functions (where possible): Start location: f0 9: f11 -> f2 : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ B>=A && B>=0 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: 1 10: f11 -> f2 : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ B>=A && B>=0 && free_71>=2 && J>=1 && 2<=H1 ], cost: 1 11: f11 -> f11 : B'=A, C'=free, D'=free, E'=free, F'=free_1, G'=-1+A, H'=Q, [ A>=1+B && B>=0 ], cost: -B+A 12: f2 -> [6] : [ 0>=1+J && free_2>=2 ], cost: NONTERM 13: f2 -> [6] : [ J>=1 && free_4>=2 ], cost: NONTERM 14: f5 -> [7] : [ 0>=1+J ], cost: NONTERM 15: f5 -> [7] : [ J>=1 ], cost: NONTERM 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 7: f0 -> f5 : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f0 9: f11 -> f2 : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ B>=A && B>=0 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: 1 10: f11 -> f2 : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ B>=A && B>=0 && free_71>=2 && J>=1 && 2<=H1 ], cost: 1 17: f11 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ B>=A && B>=0 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 18: f11 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ B>=A && B>=0 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 7: f0 -> f5 : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: 1 16: f0 -> f11 : A'=free_9, B'=free_9, C'=free, D'=free, E'=free, F'=free_1, G'=-1+free_9, H'=Q, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=3 ], cost: -1+free_9 19: f0 -> [7] : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: NONTERM 20: f0 -> [7] : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: f0 17: f11 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, W'=free_66, Z'=free_62, [ B>=A && B>=0 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 18: f11 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, W'=free_78, Z'=free_74, [ B>=A && B>=0 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM 5: f0 -> f11 : A'=free_9, B'=2, C'=free_12, D'=free_10, E'=free_12, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=2 ], cost: 1 16: f0 -> f11 : A'=free_9, B'=free_9, C'=free, D'=free, E'=free, F'=free_1, G'=-1+free_9, H'=Q, K'=free_9, V'=free_8, W'=free_12, X'=free_11, [ free_9>=3 ], cost: -1+free_9 19: f0 -> [7] : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: NONTERM 20: f0 -> [7] : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: f0 19: f0 -> [7] : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: NONTERM 20: f0 -> [7] : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: NONTERM 21: f0 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, V'=free_8, W'=free_66, X'=free_11, Z'=free_62, [ free_9>=2 && 2>=free_9 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 22: f0 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, V'=free_8, W'=free_78, X'=free_11, Z'=free_74, [ free_9>=2 && 2>=free_9 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM 23: f0 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, F'=free_1, G'=-1+free_9, H'=Q, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, V'=free_8, W'=free_66, X'=free_11, Z'=free_62, [ free_9>=3 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 24: f0 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, F'=free_1, G'=-1+free_9, H'=Q, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, V'=free_8, W'=free_78, X'=free_11, Z'=free_74, [ free_9>=3 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f0 19: f0 -> [7] : A'=free_40, A1'=free_37, B'=free_45, C'=free_42, D'=free_38, E'=free_43, K'=1, L'=free_39, M'=J, N'=free_39, O'=J, V'=free_36, W'=free_44, Z'=free_41, [ 0>=1+J ], cost: NONTERM 20: f0 -> [7] : A'=free_50, A1'=free_47, B'=free_55, C'=free_52, D'=free_48, E'=free_53, K'=1, L'=free_49, M'=J, N'=free_49, O'=J, V'=free_46, W'=free_54, Z'=free_51, [ J>=1 ], cost: NONTERM 21: f0 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, V'=free_8, W'=free_66, X'=free_11, Z'=free_62, [ free_9>=2 && 2>=free_9 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 22: f0 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, V'=free_8, W'=free_78, X'=free_11, Z'=free_74, [ free_9>=2 && 2>=free_9 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM 23: f0 -> [6] : A'=free_60, A1'=free_57, B'=free_67, C'=free_63, D'=free_58, E'=free_65, F'=free_1, G'=-1+free_9, H'=Q, K'=free_59, L'=free_56, M'=J, N'=free_56, O'=J, V'=free_8, W'=free_66, X'=free_11, Z'=free_62, [ free_9>=3 && free_59>=2 && 0>=1+J && 2<=H1 ], cost: NONTERM 24: f0 -> [6] : A'=free_72, A1'=free_69, B'=free_79, C'=free_75, D'=free_70, E'=free_77, F'=free_1, G'=-1+free_9, H'=Q, K'=free_71, L'=free_68, M'=J, N'=free_68, O'=J, V'=free_8, W'=free_78, X'=free_11, Z'=free_74, [ free_9>=3 && free_71>=2 && J>=1 && 2<=H1 ], cost: NONTERM Computing asymptotic complexity for rule 19 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: [ 0>=1+J ] NO ---------------------------------------- (2) BOUNDS(INF, INF)