/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).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, 1476 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f33(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) -> Com_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, Y, Z, A1, B1, C1, D1, E1, F1)) :|: TRUE 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, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f25(G1, B, B, 0, 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)) :|: A >= 1 && B >= 1 && G1 >= 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, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f25(G1, B, B, 0, 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)) :|: A >= 1 && 0 >= B + 1 && G1 >= 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, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f16(J, B, C, D, G1, H1, H1, H1, H1, 1 + J, H1, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: TRUE 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, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f16(1 + H1, B, C, D, E, G1, G1, G1, G1, 1 + J, G1, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: H1 >= 0 && A >= 0 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, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f22(G1, L, 0, 0, E, F, G, H, L, J, K, L, L, L, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: H1 >= 1 && A >= 1 && B >= 0 && B <= 0 f23(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) -> Com_1(f17(A, B, C, D, E, F, G, H, I, K1, 0, L, 0, N, G1, H1, J1, G1, L1, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: G1 >= 1 && 0 >= I1 f23(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) -> Com_1(f17(A, B, C, D, E, F, G, H, I, K1, 0, L, 0, N, G1, H1, J1, G1, L1, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: 0 >= G1 + 1 && 0 >= I1 f23(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) -> Com_1(f21(A, B, C, D, E, F, G, H, G1, K1, 0, L, 0, N, 0, H1, J1, 0, L1, 0, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: 0 >= I1 f16(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) -> Com_1(f16(1 + H1, B, C, D, E, G1, G1, G1, G1, 1 + L1, G1, L, M, N, O, J1, K1, R, S, T, I1, N1, O1, P1, Q1, Z, A1, B1, C1, D1, E1, F1)) :|: A >= 0 && M1 >= 0 && Q >= 1 + J && H1 >= 0 f16(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) -> Com_1(f18(G1, B, C, D, E, F, G, H, I, K1, K, L, 0, N, 0, H1, J1, 0, S, T, U, V, W, X, Y, L1, A1, B1, C1, D1, E1, F1)) :|: A >= 0 && I1 >= 0 && J >= Q && G1 >= 0 f16(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) -> Com_1(f3(G1, N1, C, D, E, F, G, H, I, I1, J1, Q1, 0, N, H1, K1, L1, M1, S, T, U, V, W, X, Y, V1, O1, P1, T1, U1, E1, F1)) :|: A >= 0 && R1 >= 0 && S1 >= 0 && J >= Q && O1 >= 1 f16(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) -> Com_1(f3(G1, N1, C, D, E, F, G, H, I, I1, J1, Q1, 0, N, H1, K1, L1, M1, S, T, U, V, W, X, Y, V1, O1, P1, T1, U1, E1, F1)) :|: A >= 0 && R1 >= 0 && S1 >= 0 && J >= Q && 0 >= O1 + 1 f23(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) -> Com_1(f16(H1, B, C, D, E, G1, G1, G1, G1, 1 + H1, G1, L, M, N, O, J1, K1, R, S, T, L1, I1, N1, X, Y, Z, A1, B1, C1, D1, O1, P1)) :|: Q1 >= 1 The start-symbols are:[f33_32] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f33 0: f33 -> f3 : [], cost: 1 1: f3 -> f25 : A'=free, A1'=B, B1'=0, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=J, F'=K, F1'=L, G'=M, G1'=N, H'=O, H1'=P, Q'=Q_1, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ A>=1 && B>=1 && free>=1 ], cost: 1 2: f3 -> f25 : A'=free_1, A1'=B, B1'=0, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=J, F'=K, F1'=L, G'=M, G1'=N, H'=O, H1'=P, Q'=Q_1, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ A>=1 && 0>=1+B && free_1>=1 ], cost: 1 3: f3 -> f16 : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [], cost: 1 4: f3 -> f16 : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 ], cost: 1 5: f3 -> f22 : A'=free_7, A1'=L, B'=0, B1'=0, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=L, F'=K, F1'=L, G'=L, G1'=L, H'=O, H1'=P, Q'=Q_1, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ free_6>=1 && A>=1 && B==0 ], cost: 1 6: f23 -> f17 : A1'=B, B'=C, B1'=D, C'=free_10, C1'=F, D'=G, D1'=H, E'=Q, E1'=J, F'=0, F1'=L, G'=0, G1'=N, H'=free_8, H1'=free_9, Q'=free_13, Q1'=free_8, J'=free_11, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ free_8>=1 && 0>=free_12 ], cost: 1 7: f23 -> f17 : A1'=B, B'=C, B1'=D, C'=free_16, C1'=F, D'=G, D1'=H, E'=Q, E1'=J, F'=0, F1'=L, G'=0, G1'=N, H'=free_14, H1'=free_15, Q'=free_19, Q1'=free_14, J'=free_17, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ 0>=1+free_14 && 0>=free_18 ], cost: 1 8: f23 -> f21 : A1'=B, B'=C, B1'=D, C'=free_20, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_22, F'=0, F1'=L, G'=0, G1'=N, H'=0, H1'=free_21, Q'=free_25, Q1'=0, J'=free_23, J1'=0, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=Z, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ 0>=free_24 ], cost: 1 13: f23 -> f16 : A'=free_79, E'=1+free_79, E1'=free_78, F1'=free_75, G'=free_76, H'=free_76, Q'=free_76, J'=free_76, K'=free_76, P'=free_77, Q_1'=free_84, U'=free_80, V'=free_82, W'=free_83, [ free_81>=1 ], cost: 1 9: f16 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && free_28>=0 && Q_1>=1+E && free_31>=0 ], cost: 1 10: f16 -> f18 : A'=free_39, A1'=B, B'=C, B1'=D, C'=free_37, C1'=F, D'=G, D1'=H, E'=Q, E1'=J, F'=K, F1'=L, G'=0, G1'=N, H'=0, H1'=free_38, Q'=free_42, Q1'=0, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, M1'=free_40, N'=A1, N1'=B1, O'=C1, O1'=D1, P'=E1, P1'=F1, [ A>=0 && free_41>=0 && E>=Q_1 && free_39>=0 ], cost: 1 11: f16 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ A>=0 && free_47>=0 && free_57>=0 && E>=Q_1 && free_46>=1 ], cost: 1 12: f16 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && free_63>=0 && free_73>=0 && E>=Q_1 && 0>=1+free_62 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: f33 -> f3 : [], cost: 1 Removed unreachable and leaf rules: Start location: f33 0: f33 -> f3 : [], cost: 1 3: f3 -> f16 : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [], cost: 1 4: f3 -> f16 : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 ], cost: 1 9: f16 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && free_28>=0 && Q_1>=1+E && free_31>=0 ], cost: 1 11: f16 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ A>=0 && free_47>=0 && free_57>=0 && E>=Q_1 && free_46>=1 ], cost: 1 12: f16 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && free_63>=0 && free_73>=0 && E>=Q_1 && 0>=1+free_62 ], cost: 1 Simplified all rules, resulting in: Start location: f33 0: f33 -> f3 : [], cost: 1 3: f3 -> f16 : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [], cost: 1 4: f3 -> f16 : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 ], cost: 1 9: f16 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && Q_1>=1+E && free_31>=0 ], cost: 1 11: f16 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ A>=0 && E>=Q_1 && free_46>=1 ], cost: 1 12: f16 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && E>=Q_1 && 0>=1+free_62 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 9: f16 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && Q_1>=1+E && free_31>=0 ], cost: 1 Accelerated rule 9 with NONTERM (after strengthening guard), yielding the new rule 14. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f33 0: f33 -> f3 : [], cost: 1 3: f3 -> f16 : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [], cost: 1 4: f3 -> f16 : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 ], cost: 1 9: f16 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && Q_1>=1+E && free_31>=0 ], cost: 1 11: f16 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ A>=0 && E>=Q_1 && free_46>=1 ], cost: 1 12: f16 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && E>=Q_1 && 0>=1+free_62 ], cost: 1 14: f16 -> [9] : [ A>=0 && Q_1>=1+E && free_31>=0 && free_32>=2+free_29 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: f33 0: f33 -> f3 : [], cost: 1 3: f3 -> f16 : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [], cost: 1 4: f3 -> f16 : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 ], cost: 1 15: f3 -> f16 : A'=1+free_31, E'=1+free_29, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ E>=0 && Q_1>=2+E && free_31>=0 ], cost: 2 16: f3 -> f16 : A'=1+free_31, E'=1+free_29, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_27, P'=free_36, Q_1'=free_32, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, [ A>=0 && Q_1>=2+E && free_31>=0 ], cost: 2 17: f3 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 18: f3 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 11: f16 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ A>=0 && E>=Q_1 && free_46>=1 ], cost: 1 12: f16 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && E>=Q_1 && 0>=1+free_62 ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: f33 0: f33 -> f3 : [], cost: 1 17: f3 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 18: f3 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 19: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 2 20: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 21: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ free_5>=0 && A>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 2 22: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ free_5>=0 && A>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 23: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && free_46>=1 ], cost: 3 24: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && 0>=1+free_62 ], cost: 3 25: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ A>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && free_46>=1 ], cost: 3 26: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ A>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && 0>=1+free_62 ], cost: 3 Applied pruning (of leafs and parallel rules): Start location: f33 0: f33 -> f3 : [], cost: 1 17: f3 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 18: f3 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 19: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 2 20: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 22: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ free_5>=0 && A>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 23: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && free_46>=1 ], cost: 3 24: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && free_31>=0 && 1+free_29>=free_32 && 0>=1+free_62 ], cost: 3 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 19: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 2 20: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 22: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 23: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_46>=1 ], cost: 3 24: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && 0>=1+free_62 ], cost: 3 Accelerated rule 19 with NONTERM (after strengthening guard), yielding the new rule 27. Accelerated rule 20 with NONTERM (after strengthening guard), yielding the new rule 28. Accelerated rule 22 with NONTERM (after strengthening guard), yielding the new rule 29. Accelerated rule 23 with NONTERM (after strengthening guard), yielding the new rule 30. Accelerated rule 24 with NONTERM (after strengthening guard), yielding the new rule 31. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f33 0: f33 -> f3 : [], cost: 1 17: f3 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 18: f3 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 19: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 2 20: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 22: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 2 23: f3 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_46>=1 ], cost: 3 24: f3 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && 0>=1+free_62 ], cost: 3 27: f3 -> [10] : [ E>=0 && 1+E>=Q_1 && free_46>=1 && free_48>=0 && 1+free_48>=free_49 ], cost: NONTERM 28: f3 -> [10] : [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_64>=0 && 1+free_64>=free_65 ], cost: NONTERM 29: f3 -> [10] : [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_66>=0 && 1+free_64>=free_65 ], cost: NONTERM 30: f3 -> [10] : [ E>=0 && Q_1>=2+E && free_46>=1 && free_48>=0 && free_49>=2+free_48 ], cost: NONTERM 31: f3 -> [10] : [ E>=0 && Q_1>=2+E && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: f33 0: f33 -> f3 : [], cost: 1 32: f33 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 ], cost: 3 33: f33 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 3 34: f33 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 ], cost: 3 35: f33 -> f3 : A'=free_50, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=free_48, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_58, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_46>=1 ], cost: 4 36: f33 -> f3 : A'=free_66, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=free_64, F'=free_3, G'=free_27, H'=free_27, Q'=free_27, J'=free_27, K'=free_74, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && 0>=1+free_62 ], cost: 4 37: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 38: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 39: f33 -> [10] : [ A>=0 && 1+E>=Q_1 ], cost: NONTERM 40: f33 -> [10] : [ E>=0 && Q_1>=2+E ], cost: NONTERM 41: f33 -> [10] : [ E>=0 && Q_1>=2+E ], cost: NONTERM 17: f3 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 18: f3 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: f33 37: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 38: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 39: f33 -> [10] : [ A>=0 && 1+E>=Q_1 ], cost: NONTERM 40: f33 -> [10] : [ E>=0 && Q_1>=2+E ], cost: NONTERM 41: f33 -> [10] : [ E>=0 && Q_1>=2+E ], cost: NONTERM 42: f33 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 43: f33 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 44: f33 -> [9] : A'=free_48, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 && free_48>=0 && free_49>=2+free_48 ], cost: NONTERM 45: f33 -> [9] : A'=1+free_5, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 && free_5>=0 && free_50>=0 && free_49>=2+free_48 ], cost: NONTERM 46: f33 -> [9] : A'=free_64, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM 47: f33 -> [9] : A'=1+free_5, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_5>=0 && free_66>=0 && free_65>=2+free_64 ], cost: NONTERM 48: f33 -> [9] : A'=free_64, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM 49: f33 -> [9] : A'=1+free_5, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_5>=0 && free_66>=0 && free_65>=2+free_64 ], cost: NONTERM 50: f33 -> [9] : A'=free_48, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_46>=1 && free_48>=0 && free_49>=2+free_48 ], cost: NONTERM 51: f33 -> [9] : A'=1+free_5, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_53, [ E>=0 && Q_1>=2+E && free_46>=1 && free_5>=0 && free_50>=0 && free_49>=2+free_48 ], cost: NONTERM 52: f33 -> [9] : A'=free_64, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM 53: f33 -> [9] : A'=1+free_5, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, U'=free_34, V'=free_35, W'=free_30, X'=free_26, Y'=free_33, Z'=free_69, [ E>=0 && Q_1>=2+E && 0>=1+free_62 && free_5>=0 && free_66>=0 && free_65>=2+free_64 ], cost: NONTERM Applied pruning (of leafs and parallel rules): Start location: f33 38: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 39: f33 -> [10] : [ A>=0 && 1+E>=Q_1 ], cost: NONTERM 41: f33 -> [10] : [ E>=0 && Q_1>=2+E ], cost: NONTERM 42: f33 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 43: f33 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 45: f33 -> [9] : A'=1+free_5, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 && free_5>=0 && free_50>=0 && free_49>=2+free_48 ], cost: NONTERM 47: f33 -> [9] : A'=1+free_5, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_5>=0 && free_66>=0 && free_65>=2+free_64 ], cost: NONTERM 48: f33 -> [9] : A'=free_64, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f33 38: f33 -> [10] : [ E>=0 && 1+E>=Q_1 ], cost: NONTERM 39: f33 -> [10] : [ A>=0 && 1+E>=Q_1 ], cost: NONTERM 42: f33 -> [9] : A'=E, E'=1+E, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, [ E>=0 && Q_1>=2+E ], cost: NONTERM 43: f33 -> [9] : A'=1+free_5, E'=1+E, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, [ free_5>=0 && A>=0 && Q_1>=2+E ], cost: NONTERM 45: f33 -> [9] : A'=1+free_5, A1'=free_46, B'=free_44, B1'=free_51, C1'=free_45, D1'=free_55, E'=1+free_48, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_52, M'=0, O'=free_54, P'=free_56, Q_1'=free_49, R'=free_43, Z'=free_53, [ E>=0 && 1+E>=Q_1 && free_46>=1 && free_5>=0 && free_50>=0 && free_49>=2+free_48 ], cost: NONTERM 47: f33 -> [9] : A'=1+free_5, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_4, H'=free_4, Q'=free_4, J'=free_4, K'=free_4, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ E>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_5>=0 && free_66>=0 && free_65>=2+free_64 ], cost: NONTERM 48: f33 -> [9] : A'=free_64, A1'=free_62, B'=free_60, B1'=free_67, C1'=free_61, D1'=free_71, E'=1+free_64, F'=free_3, G'=free_2, H'=free_2, Q'=free_2, J'=free_2, K'=free_2, L'=free_68, M'=0, O'=free_70, P'=free_72, Q_1'=free_65, R'=free_59, Z'=free_69, [ A>=0 && 1+E>=Q_1 && 0>=1+free_62 && free_64>=0 && free_65>=2+free_64 ], cost: NONTERM Computing asymptotic complexity for rule 38 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: [ E>=0 && 1+E>=Q_1 ] NO ---------------------------------------- (2) BOUNDS(INF, INF)