/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 2632 ms]
(2) BOUNDS(INF, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f1(A, 1 + B, D, G1, D, H1, 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)) :|: A >= B + 1 && B >= 0
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: I1 >= J + 1 && K >= 0 && H1 >= I1 + 1 && G1 >= 2
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: I1 >= J + 1 && K >= 0 && I1 >= H1 + 1 && G1 >= 2
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J >= I1 + 1 && K >= 0 && H1 >= I1 + 1 && G1 >= 2
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J >= I1 + 1 && K >= 0 && I1 >= H1 + 1 && G1 >= 2
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f4(A, B, C, D, E, F, G, H, I, M1, K, G1, L1, N, H1, J1, K1, N1, I1, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: K >= 0 && G1 >= J1 + 1 && H1 >= 2 && M >= J && M <= J
f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f4(A, B, C, D, E, F, G, H, I, M1, K, G1, L1, N, H1, J1, K1, N1, I1, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: K >= 0 && J1 >= G1 + 1 && H1 >= 2 && M >= J && M <= J
f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, -(1) + T, I1, I, -(1) + T, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J1 >= J + 1 && T >= 0 && H1 >= J1 + 1 && G1 >= 2
f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, -(1) + T, I1, I, -(1) + T, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J1 >= J + 1 && T >= 0 && J1 >= H1 + 1 && G1 >= 2
f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, -(1) + T, I1, I, -(1) + T, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J >= J1 + 1 && T >= 0 && H1 >= J1 + 1 && G1 >= 2
f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, M, M, M, G1, H1, H1, J, S, -(1) + T, I1, I, -(1) + T, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: J >= J1 + 1 && T >= 0 && J1 >= H1 + 1 && G1 >= 2
f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f4(A, B, C, D, E, F, G, H, I, K1, K, L, J1, N, G1, P, I1, L1, H1, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1)) :|: G1 >= 2 && T >= 0 && M >= J && M <= J
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(f4(J1, M1, L1, T1, S1, F, G, H, I, W1, K, X, V1, X, I1, X, U1, X1, Q1, T, U, V, W, G1, H1, K1, N1, R1, C1, D1, E1, F1)) :|: 0 >= O1 && 0 >= I1 && 0 >= P1
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(f1(J1, 2, K1, L1, K1, F, G, H, I, J, K, G1, M, G1, J1, P, Q, R, S, T, U, V, W, H1, I1, G1, A1, K1, M1, D1, E1, F1)) :|: J1 >= 2
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, C1, D1, E1, F1) -> Com_1(f10(H1, K1, J1, R1, Q1, F, G, H, I, C, T, N, N, N, G1, C, C, C, M1, T, U, V, W, X, Y, I1, L1, N1, C1, T + 1, I, S1)) :|: B >= A && B >= 0 && T1 >= G1 && U1 >= 2 && K1 >= U1 && C >= N + 1 && K1 >= 0 && G1 >= 2 && N >= C + 1
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1) -> Com_1(f10(H1, K1, J1, R1, Q1, F, G, H, I, C, T, N, N, N, G1, C, C, C, M1, T, U, V, W, X, Y, I1, L1, N1, C1, T + 1, I, S1)) :|: B >= A && B >= 0 && T1 >= G1 && U1 >= 2 && K1 >= U1 && C >= N + 1 && K1 >= 0 && G1 >= 2
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, C1, D1, E1, F1) -> Com_1(f10(H1, K1, J1, R1, Q1, F, G, H, I, C, T, N, N, N, G1, C, C, C, M1, T, U, V, W, X, Y, I1, L1, N1, C1, T + 1, I, S1)) :|: B >= A && B >= 0 && T1 >= G1 && U1 >= 2 && K1 >= U1 && N >= C + 1 && K1 >= 0 && G1 >= 2
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(f4(J1, M1, L1, T1, S1, F, G, H, I, X1, K, G1, W1, D, 1, U1, V1, O1, Q1, T, U, V, W, H1, I1, K1, N1, R1, C1, D1, E1, F1)) :|: 0 >= 1 && G1 >= U1 + 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(f4(J1, M1, L1, T1, S1, F, G, H, I, X1, K, G1, W1, D, 1, U1, V1, O1, Q1, T, U, V, W, H1, I1, K1, N1, R1, C1, D1, E1, F1)) :|: 0 >= 1 && U1 >= G1 + 1

The start-symbols are:[f3_32]


----------------------------------------

(1) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: f3

      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1

     14: f1 -> f10 : A'=free_85, A1'=free_78, B'=free_80, B1'=free_86, C'=free_88, D'=free_79, D1'=1+T, E'=free_83, E1'=Q, F1'=free_81, J'=C, K'=T, L'=N, M'=N, O'=free_87, P'=C, Q_1'=C, R'=C, S'=free_82, Z'=free_77, [ B>=A && B>=0 && free_89>=free_87 && free_84>=2 && free_80>=free_84 && C>=1+N && free_80>=0 && free_87>=2 && N>=1+C ], cost: 1

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && free_102>=free_100 && free_97>=2 && free_93>=free_97 && C>=1+N && free_93>=0 && free_100>=2 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && free_115>=free_113 && free_110>=2 && free_106>=free_110 && N>=1+C && free_106>=0 && free_113>=2 ], cost: 1

      1: f9 -> f10 : L'=M, N'=M, O'=free_3, P'=free_2, Q_1'=free_2, R'=J, [ free_4>=1+J && K>=0 && free_2>=1+free_4 && free_3>=2 ], cost: 1

      2: f9 -> f10 : L'=M, N'=M, O'=free_6, P'=free_5, Q_1'=free_5, R'=J, [ free_7>=1+J && K>=0 && free_7>=1+free_5 && free_6>=2 ], cost: 1

      3: f9 -> f10 : L'=M, N'=M, O'=free_9, P'=free_8, Q_1'=free_8, R'=J, [ J>=1+free_10 && K>=0 && free_8>=1+free_10 && free_9>=2 ], cost: 1

      4: f9 -> f10 : L'=M, N'=M, O'=free_12, P'=free_11, Q_1'=free_11, R'=J, [ J>=1+free_13 && K>=0 && free_13>=1+free_11 && free_12>=2 ], cost: 1

      5: f9 -> f4 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_19, F'=K, F1'=free_16, G'=free_21, G1'=N, H'=free_15, H1'=free_18, Q'=free_20, Q1'=free_17, J'=free_14, 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, [ K>=0 && free_16>=1+free_18 && free_15>=2 && M==J ], cost: 1

      6: f9 -> f4 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_27, F'=K, F1'=free_24, G'=free_29, G1'=N, H'=free_23, H1'=free_26, Q'=free_28, Q1'=free_25, J'=free_22, 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, [ K>=0 && free_26>=1+free_24 && free_23>=2 && M==J ], cost: 1

      7: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1+T, U'=free_33, V'=Q, W'=-1+T, [ free_30>=1+J && T>=0 && free_31>=1+free_30 && free_32>=2 ], cost: 1

      8: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1+T, U'=free_37, V'=Q, W'=-1+T, [ free_34>=1+J && T>=0 && free_34>=1+free_35 && free_36>=2 ], cost: 1

      9: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1+T, U'=free_41, V'=Q, W'=-1+T, [ J>=1+free_38 && T>=0 && free_39>=1+free_38 && free_40>=2 ], cost: 1

     10: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1+T, U'=free_45, V'=Q, W'=-1+T, [ J>=1+free_42 && T>=0 && free_42>=1+free_43 && free_44>=2 ], cost: 1

     11: f10 -> f4 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_49, F'=K, F1'=L, G'=free_47, G1'=N, H'=free_51, H1'=P, Q'=free_46, Q1'=free_48, J'=free_50, 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_51>=2 && T>=0 && M==J ], cost: 1

     12: f3 -> f4 : A'=free_63, A1'=free_56, B'=free_68, B1'=free_54, C'=free_61, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_65, F'=K, F1'=X, G'=free_58, G1'=X, H'=free_52, H1'=X, Q'=free_53, Q1'=free_64, J'=free_57, J1'=T, K'=U, K1'=V, L'=W, L1'=free_69, M'=free_62, M1'=free_55, N'=free_66, N1'=free_59, O'=C1, O1'=D1, P'=E1, P1'=F1, [ 0>=free_67 && 0>=free_52 && 0>=free_60 ], cost: 1

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1

     17: f3 -> f4 : A'=free_126, A1'=free_120, B'=free_131, B1'=free_118, C'=free_124, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_128, F'=K, F1'=free_122, G'=free_116, G1'=D, H'=1, H1'=free_117, Q'=free_127, Q1'=free_121, J'=free_132, J1'=T, K'=U, K1'=V, L'=W, L1'=free_125, M'=free_119, M1'=free_129, N'=free_123, N1'=free_130, O'=C1, O1'=D1, P'=E1, P1'=F1, [ 0>=1 && free_122>=1+free_117 ], cost: 1

     18: f3 -> f4 : A'=free_143, A1'=free_137, B'=free_148, B1'=free_135, C'=free_141, C1'=F, D'=G, D1'=H, E'=Q, E1'=free_145, F'=K, F1'=free_139, G'=free_133, G1'=D, H'=1, H1'=free_134, Q'=free_144, Q1'=free_138, J'=free_149, J1'=T, K'=U, K1'=V, L'=W, L1'=free_142, M'=free_136, M1'=free_146, N'=free_140, N1'=free_147, O'=C1, O1'=D1, P'=E1, P1'=F1, [ 0>=1 && free_134>=1+free_139 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f3

      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1

     14: f1 -> f10 : A'=free_85, A1'=free_78, B'=free_80, B1'=free_86, C'=free_88, D'=free_79, D1'=1+T, E'=free_83, E1'=Q, F1'=free_81, J'=C, K'=T, L'=N, M'=N, O'=free_87, P'=C, Q_1'=C, R'=C, S'=free_82, Z'=free_77, [ B>=A && B>=0 && free_89>=free_87 && free_84>=2 && free_80>=free_84 && C>=1+N && free_80>=0 && free_87>=2 && N>=1+C ], cost: 1

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && free_102>=free_100 && free_97>=2 && free_93>=free_97 && C>=1+N && free_93>=0 && free_100>=2 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && free_115>=free_113 && free_110>=2 && free_106>=free_110 && N>=1+C && free_106>=0 && free_113>=2 ], cost: 1

      7: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1+T, U'=free_33, V'=Q, W'=-1+T, [ free_30>=1+J && T>=0 && free_31>=1+free_30 && free_32>=2 ], cost: 1

      8: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1+T, U'=free_37, V'=Q, W'=-1+T, [ free_34>=1+J && T>=0 && free_34>=1+free_35 && free_36>=2 ], cost: 1

      9: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1+T, U'=free_41, V'=Q, W'=-1+T, [ J>=1+free_38 && T>=0 && free_39>=1+free_38 && free_40>=2 ], cost: 1

     10: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1+T, U'=free_45, V'=Q, W'=-1+T, [ J>=1+free_42 && T>=0 && free_42>=1+free_43 && free_44>=2 ], cost: 1

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1



Removed rules with unsatisfiable guard:

   Start location: f3

      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && free_102>=free_100 && free_97>=2 && free_93>=free_97 && C>=1+N && free_93>=0 && free_100>=2 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && free_115>=free_113 && free_110>=2 && free_106>=free_110 && N>=1+C && free_106>=0 && free_113>=2 ], cost: 1

      7: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1+T, U'=free_33, V'=Q, W'=-1+T, [ free_30>=1+J && T>=0 && free_31>=1+free_30 && free_32>=2 ], cost: 1

      8: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1+T, U'=free_37, V'=Q, W'=-1+T, [ free_34>=1+J && T>=0 && free_34>=1+free_35 && free_36>=2 ], cost: 1

      9: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1+T, U'=free_41, V'=Q, W'=-1+T, [ J>=1+free_38 && T>=0 && free_39>=1+free_38 && free_40>=2 ], cost: 1

     10: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1+T, U'=free_45, V'=Q, W'=-1+T, [ J>=1+free_42 && T>=0 && free_42>=1+free_43 && free_44>=2 ], cost: 1

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1



Simplified all rules, resulting in:

   Start location: f3

      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && C>=1+N && free_100>=2 && 2<=free_93 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && N>=1+C && free_113>=2 && 2<=free_106 ], cost: 1

      7: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1+T, U'=free_33, V'=Q, W'=-1+T, [ T>=0 && free_32>=2 && 1+J<=-1+free_31 ], cost: 1

      8: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1+T, U'=free_37, V'=Q, W'=-1+T, [ T>=0 && free_36>=2 ], cost: 1

      9: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1+T, U'=free_41, V'=Q, W'=-1+T, [ T>=0 && free_40>=2 ], cost: 1

     10: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1+T, U'=free_45, V'=Q, W'=-1+T, [ T>=0 && free_44>=2 && 1+free_43<=-1+J ], cost: 1

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1



   Accelerated rule 0 with metering function -B+A, yielding the new rule 19.

   Removing the simple loops: 0.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      7: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1+T, U'=free_33, V'=Q, W'=-1+T, [ T>=0 && free_32>=2 && 1+J<=-1+free_31 ], cost: 1

      8: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1+T, U'=free_37, V'=Q, W'=-1+T, [ T>=0 && free_36>=2 ], cost: 1

      9: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1+T, U'=free_41, V'=Q, W'=-1+T, [ T>=0 && free_40>=2 ], cost: 1

     10: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1+T, U'=free_45, V'=Q, W'=-1+T, [ T>=0 && free_44>=2 && 1+free_43<=-1+J ], cost: 1



   Accelerated rule 7 with metering function 1+T, yielding the new rule 20.

   Accelerated rule 8 with metering function 1+T, yielding the new rule 21.

   Accelerated rule 9 with metering function 1+T, yielding the new rule 22.

   Accelerated rule 10 with metering function 1+T, yielding the new rule 23.

   Removing the simple loops: 7 8 9 10.



Accelerated all simple loops using metering functions (where possible):

   Start location: f3

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && C>=1+N && free_100>=2 && 2<=free_93 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && N>=1+C && free_113>=2 && 2<=free_106 ], cost: 1

     19: f1 -> f1 : B'=A, C'=free_1, D'=free_1, E'=free_1, F'=free, G'=-1+A, H'=Q, [ A>=1+B && B>=0 ], cost: -B+A

     20: f10 -> f10 : L'=M, N'=M, O'=free_32, P'=free_31, Q_1'=free_31, R'=J, T'=-1, U'=free_33, V'=Q, W'=-1, [ T>=0 && free_32>=2 && 1+J<=-1+free_31 ], cost: 1+T

     21: f10 -> f10 : L'=M, N'=M, O'=free_36, P'=free_35, Q_1'=free_35, R'=J, T'=-1, U'=free_37, V'=Q, W'=-1, [ T>=0 && free_36>=2 ], cost: 1+T

     22: f10 -> f10 : L'=M, N'=M, O'=free_40, P'=free_39, Q_1'=free_39, R'=J, T'=-1, U'=free_41, V'=Q, W'=-1, [ T>=0 && free_40>=2 ], cost: 1+T

     23: f10 -> f10 : L'=M, N'=M, O'=free_44, P'=free_43, Q_1'=free_43, R'=J, T'=-1, U'=free_45, V'=Q, W'=-1, [ T>=0 && free_44>=2 && 1+free_43<=-1+J ], cost: 1+T

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f3

     15: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_100, P'=C, Q_1'=C, R'=C, S'=free_95, Z'=free_90, [ B>=A && B>=0 && C>=1+N && free_100>=2 && 2<=free_93 ], cost: 1

     16: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_113, P'=C, Q_1'=C, R'=C, S'=free_108, Z'=free_103, [ B>=A && B>=0 && N>=1+C && free_113>=2 && 2<=free_106 ], cost: 1

     25: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_32, P'=free_31, Q_1'=free_31, R'=C, S'=free_95, T'=-1, U'=free_33, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_32>=2 && 1+C<=-1+free_31 ], cost: 2+T

     26: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_32, P'=free_31, Q_1'=free_31, R'=C, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_32>=2 && 1+C<=-1+free_31 ], cost: 2+T

     27: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_36, P'=free_35, Q_1'=free_35, R'=C, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_36>=2 ], cost: 2+T

     28: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_36, P'=free_35, Q_1'=free_35, R'=C, S'=free_108, T'=-1, U'=free_37, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_36>=2 ], cost: 2+T

     29: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_40, P'=free_39, Q_1'=free_39, R'=C, S'=free_95, T'=-1, U'=free_41, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_40>=2 ], cost: 2+T

     30: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_40, P'=free_39, Q_1'=free_39, R'=C, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_40>=2 ], cost: 2+T

     31: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_44, P'=free_43, Q_1'=free_43, R'=C, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+C ], cost: 2+T

     32: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_44, P'=free_43, Q_1'=free_43, R'=C, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+C ], cost: 2+T

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1

     24: f3 -> f1 : A'=free_74, B'=free_74, B1'=free_71, C'=free_1, C1'=free_72, D'=free_1, E'=free_1, F'=free, G'=-1+free_74, H'=Q, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=3 ], cost: -1+free_74



Removed unreachable locations (and leaf rules with constant cost):

   Start location: f3

     25: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_32, P'=free_31, Q_1'=free_31, R'=C, S'=free_95, T'=-1, U'=free_33, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_32>=2 && 1+C<=-1+free_31 ], cost: 2+T

     26: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_32, P'=free_31, Q_1'=free_31, R'=C, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_32>=2 && 1+C<=-1+free_31 ], cost: 2+T

     27: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_36, P'=free_35, Q_1'=free_35, R'=C, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_36>=2 ], cost: 2+T

     28: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_36, P'=free_35, Q_1'=free_35, R'=C, S'=free_108, T'=-1, U'=free_37, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_36>=2 ], cost: 2+T

     29: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_40, P'=free_39, Q_1'=free_39, R'=C, S'=free_95, T'=-1, U'=free_41, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_40>=2 ], cost: 2+T

     30: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_40, P'=free_39, Q_1'=free_39, R'=C, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_40>=2 ], cost: 2+T

     31: f1 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=C, K'=T, L'=N, M'=N, O'=free_44, P'=free_43, Q_1'=free_43, R'=C, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, Z'=free_90, [ B>=A && B>=0 && C>=1+N && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+C ], cost: 2+T

     32: f1 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=C, K'=T, L'=N, M'=N, O'=free_44, P'=free_43, Q_1'=free_43, R'=C, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, Z'=free_103, [ B>=A && B>=0 && N>=1+C && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+C ], cost: 2+T

     13: f3 -> f1 : A'=free_74, B'=2, B1'=free_71, C'=free_71, C1'=free_72, D'=free_76, E'=free_71, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=2 ], cost: 1

     24: f3 -> f1 : A'=free_74, B'=free_74, B1'=free_71, C'=free_1, C1'=free_72, D'=free_1, E'=free_1, F'=free, G'=-1+free_74, H'=Q, L'=free_70, N'=free_70, O'=free_74, X'=free_73, Y'=free_75, Z'=free_70, [ free_74>=3 ], cost: -1+free_74



Eliminated locations (on tree-shaped paths):

   Start location: f3

     33: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_71, S'=free_95, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=2 && 2>=free_74 && free_71>=1+free_70 && 2<=free_93 && T>=0 && free_32>=2 && 1+free_71<=-1+free_31 ], cost: 3+T

     34: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_71, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=2 && 2>=free_74 && free_70>=1+free_71 && 2<=free_106 && T>=0 && free_32>=2 && 1+free_71<=-1+free_31 ], cost: 3+T

     35: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_71, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=2 && 2>=free_74 && free_71>=1+free_70 && 2<=free_93 && T>=0 && free_36>=2 ], cost: 3+T

     36: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_71, S'=free_108, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=2 && 2>=free_74 && free_70>=1+free_71 && 2<=free_106 && T>=0 && free_36>=2 ], cost: 3+T

     37: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_71, S'=free_95, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=2 && 2>=free_74 && free_71>=1+free_70 && 2<=free_93 && T>=0 && free_40>=2 ], cost: 3+T

     38: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_71, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=2 && 2>=free_74 && free_70>=1+free_71 && 2<=free_106 && T>=0 && free_40>=2 ], cost: 3+T

     39: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F1'=free_94, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_71, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=2 && 2>=free_74 && free_71>=1+free_70 && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+free_71 ], cost: 3+T

     40: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F1'=free_107, J'=free_71, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_71, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=2 && 2>=free_74 && free_70>=1+free_71 && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+free_71 ], cost: 3+T

     41: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_1, S'=free_95, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_32>=2 && 1+free_1<=-1+free_31 ], cost: 1+T+free_74

     42: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_1, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_32>=2 && 1+free_1<=-1+free_31 ], cost: 1+T+free_74

     43: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_1, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_36>=2 ], cost: 1+T+free_74

     44: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_1, S'=free_108, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_36>=2 ], cost: 1+T+free_74

     45: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_1, S'=free_95, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_40>=2 ], cost: 1+T+free_74

     46: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_1, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_40>=2 ], cost: 1+T+free_74

     47: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74

     48: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74



Applied pruning (of leafs and parallel rules):

   Start location: f3

     42: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_1, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_32>=2 && 1+free_1<=-1+free_31 ], cost: 1+T+free_74

     43: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_1, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_36>=2 ], cost: 1+T+free_74

     46: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_1, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_40>=2 ], cost: 1+T+free_74

     47: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74

     48: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f3

     42: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_32, P'=free_31, Q_1'=free_31, R'=free_1, S'=free_108, T'=-1, U'=free_33, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_32>=2 && 1+free_1<=-1+free_31 ], cost: 1+T+free_74

     43: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_36, P'=free_35, Q_1'=free_35, R'=free_1, S'=free_95, T'=-1, U'=free_37, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_36>=2 ], cost: 1+T+free_74

     46: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_40, P'=free_39, Q_1'=free_39, R'=free_1, S'=free_108, T'=-1, U'=free_41, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_40>=2 ], cost: 1+T+free_74

     47: f3 -> f10 : A'=free_98, A1'=free_91, B'=free_93, B1'=free_99, C'=free_101, C1'=free_72, D'=free_92, D1'=1+T, E'=free_96, E1'=Q, F'=free, F1'=free_94, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_95, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_90, [ free_74>=3 && free_1>=1+free_70 && 2<=free_93 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74

     48: f3 -> f10 : A'=free_111, A1'=free_104, B'=free_106, B1'=free_112, C'=free_114, C1'=free_72, D'=free_105, D1'=1+T, E'=free_109, E1'=Q, F'=free, F1'=free_107, G'=-1+free_74, H'=Q, J'=free_1, K'=T, L'=free_70, M'=free_70, N'=free_70, O'=free_44, P'=free_43, Q_1'=free_43, R'=free_1, S'=free_108, T'=-1, U'=free_45, V'=Q, W'=-1, X'=free_73, Y'=free_75, Z'=free_103, [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_44>=2 && 1+free_43<=-1+free_1 ], cost: 1+T+free_74



Computing asymptotic complexity for rule 42

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      free_70-free_1 (+/+!), -1+free_32 (+/+!), 1+T+free_74 (+), -1+free_31-free_1 (+/+!), -2+free_74 (+/+!), -1+free_106 (+/+!), 1+T (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {free_31==2,free_70==1,free_32==n,T==0,free_1==0,free_74==n,free_106==n}

      resulting limit problem:

      [solved]



   Solution:

      free_31 / 2

      free_70 / 1

      free_32 / n

      T / 0

      free_1 / 0

      free_74 / n

      free_106 / n

   Resulting cost 1+n has complexity: Unbounded



Found new complexity Unbounded.



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Unbounded

   Cpx degree:  Unbounded

   Solved cost: 1+n

   Rule cost:   1+T+free_74

   Rule guard:  [ free_74>=3 && free_70>=1+free_1 && 2<=free_106 && T>=0 && free_32>=2 && 1+free_1<=-1+free_31 ]



WORST_CASE(INF,?)


----------------------------------------

(2)
BOUNDS(INF, INF)