10.75/4.49	WORST_CASE(NON_POLY, ?)
10.75/4.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
10.75/4.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.75/4.50	
10.75/4.50	
10.75/4.50	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
10.75/4.50	
10.75/4.50	(0) CpxIntTrs
10.75/4.50	(1) Loat Proof [FINISHED, 2664 ms]
10.75/4.50	(2) BOUNDS(INF, INF)
10.75/4.50	
10.75/4.50	
10.75/4.50	----------------------------------------
10.75/4.50	
10.75/4.50	(0)
10.75/4.50	Obligation:
10.75/4.50	Complexity Int TRS consisting of the following rules:
10.75/4.50	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) -> Com_1(f1(A, 1 + B, D, Z, D, A1, B, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y)) :|: A >= B + 1 && B >= 0
10.75/4.50	f7(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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, R, S, T, U, V, W, X, Y)) :|: B1 >= H + 1 && I >= 0 && A1 >= B1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	f7(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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, R, S, T, U, V, W, X, Y)) :|: B1 >= H + 1 && I >= 0 && B1 >= A1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	f7(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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, R, S, T, U, V, W, X, Y)) :|: H >= B1 + 1 && I >= 0 && A1 >= B1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	f7(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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, R, S, T, U, V, W, X, Y)) :|: H >= B1 + 1 && I >= 0 && B1 >= A1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	f7(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) -> Com_1(f10(A, B, C, D, E, F, G, G1, I, F1, Z, B1, C1, D1, E1, H1, A1, R, S, T, U, V, W, X, Y)) :|: I >= 0 && 0 >= B1 + 1 && Z >= 2 && J >= H && J <= H
10.75/4.50	f7(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) -> Com_1(f10(A, B, C, D, E, F, G, G1, I, F1, Z, B1, C1, D1, E1, H1, A1, R, S, T, U, V, W, X, Y)) :|: I >= 0 && B1 >= 1 && Z >= 2 && J >= H && J <= H
10.75/4.50	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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, -(1) + R, B1, -(1) + R, U, V, W, X, Y)) :|: C1 >= H + 1 && R >= 0 && A1 >= C1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, -(1) + R, B1, -(1) + R, U, V, W, X, Y)) :|: C1 >= H + 1 && R >= 0 && C1 >= A1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, -(1) + R, B1, -(1) + R, U, V, W, X, Y)) :|: H >= C1 + 1 && R >= 0 && A1 >= C1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	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) -> Com_1(f8(A, B, C, D, E, F, G, H, I, 0, Z, A1, A1, 0, A1, H, Q, -(1) + R, B1, -(1) + R, U, V, W, X, Y)) :|: H >= C1 + 1 && R >= 0 && C1 >= A1 + 1 && Z >= 2 && J >= 0 && J <= 0
10.75/4.50	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) -> Com_1(f10(A, B, C, D, E, F, G, F1, I, E1, Z, L, B1, C1, D1, G1, A1, R, S, T, U, V, W, X, Y)) :|: Z >= 2 && R >= 0 && J >= H && J <= H
10.75/4.50	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) -> Com_1(f10(B1, D1, C1, K1, H1, F, G, P1, I, O1, A1, 0, L1, M1, N1, Q1, F1, R, S, T, Z, E1, G1, X, Y)) :|: 0 >= I1 && 0 >= A1 && 0 >= J1
10.75/4.50	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) -> Com_1(f1(A1, 2, B1, C1, B1, F, G, H, I, J, A1, L, M, N, O, P, Q, R, S, T, Z, V, B1, D1, Y)) :|: A1 >= 2
10.75/4.50	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) -> Com_1(f8(A1, C1, B1, H1, G1, F, G, C, R, 0, Z, C, C, 0, C, C, E1, R, S, T, U, D1, F1, X, R + 1)) :|: K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2 && 0 >= C + 1
10.75/4.50	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) -> Com_1(f8(A1, C1, B1, H1, G1, F, G, C, R, 0, Z, C, C, 0, C, C, E1, R, S, T, U, D1, F1, X, R + 1)) :|: K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && C >= 1 && C1 >= 0 && Z >= 2
10.75/4.50	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) -> Com_1(f8(A1, C1, B1, H1, G1, F, G, C, R, 0, Z, C, C, 0, C, C, E1, R, S, T, U, D1, F1, X, R + 1)) :|: K1 >= Z && L1 >= 2 && C1 >= L1 && B >= A && B >= 0 && 0 >= C + 1 && C1 >= 0 && Z >= 2
10.75/4.50	
10.75/4.50	The start-symbols are:[f9_25]
10.75/4.50	
10.75/4.50	
10.75/4.50	----------------------------------------
10.75/4.50	
10.75/4.50	(1) Loat Proof (FINISHED)
10.75/4.50	
10.75/4.50	
10.75/4.50	### Pre-processing the ITS problem ###
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Initial linear ITS problem
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	      0: f1 -> f1 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, [ A>=1+B && B>=0 ], cost: 1
10.75/4.50	
10.75/4.50	     14: f1 -> f8 : A'=free_88, B'=free_89, C'=free_84, D'=free_81, E'=free_87, H'=C, Q'=R, J'=0, K'=free_83, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_79, V'=free_85, W'=free_82, Y'=1+R, [ free_80>=free_83 && free_86>=2 && free_89>=free_86 && B>=A && B>=0 && C>=1 && free_89>=0 && free_83>=2 && 0>=1+C ], cost: 1
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ free_91>=free_94 && free_97>=2 && free_100>=free_97 && B>=A && B>=0 && C>=1 && free_100>=0 && free_94>=2 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ free_102>=free_105 && free_108>=2 && free_111>=free_108 && B>=A && B>=0 && 0>=1+C && free_111>=0 && free_105>=2 ], cost: 1
10.75/4.50	
10.75/4.50	      1: f7 -> f8 : J'=0, K'=free_3, L'=free_4, M'=free_4, N'=0, O'=free_4, P'=H, [ free_2>=1+H && Q>=0 && free_4>=1+free_2 && free_3>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      2: f7 -> f8 : J'=0, K'=free_6, L'=free_7, M'=free_7, N'=0, O'=free_7, P'=H, [ free_5>=1+H && Q>=0 && free_5>=1+free_7 && free_6>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      3: f7 -> f8 : J'=0, K'=free_9, L'=free_10, M'=free_10, N'=0, O'=free_10, P'=H, [ H>=1+free_8 && Q>=0 && free_10>=1+free_8 && free_9>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      4: f7 -> f8 : J'=0, K'=free_12, L'=free_13, M'=free_13, N'=0, O'=free_13, P'=H, [ H>=1+free_11 && Q>=0 && free_11>=1+free_13 && free_12>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      5: f7 -> f10 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=free_21, E'=Q, E1'=free_22, F'=free_18, F1'=free_15, G'=free_20, G1'=free_17, H'=free_14, H1'=free_19, Q'=free_16, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, [ Q>=0 && 0>=1+free_15 && free_18>=2 && J==H ], cost: 1
10.75/4.50	
10.75/4.50	      6: f7 -> f10 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=free_30, E'=Q, E1'=free_31, F'=free_27, F1'=free_24, G'=free_29, G1'=free_26, H'=free_23, H1'=free_28, Q'=free_25, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, [ Q>=0 && free_24>=1 && free_27>=2 && J==H ], cost: 1
10.75/4.50	
10.75/4.50	      7: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1+R, S'=free_33, T'=-1+R, [ free_32>=1+H && R>=0 && free_35>=1+free_32 && free_34>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      8: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1+R, S'=free_37, T'=-1+R, [ free_36>=1+H && R>=0 && free_36>=1+free_39 && free_38>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      9: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1+R, S'=free_41, T'=-1+R, [ H>=1+free_40 && R>=0 && free_43>=1+free_40 && free_42>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     10: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1+R, S'=free_45, T'=-1+R, [ H>=1+free_44 && R>=0 && free_44>=1+free_47 && free_46>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     11: f8 -> f10 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=free_54, E'=Q, E1'=free_55, F'=free_51, F1'=L, G'=free_49, G1'=free_53, H'=free_50, H1'=free_48, Q'=free_52, Q1'=R, J'=S, J1'=T, K'=U, K1'=V, L'=W, L1'=X, M'=Y, [ free_51>=2 && R>=0 && J==H ], cost: 1
10.75/4.50	
10.75/4.50	     12: f9 -> f10 : A'=free_71, A1'=free_73, B'=free_66, B1'=free_60, C'=free_69, C1'=F, D'=G, D1'=free_63, E'=Q, E1'=free_57, F'=free_67, F1'=0, G'=free_61, G1'=free_59, H'=free_68, H1'=free_62, Q'=free_56, Q1'=R, J'=S, J1'=T, K'=free_70, K1'=free_64, L'=free_58, L1'=X, M'=Y, [ 0>=free_72 && 0>=free_67 && 0>=free_65 ], cost: 1
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Removed unreachable and leaf rules:
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	      0: f1 -> f1 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, [ A>=1+B && B>=0 ], cost: 1
10.75/4.50	
10.75/4.50	     14: f1 -> f8 : A'=free_88, B'=free_89, C'=free_84, D'=free_81, E'=free_87, H'=C, Q'=R, J'=0, K'=free_83, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_79, V'=free_85, W'=free_82, Y'=1+R, [ free_80>=free_83 && free_86>=2 && free_89>=free_86 && B>=A && B>=0 && C>=1 && free_89>=0 && free_83>=2 && 0>=1+C ], cost: 1
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ free_91>=free_94 && free_97>=2 && free_100>=free_97 && B>=A && B>=0 && C>=1 && free_100>=0 && free_94>=2 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ free_102>=free_105 && free_108>=2 && free_111>=free_108 && B>=A && B>=0 && 0>=1+C && free_111>=0 && free_105>=2 ], cost: 1
10.75/4.50	
10.75/4.50	      7: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1+R, S'=free_33, T'=-1+R, [ free_32>=1+H && R>=0 && free_35>=1+free_32 && free_34>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      8: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1+R, S'=free_37, T'=-1+R, [ free_36>=1+H && R>=0 && free_36>=1+free_39 && free_38>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      9: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1+R, S'=free_41, T'=-1+R, [ H>=1+free_40 && R>=0 && free_43>=1+free_40 && free_42>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     10: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1+R, S'=free_45, T'=-1+R, [ H>=1+free_44 && R>=0 && free_44>=1+free_47 && free_46>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Removed rules with unsatisfiable guard:
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	      0: f1 -> f1 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, [ A>=1+B && B>=0 ], cost: 1
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ free_91>=free_94 && free_97>=2 && free_100>=free_97 && B>=A && B>=0 && C>=1 && free_100>=0 && free_94>=2 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ free_102>=free_105 && free_108>=2 && free_111>=free_108 && B>=A && B>=0 && 0>=1+C && free_111>=0 && free_105>=2 ], cost: 1
10.75/4.50	
10.75/4.50	      7: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1+R, S'=free_33, T'=-1+R, [ free_32>=1+H && R>=0 && free_35>=1+free_32 && free_34>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      8: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1+R, S'=free_37, T'=-1+R, [ free_36>=1+H && R>=0 && free_36>=1+free_39 && free_38>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      9: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1+R, S'=free_41, T'=-1+R, [ H>=1+free_40 && R>=0 && free_43>=1+free_40 && free_42>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     10: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1+R, S'=free_45, T'=-1+R, [ H>=1+free_44 && R>=0 && free_44>=1+free_47 && free_46>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Simplified all rules, resulting in:
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	      0: f1 -> f1 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, [ A>=1+B && B>=0 ], cost: 1
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && free_94>=2 && 2<=free_100 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && free_105>=2 && 2<=free_111 ], cost: 1
10.75/4.50	
10.75/4.50	      7: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1+R, S'=free_33, T'=-1+R, [ R>=0 && free_34>=2 && J==0 && 1+H<=-1+free_35 ], cost: 1
10.75/4.50	
10.75/4.50	      8: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1+R, S'=free_37, T'=-1+R, [ R>=0 && free_38>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      9: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1+R, S'=free_41, T'=-1+R, [ R>=0 && free_42>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     10: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1+R, S'=free_45, T'=-1+R, [ R>=0 && free_46>=2 && J==0 && 1+free_47<=-1+H ], cost: 1
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	### Simplification by acceleration and chaining ###
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Accelerating simple loops of location 0.
10.75/4.50	
10.75/4.50	   Accelerating the following rules:
10.75/4.50	
10.75/4.50	      0: f1 -> f1 : B'=1+B, C'=D, D'=free, E'=D, F'=free_1, G'=B, [ A>=1+B && B>=0 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	   Accelerated rule 0 with metering function -B+A, yielding the new rule 17.
10.75/4.50	
10.75/4.50	   Removing the simple loops: 0.
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Accelerating simple loops of location 2.
10.75/4.50	
10.75/4.50	   Accelerating the following rules:
10.75/4.50	
10.75/4.50	      7: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1+R, S'=free_33, T'=-1+R, [ R>=0 && free_34>=2 && J==0 && 1+H<=-1+free_35 ], cost: 1
10.75/4.50	
10.75/4.50	      8: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1+R, S'=free_37, T'=-1+R, [ R>=0 && free_38>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	      9: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1+R, S'=free_41, T'=-1+R, [ R>=0 && free_42>=2 && J==0 ], cost: 1
10.75/4.50	
10.75/4.50	     10: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1+R, S'=free_45, T'=-1+R, [ R>=0 && free_46>=2 && J==0 && 1+free_47<=-1+H ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	   Accelerated rule 7 with metering function 1+R, yielding the new rule 18.
10.75/4.50	
10.75/4.50	   Accelerated rule 8 with metering function 1+R, yielding the new rule 19.
10.75/4.50	
10.75/4.50	   Accelerated rule 9 with metering function 1+R, yielding the new rule 20.
10.75/4.50	
10.75/4.50	   Accelerated rule 10 with metering function 1+R, yielding the new rule 21.
10.75/4.50	
10.75/4.50	   Removing the simple loops: 7 8 9 10.
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Accelerated all simple loops using metering functions (where possible):
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && free_94>=2 && 2<=free_100 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && free_105>=2 && 2<=free_111 ], cost: 1
10.75/4.50	
10.75/4.50	     17: f1 -> f1 : B'=A, C'=free, D'=free, E'=free, F'=free_1, G'=-1+A, [ A>=1+B && B>=0 ], cost: -B+A
10.75/4.50	
10.75/4.50	     18: f8 -> f8 : J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=H, R'=-1, S'=free_33, T'=-1, [ R>=0 && free_34>=2 && J==0 && 1+H<=-1+free_35 ], cost: 1+R
10.75/4.50	
10.75/4.50	     19: f8 -> f8 : J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=H, R'=-1, S'=free_37, T'=-1, [ R>=0 && free_38>=2 && J==0 ], cost: 1+R
10.75/4.50	
10.75/4.50	     20: f8 -> f8 : J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=H, R'=-1, S'=free_41, T'=-1, [ R>=0 && free_42>=2 && J==0 ], cost: 1+R
10.75/4.50	
10.75/4.50	     21: f8 -> f8 : J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=H, R'=-1, S'=free_45, T'=-1, [ R>=0 && free_46>=2 && J==0 && 1+free_47<=-1+H ], cost: 1+R
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Chained accelerated rules (with incoming rules):
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     15: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_94, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_90, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && free_94>=2 && 2<=free_100 ], cost: 1
10.75/4.50	
10.75/4.50	     16: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_105, L'=C, M'=C, N'=0, O'=C, P'=C, Q_1'=free_101, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && free_105>=2 && 2<=free_111 ], cost: 1
10.75/4.50	
10.75/4.50	     23: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=C, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+C<=-1+free_35 ], cost: 2+R
10.75/4.50	
10.75/4.50	     24: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=C, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_34>=2 && 1+C<=-1+free_35 ], cost: 2+R
10.75/4.50	
10.75/4.50	     25: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=C, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     26: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=C, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_38>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     27: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=C, Q_1'=free_90, R'=-1, S'=free_41, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_42>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     28: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=C, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_42>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     29: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=C, Q_1'=free_90, R'=-1, S'=free_45, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_46>=2 && 1+free_47<=-1+C ], cost: 2+R
10.75/4.50	
10.75/4.50	     30: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=C, Q_1'=free_101, R'=-1, S'=free_45, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_46>=2 && 1+free_47<=-1+C ], cost: 2+R
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	     22: f9 -> f1 : A'=free_77, B'=free_77, C'=free, D'=free, E'=free, F'=free_1, G'=-1+free_77, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=3 ], cost: -1+free_77
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Removed unreachable locations (and leaf rules with constant cost):
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     23: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=C, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+C<=-1+free_35 ], cost: 2+R
10.75/4.50	
10.75/4.50	     24: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=C, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_34>=2 && 1+C<=-1+free_35 ], cost: 2+R
10.75/4.50	
10.75/4.50	     25: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=C, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     26: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=C, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_38>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     27: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=C, Q_1'=free_90, R'=-1, S'=free_41, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_42>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     28: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=C, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_42>=2 ], cost: 2+R
10.75/4.50	
10.75/4.50	     29: f1 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=C, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=C, Q_1'=free_90, R'=-1, S'=free_45, T'=-1, V'=free_96, W'=free_93, Y'=1+R, [ B>=A && B>=0 && C>=1 && 2<=free_100 && R>=0 && free_46>=2 && 1+free_47<=-1+C ], cost: 2+R
10.75/4.50	
10.75/4.50	     30: f1 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=C, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=C, Q_1'=free_101, R'=-1, S'=free_45, T'=-1, V'=free_107, W'=free_104, Y'=1+R, [ B>=A && B>=0 && 0>=1+C && 2<=free_111 && R>=0 && free_46>=2 && 1+free_47<=-1+C ], cost: 2+R
10.75/4.50	
10.75/4.50	     13: f9 -> f1 : A'=free_77, B'=2, C'=free_78, D'=free_75, E'=free_78, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=2 ], cost: 1
10.75/4.50	
10.75/4.50	     22: f9 -> f1 : A'=free_77, B'=free_77, C'=free, D'=free, E'=free, F'=free_1, G'=-1+free_77, K'=free_77, U'=free_74, W'=free_78, X'=free_76, [ free_77>=3 ], cost: -1+free_77
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Eliminated locations (on tree-shaped paths):
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     31: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=free_78, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free_78, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && free_78>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+free_78<=-1+free_35 ], cost: 3+R
10.75/4.50	
10.75/4.50	     32: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=free_78, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free_78, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && 0>=1+free_78 && 2<=free_111 && R>=0 && free_34>=2 && 1+free_78<=-1+free_35 ], cost: 3+R
10.75/4.50	
10.75/4.50	     33: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=free_78, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free_78, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && free_78>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 3+R
10.75/4.50	
10.75/4.50	     34: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=free_78, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free_78, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && 0>=1+free_78 && 2<=free_111 && R>=0 && free_38>=2 ], cost: 3+R
10.75/4.50	
10.75/4.50	     35: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=free_78, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free_78, Q_1'=free_90, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && free_78>=1 && 2<=free_100 && R>=0 && free_42>=2 ], cost: 3+R
10.75/4.50	
10.75/4.50	     36: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=free_78, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free_78, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && 0>=1+free_78 && 2<=free_111 && R>=0 && free_42>=2 ], cost: 3+R
10.75/4.50	
10.75/4.50	     37: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, H'=free_78, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=free_78, Q_1'=free_90, R'=-1, S'=free_45, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && free_78>=1 && 2<=free_100 && R>=0 && free_46>=2 && 1+free_47<=-1+free_78 ], cost: 3+R
10.75/4.50	
10.75/4.50	     38: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, H'=free_78, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=free_78, Q_1'=free_101, R'=-1, S'=free_45, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=2 && 2>=free_77 && 0>=1+free_78 && 2<=free_111 && R>=0 && free_46>=2 && 1+free_47<=-1+free_78 ], cost: 3+R
10.75/4.50	
10.75/4.50	     39: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     40: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     41: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     42: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     43: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free, Q_1'=free_90, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_42>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     44: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_42>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     45: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=free, Q_1'=free_90, R'=-1, S'=free_45, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_46>=2 && 1+free_47<=-1+free ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     46: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_46, L'=free_47, M'=free_47, N'=0, O'=free_47, P'=free, Q_1'=free_101, R'=-1, S'=free_45, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_46>=2 && 1+free_47<=-1+free ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Applied pruning (of leafs and parallel rules):
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     39: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     40: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     41: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     42: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     44: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_42>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	### Computing asymptotic complexity ###
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Fully simplified ITS problem
10.75/4.50	
10.75/4.50	   Start location: f9
10.75/4.50	
10.75/4.50	     39: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_90, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     40: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_34, L'=free_35, M'=free_35, N'=0, O'=free_35, P'=free, Q_1'=free_101, R'=-1, S'=free_33, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     41: f9 -> f8 : A'=free_99, B'=free_100, C'=free_95, D'=free_92, E'=free_98, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_90, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_96, W'=free_93, X'=free_76, Y'=1+R, [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     42: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_38, L'=free_39, M'=free_39, N'=0, O'=free_39, P'=free, Q_1'=free_101, R'=-1, S'=free_37, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_38>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	     44: f9 -> f8 : A'=free_110, B'=free_111, C'=free_106, D'=free_103, E'=free_109, F'=free_1, G'=-1+free_77, H'=free, Q'=R, J'=0, K'=free_42, L'=free_43, M'=free_43, N'=0, O'=free_43, P'=free, Q_1'=free_101, R'=-1, S'=free_41, T'=-1, U'=free_74, V'=free_107, W'=free_104, X'=free_76, Y'=1+R, [ free_77>=3 && 0>=1+free && 2<=free_111 && R>=0 && free_42>=2 ], cost: 1+R+free_77
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Computing asymptotic complexity for rule 39
10.75/4.50	
10.75/4.50	   Solved the limit problem by the following transformations:
10.75/4.50	
10.75/4.50	      Created initial limit problem:
10.75/4.50	
10.75/4.50	      free (+/+!), 1+R+free_77 (+), -2+free_77 (+/+!), 1+R (+/+!), -1+free_34 (+/+!), -1+free_100 (+/+!), -1-free+free_35 (+/+!) [not solved]
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	      removing all constraints (solved by SMT)
10.75/4.50	
10.75/4.50	      resulting limit problem: [solved]
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	      applying transformation rule (C) using substitution {free==-2+n,free_35==n,R==0,free_77==n,free_100==n,free_34==n}
10.75/4.50	
10.75/4.50	      resulting limit problem:
10.75/4.50	
10.75/4.50	      [solved]
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	   Solution:
10.75/4.50	
10.75/4.50	      free / -2+n
10.75/4.50	
10.75/4.50	      free_35 / n
10.75/4.50	
10.75/4.50	      R / 0
10.75/4.50	
10.75/4.50	      free_77 / n
10.75/4.50	
10.75/4.50	      free_100 / n
10.75/4.50	
10.75/4.50	      free_34 / n
10.75/4.50	
10.75/4.50	   Resulting cost 1+n has complexity: Unbounded
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Found new complexity Unbounded.
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	Obtained the following overall complexity (w.r.t. the length of the input n):
10.75/4.50	
10.75/4.50	   Complexity:  Unbounded
10.75/4.50	
10.75/4.50	   Cpx degree:  Unbounded
10.75/4.50	
10.75/4.50	   Solved cost: 1+n
10.75/4.50	
10.75/4.50	   Rule cost:   1+R+free_77
10.75/4.50	
10.75/4.50	   Rule guard:  [ free_77>=3 && free>=1 && 2<=free_100 && R>=0 && free_34>=2 && 1+free<=-1+free_35 ]
10.75/4.50	
10.75/4.50	
10.75/4.50	
10.75/4.50	WORST_CASE(INF,?)
10.75/4.50	
10.75/4.50	
10.75/4.50	----------------------------------------
10.75/4.50	
10.75/4.50	(2)
10.75/4.50	BOUNDS(INF, INF)
10.92/4.53	EOF