12.89/5.75 WORST_CASE(NON_POLY, ?) 13.11/5.77 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 13.11/5.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.11/5.77 13.11/5.77 13.11/5.77 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 13.11/5.77 13.11/5.77 (0) CpxIntTrs 13.11/5.77 (1) Loat Proof [FINISHED, 4010 ms] 13.11/5.77 (2) BOUNDS(INF, INF) 13.11/5.77 13.11/5.77 13.11/5.77 ---------------------------------------- 13.11/5.77 13.11/5.77 (0) 13.11/5.77 Obligation: 13.11/5.77 Complexity Int TRS consisting of the following rules: 13.11/5.77 f25(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f15(A, B, C + 1, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: A >= B + 1 13.11/5.77 f25(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f15(A, B, C + 1, Y, 0, 1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: B >= A 13.11/5.77 f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 13.11/5.77 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) -> Com_1(f36(A, B, 1, D, E, F, 0, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 13.11/5.77 f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f45(A, B, C, D, E, F, G, H, Y, Z, A1, B1, B1, N, O, P, Q, R, S, T, U, V, W, X)) :|: H >= C 13.11/5.77 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f46(A, B, C, D, E, F, G, H, I, J, K, L, M, M, O, P, Q, R, S, T, U, V, W, X)) :|: 0 >= M + 1 13.11/5.77 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f46(A, B, C, D, E, F, G, H, I, J, K, L, M, M, O, P, Q, R, S, T, U, V, W, X)) :|: M >= 1 13.11/5.77 f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f36(A, B, C + 1, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: A >= B + 1 13.11/5.77 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f36(A, B, C + 1, D, E, F, G, H, I, J, K, L, 0, 0, O, P, Q, R, S, T, U, V, W, X)) :|: M >= 0 && M <= 0 13.11/5.77 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 13.11/5.77 f63(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 13.11/5.77 f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f36(A, B, C + 1, Y, 0, F, G, H, I, J, K, L, M, N, Z, P, Q, R, S, T, U, V, W, X)) :|: B >= A 13.11/5.77 f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f45(A, B, C, D, E, F, G, H, I, Y, Z, A1, A1, N, O, B1, Q, R, S, T, U, V, W, X)) :|: B >= A 13.11/5.77 f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, 0, R, S, T, U, V, W, X)) :|: C >= 1 + H 13.11/5.77 f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f25(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, Y, Z, A1, A1, A1, X)) :|: 0 >= A1 + 1 && R >= C + 1 13.11/5.77 f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f25(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, Y, Z, A1, A1, A1, X)) :|: A1 >= 1 && R >= C + 1 13.11/5.77 f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f15(A, B, C + 1, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, Y, Z, 0, 0, 0, X)) :|: R >= C + 1 13.11/5.77 f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: C >= R 13.11/5.77 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f15(A, B, 0, D, E, F, 0, Z, I, J, K, L, M, N, O, P, 0, Y, S, T, U, V, W, 1)) :|: TRUE 13.11/5.77 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f36(A, B, 1, D, E, F, 0, A1, I, J, K, L, M, N, O, P, 0, Z, S, T, U, V, W, Y)) :|: 0 >= Y 13.11/5.77 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f36(A, B, 1, D, E, F, 0, A1, I, J, K, L, M, N, O, P, 0, Z, S, T, U, V, W, Y)) :|: Y >= 2 13.11/5.77 13.11/5.77 The start-symbols are:[f0_24] 13.11/5.77 13.11/5.77 13.11/5.77 ---------------------------------------- 13.11/5.77 13.11/5.77 (1) Loat Proof (FINISHED) 13.11/5.77 13.11/5.77 13.11/5.77 ### Pre-processing the ITS problem ### 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Initial linear ITS problem 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 0: f25 -> f15 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 1: f25 -> f15 : C'=1+C, D'=free, E'=0, F'=1, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 2: f31 -> f31 : [], cost: 1 13.11/5.77 13.11/5.77 3: f33 -> f36 : C'=1, G'=0, [], cost: 1 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 13: f36 -> f61 : Q_1'=0, [ C>=1+H ], cost: 1 13.11/5.77 13.11/5.77 5: f45 -> f46 : N'=M, [ 0>=1+M ], cost: 1 13.11/5.77 13.11/5.77 6: f45 -> f46 : N'=M, [ M>=1 ], cost: 1 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 7: f46 -> f36 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 11: f46 -> f36 : C'=1+C, D'=free_6, E'=0, O'=free_5, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 12: f46 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, P'=free_8, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 9: f61 -> f61 : [], cost: 1 13.11/5.77 13.11/5.77 10: f63 -> f65 : A1'=B, B'=C, B1'=D, C'=E, D'=F, E'=G, F'=H, G'=Q, H'=J, Q'=K, J'=L, K'=M, L'=N, M'=O, N'=P, O'=Q_1, P'=R, Q_1'=S, R'=T, S'=U, T'=V, U'=W, V'=X, [], cost: 1 13.11/5.77 13.11/5.77 14: f15 -> f25 : S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 15: f15 -> f25 : S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 16: f15 -> f15 : C'=1+C, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 17: f15 -> f31 : [ C>=R ], cost: 1 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Removed unreachable and leaf rules: 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 0: f25 -> f15 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 1: f25 -> f15 : C'=1+C, D'=free, E'=0, F'=1, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 2: f31 -> f31 : [], cost: 1 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 13: f36 -> f61 : Q_1'=0, [ C>=1+H ], cost: 1 13.11/5.77 13.11/5.77 5: f45 -> f46 : N'=M, [ 0>=1+M ], cost: 1 13.11/5.77 13.11/5.77 6: f45 -> f46 : N'=M, [ M>=1 ], cost: 1 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 7: f46 -> f36 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 11: f46 -> f36 : C'=1+C, D'=free_6, E'=0, O'=free_5, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 12: f46 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, P'=free_8, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 9: f61 -> f61 : [], cost: 1 13.11/5.77 13.11/5.77 14: f15 -> f25 : S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 15: f15 -> f25 : S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 16: f15 -> f15 : C'=1+C, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 17: f15 -> f31 : [ C>=R ], cost: 1 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 ### Simplification by acceleration and chaining ### 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerating simple loops of location 1. 13.11/5.77 13.11/5.77 Accelerating the following rules: 13.11/5.77 13.11/5.77 2: f31 -> f31 : [], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerated rule 2 with NONTERM, yielding the new rule 21. 13.11/5.77 13.11/5.77 Removing the simple loops: 2. 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerating simple loops of location 6. 13.11/5.77 13.11/5.77 Accelerating the following rules: 13.11/5.77 13.11/5.77 9: f61 -> f61 : [], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerated rule 9 with NONTERM, yielding the new rule 22. 13.11/5.77 13.11/5.77 Removing the simple loops: 9. 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerating simple loops of location 8. 13.11/5.77 13.11/5.77 Accelerating the following rules: 13.11/5.77 13.11/5.77 16: f15 -> f15 : C'=1+C, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerated rule 16 with metering function R-C, yielding the new rule 23. 13.11/5.77 13.11/5.77 Removing the simple loops: 16. 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerated all simple loops using metering functions (where possible): 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 0: f25 -> f15 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 1: f25 -> f15 : C'=1+C, D'=free, E'=0, F'=1, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 21: f31 -> [11] : [], cost: INF 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 13: f36 -> f61 : Q_1'=0, [ C>=1+H ], cost: 1 13.11/5.77 13.11/5.77 5: f45 -> f46 : N'=M, [ 0>=1+M ], cost: 1 13.11/5.77 13.11/5.77 6: f45 -> f46 : N'=M, [ M>=1 ], cost: 1 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 7: f46 -> f36 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 11: f46 -> f36 : C'=1+C, D'=free_6, E'=0, O'=free_5, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 12: f46 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, P'=free_8, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 22: f61 -> [12] : [], cost: INF 13.11/5.77 13.11/5.77 14: f15 -> f25 : S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 15: f15 -> f25 : S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 17: f15 -> f31 : [ C>=R ], cost: 1 13.11/5.77 13.11/5.77 23: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ R>=1+C ], cost: R-C 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Chained accelerated rules (with incoming rules): 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 0: f25 -> f15 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 1: f25 -> f15 : C'=1+C, D'=free, E'=0, F'=1, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 26: f25 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ A>=1+B && R>=2+C ], cost: R-C 13.11/5.77 13.11/5.77 27: f25 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ B>=A && R>=2+C ], cost: R-C 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 13: f36 -> f61 : Q_1'=0, [ C>=1+H ], cost: 1 13.11/5.77 13.11/5.77 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.77 13.11/5.77 5: f45 -> f46 : N'=M, [ 0>=1+M ], cost: 1 13.11/5.77 13.11/5.77 6: f45 -> f46 : N'=M, [ M>=1 ], cost: 1 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 7: f46 -> f36 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 11: f46 -> f36 : C'=1+C, D'=free_6, E'=0, O'=free_5, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 12: f46 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, P'=free_8, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 14: f15 -> f25 : S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 15: f15 -> f25 : S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 17: f15 -> f31 : [ C>=R ], cost: 1 13.11/5.77 13.11/5.77 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Removed unreachable locations (and leaf rules with constant cost): 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 0: f25 -> f15 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 1: f25 -> f15 : C'=1+C, D'=free, E'=0, F'=1, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 26: f25 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ A>=1+B && R>=2+C ], cost: R-C 13.11/5.77 13.11/5.77 27: f25 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ B>=A && R>=2+C ], cost: R-C 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.77 13.11/5.77 5: f45 -> f46 : N'=M, [ 0>=1+M ], cost: 1 13.11/5.77 13.11/5.77 6: f45 -> f46 : N'=M, [ M>=1 ], cost: 1 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 7: f46 -> f36 : C'=1+C, [ A>=1+B ], cost: 1 13.11/5.77 13.11/5.77 11: f46 -> f36 : C'=1+C, D'=free_6, E'=0, O'=free_5, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 12: f46 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, P'=free_8, [ B>=A ], cost: 1 13.11/5.77 13.11/5.77 14: f15 -> f25 : S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 15: f15 -> f25 : S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C ], cost: 1 13.11/5.77 13.11/5.77 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Eliminated locations (on tree-shaped paths): 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 29: f45 -> f36 : C'=1+C, N'=M, [ 0>=1+M && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 30: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ 0>=1+M && B>=A ], cost: 2 13.11/5.77 13.11/5.77 31: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ 0>=1+M && B>=A ], cost: 2 13.11/5.77 13.11/5.77 32: f45 -> f36 : C'=1+C, N'=M, [ M>=1 && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 33: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ M>=1 && B>=A ], cost: 2 13.11/5.77 13.11/5.77 34: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ M>=1 && B>=A ], cost: 2 13.11/5.77 13.11/5.77 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.77 13.11/5.77 35: f15 -> f15 : C'=1+C, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 36: f15 -> f15 : C'=1+C, D'=free, E'=0, F'=1, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C && B>=A ], cost: 2 13.11/5.77 13.11/5.77 37: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ 0>=1+free_13 && A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 38: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ 0>=1+free_13 && B>=A && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 39: f15 -> f15 : C'=1+C, S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 40: f15 -> f15 : C'=1+C, D'=free, E'=0, F'=1, S'=free_15, T'=free_14, U'=free_16, V'=free_16, W'=free_16, [ free_16>=1 && R>=1+C && B>=A ], cost: 2 13.11/5.77 13.11/5.77 41: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ free_16>=1 && A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 42: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ free_16>=1 && B>=A && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Applied pruning (of leafs and parallel rules): 13.11/5.77 13.11/5.77 Start location: f0 13.11/5.77 13.11/5.77 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.77 13.11/5.77 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.77 13.11/5.77 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.77 13.11/5.77 29: f45 -> f36 : C'=1+C, N'=M, [ 0>=1+M && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 30: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ 0>=1+M && B>=A ], cost: 2 13.11/5.77 13.11/5.77 31: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ 0>=1+M && B>=A ], cost: 2 13.11/5.77 13.11/5.77 32: f45 -> f36 : C'=1+C, N'=M, [ M>=1 && A>=1+B ], cost: 2 13.11/5.77 13.11/5.77 33: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ M>=1 && B>=A ], cost: 2 13.11/5.77 13.11/5.77 34: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ M>=1 && B>=A ], cost: 2 13.11/5.77 13.11/5.77 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.77 13.11/5.77 36: f15 -> f15 : C'=1+C, D'=free, E'=0, F'=1, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C && B>=A ], cost: 2 13.11/5.77 13.11/5.77 37: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ 0>=1+free_13 && A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 38: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ 0>=1+free_13 && B>=A && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 41: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ free_16>=1 && A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 42: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ free_16>=1 && B>=A && R>=2+C ], cost: 1+R-C 13.11/5.77 13.11/5.77 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.77 13.11/5.77 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.77 13.11/5.77 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.77 13.11/5.77 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerating simple loops of location 4. 13.11/5.77 13.11/5.77 Accelerating the following rules: 13.11/5.77 13.11/5.77 31: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ 0>=1+M && B>=A ], cost: 2 13.11/5.77 13.11/5.77 34: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ M>=1 && B>=A ], cost: 2 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerated rule 31 with NONTERM (after strengthening guard), yielding the new rule 43. 13.11/5.77 13.11/5.77 Accelerated rule 34 with NONTERM (after strengthening guard), yielding the new rule 44. 13.11/5.77 13.11/5.77 Removing the simple loops:. 13.11/5.77 13.11/5.77 13.11/5.77 13.11/5.77 Accelerating simple loops of location 8. 13.11/5.77 13.11/5.77 Simplified some of the simple loops (and removed duplicate rules). 13.11/5.77 13.11/5.77 Accelerating the following rules: 13.11/5.77 13.11/5.77 36: f15 -> f15 : C'=1+C, D'=free, E'=0, F'=1, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C && B>=A ], cost: 2 13.11/5.77 13.11/5.77 41: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.78 13.11/5.78 42: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ B>=A && R>=2+C ], cost: 1+R-C 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Accelerated rule 36 with metering function R-C, yielding the new rule 45. 13.11/5.78 13.11/5.78 Found no metering function for rule 41. 13.11/5.78 13.11/5.78 Found no metering function for rule 42. 13.11/5.78 13.11/5.78 Removing the simple loops: 36. 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Accelerated all simple loops using metering functions (where possible): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.78 13.11/5.78 29: f45 -> f36 : C'=1+C, N'=M, [ 0>=1+M && A>=1+B ], cost: 2 13.11/5.78 13.11/5.78 30: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ 0>=1+M && B>=A ], cost: 2 13.11/5.78 13.11/5.78 31: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ 0>=1+M && B>=A ], cost: 2 13.11/5.78 13.11/5.78 32: f45 -> f36 : C'=1+C, N'=M, [ M>=1 && A>=1+B ], cost: 2 13.11/5.78 13.11/5.78 33: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ M>=1 && B>=A ], cost: 2 13.11/5.78 13.11/5.78 34: f45 -> f45 : J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=M, P'=free_8, [ M>=1 && B>=A ], cost: 2 13.11/5.78 13.11/5.78 43: f45 -> [14] : [ 0>=1+M && B>=A && 0>=1+free_10 ], cost: INF 13.11/5.78 13.11/5.78 44: f45 -> [14] : [ M>=1 && B>=A && free_10>=1 ], cost: INF 13.11/5.78 13.11/5.78 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.78 13.11/5.78 41: f15 -> f15 : C'=R, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ A>=1+B && R>=2+C ], cost: 1+R-C 13.11/5.78 13.11/5.78 42: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, [ B>=A && R>=2+C ], cost: 1+R-C 13.11/5.78 13.11/5.78 45: f15 -> f15 : C'=R, D'=free, E'=0, F'=1, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, [ 0>=1+free_13 && R>=1+C && B>=A ], cost: 2*R-2*C 13.11/5.78 13.11/5.78 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Chained accelerated rules (with incoming rules): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 4: f36 -> f45 : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C ], cost: 1 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 46: f36 -> f45 : Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_2, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A ], cost: 3 13.11/5.78 13.11/5.78 47: f36 -> f45 : Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_2, P'=free_8, [ H>=C && free_2>=1 && B>=A ], cost: 3 13.11/5.78 13.11/5.78 48: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 49: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 8: f45 -> f36 : C'=1+C, M'=0, N'=0, [ M==0 ], cost: 1 13.11/5.78 13.11/5.78 29: f45 -> f36 : C'=1+C, N'=M, [ 0>=1+M && A>=1+B ], cost: 2 13.11/5.78 13.11/5.78 30: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ 0>=1+M && B>=A ], cost: 2 13.11/5.78 13.11/5.78 32: f45 -> f36 : C'=1+C, N'=M, [ M>=1 && A>=1+B ], cost: 2 13.11/5.78 13.11/5.78 33: f45 -> f36 : C'=1+C, D'=free_6, E'=0, N'=M, O'=free_5, [ M>=1 && B>=A ], cost: 2 13.11/5.78 13.11/5.78 24: f15 -> [11] : [ C>=R ], cost: INF 13.11/5.78 13.11/5.78 18: f0 -> f15 : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [], cost: 1 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 28: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: 1+free_19 13.11/5.78 13.11/5.78 50: f0 -> f15 : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: 2+free_19 13.11/5.78 13.11/5.78 51: f0 -> f15 : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: 2+free_19 13.11/5.78 13.11/5.78 52: f0 -> f15 : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: 1+2*free_19 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Eliminated locations (on tree-shaped paths): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 48: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 49: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 58: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=0, N'=0, [ H>=C && free_2==0 ], cost: 2 13.11/5.78 13.11/5.78 59: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && 0>=1+free_2 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 60: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, O'=free_5, [ H>=C && 0>=1+free_2 && B>=A ], cost: 3 13.11/5.78 13.11/5.78 61: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && free_2>=1 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 62: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, O'=free_5, [ H>=C && free_2>=1 && B>=A ], cost: 3 13.11/5.78 13.11/5.78 63: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=0, N'=0, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A && free_10==0 ], cost: 4 13.11/5.78 13.11/5.78 64: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A && 0>=1+free_10 ], cost: 5 13.11/5.78 13.11/5.78 65: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A && free_10>=1 ], cost: 5 13.11/5.78 13.11/5.78 66: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=0, N'=0, P'=free_8, [ H>=C && free_2>=1 && B>=A && free_10==0 ], cost: 4 13.11/5.78 13.11/5.78 67: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && free_2>=1 && B>=A && 0>=1+free_10 ], cost: 5 13.11/5.78 13.11/5.78 68: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && free_2>=1 && B>=A && free_10>=1 ], cost: 5 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Applied pruning (of leafs and parallel rules): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 48: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 49: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 58: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=0, N'=0, [ H>=C && free_2==0 ], cost: 2 13.11/5.78 13.11/5.78 59: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && 0>=1+free_2 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 61: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && free_2>=1 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 63: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=0, N'=0, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A && free_10==0 ], cost: 4 13.11/5.78 13.11/5.78 64: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && 0>=1+free_2 && B>=A && 0>=1+free_10 ], cost: 5 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Accelerating simple loops of location 3. 13.11/5.78 13.11/5.78 Simplified some of the simple loops (and removed duplicate rules). 13.11/5.78 13.11/5.78 Accelerating the following rules: 13.11/5.78 13.11/5.78 58: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, [ H>=C ], cost: 2 13.11/5.78 13.11/5.78 59: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && 0>=1+free_2 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 61: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && free_2>=1 && A>=1+B ], cost: 3 13.11/5.78 13.11/5.78 63: f36 -> f36 : C'=1+C, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, [ H>=C && B>=A ], cost: 4 13.11/5.78 13.11/5.78 64: f36 -> f36 : C'=1+C, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && B>=A && 0>=1+free_10 ], cost: 5 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Accelerated rule 58 with metering function 1+H-C, yielding the new rule 69. 13.11/5.78 13.11/5.78 Accelerated rule 59 with metering function 1+H-C, yielding the new rule 70. 13.11/5.78 13.11/5.78 Accelerated rule 61 with metering function 1+H-C, yielding the new rule 71. 13.11/5.78 13.11/5.78 Accelerated rule 63 with metering function 1+H-C, yielding the new rule 72. 13.11/5.78 13.11/5.78 Accelerated rule 64 with metering function 1+H-C, yielding the new rule 73. 13.11/5.78 13.11/5.78 Removing the simple loops: 58 59 61 63 64. 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Accelerated all simple loops using metering functions (where possible): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 48: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 49: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 69: f36 -> f36 : C'=1+H, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, [ H>=C ], cost: 2+2*H-2*C 13.11/5.78 13.11/5.78 70: f36 -> f36 : C'=1+H, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && 0>=1+free_2 && A>=1+B ], cost: 3+3*H-3*C 13.11/5.78 13.11/5.78 71: f36 -> f36 : C'=1+H, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, [ H>=C && free_2>=1 && A>=1+B ], cost: 3+3*H-3*C 13.11/5.78 13.11/5.78 72: f36 -> f36 : C'=1+H, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, [ H>=C && B>=A ], cost: 4+4*H-4*C 13.11/5.78 13.11/5.78 73: f36 -> f36 : C'=1+H, D'=free_6, E'=0, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, [ H>=C && B>=A && 0>=1+free_10 ], cost: 5+5*H-5*C 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Chained accelerated rules (with incoming rules): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 25: f36 -> [12] : Q_1'=0, [ C>=1+H ], cost: INF 13.11/5.78 13.11/5.78 48: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 49: f36 -> [14] : Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, [ H>=C && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 19: f0 -> f36 : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 ], cost: 1 13.11/5.78 13.11/5.78 20: f0 -> f36 : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 ], cost: 1 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 74: f0 -> f36 : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 ], cost: 1+2*free_22 13.11/5.78 13.11/5.78 75: f0 -> f36 : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 ], cost: 1+2*free_25 13.11/5.78 13.11/5.78 76: f0 -> f36 : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 77: f0 -> f36 : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 78: f0 -> f36 : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 79: f0 -> f36 : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 80: f0 -> f36 : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && B>=A ], cost: 1+4*free_22 13.11/5.78 13.11/5.78 81: f0 -> f36 : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && B>=A ], cost: 1+4*free_25 13.11/5.78 13.11/5.78 82: f0 -> f36 : C'=1+free_22, D'=free_6, E'=0, G'=0, H'=free_22, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_22 13.11/5.78 13.11/5.78 83: f0 -> f36 : C'=1+free_25, D'=free_6, E'=0, G'=0, H'=free_25, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_25 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Eliminated locations (on tree-shaped paths): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 84: f0 -> [12] : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && 1>=1+free_22 ], cost: INF 13.11/5.78 13.11/5.78 85: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 86: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 87: f0 -> [12] : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && 1>=1+free_25 ], cost: INF 13.11/5.78 13.11/5.78 88: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 89: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 90: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 ], cost: INF 13.11/5.78 13.11/5.78 91: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 ], cost: INF 13.11/5.78 13.11/5.78 92: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 93: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 94: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 95: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && free_2>=1 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 96: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 97: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_9, K'=free_7, L'=0, M'=0, N'=0, P'=free_8, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 98: f0 -> [12] : C'=1+free_22, D'=free_6, E'=0, G'=0, H'=free_22, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && B>=A && 0>=1+free_10 ], cost: INF 13.11/5.78 13.11/5.78 99: f0 -> [12] : C'=1+free_25, D'=free_6, E'=0, G'=0, H'=free_25, Q'=free_3, J'=free_9, K'=free_7, L'=free_10, M'=free_10, N'=free_10, O'=free_5, P'=free_8, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && B>=A && 0>=1+free_10 ], cost: INF 13.11/5.78 13.11/5.78 100: f0 -> [17] : [ 0>=free_23 && free_22>=1 ], cost: 1+2*free_22 13.11/5.78 13.11/5.78 101: f0 -> [17] : [ free_26>=2 && free_25>=1 ], cost: 1+2*free_25 13.11/5.78 13.11/5.78 102: f0 -> [17] : [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 103: f0 -> [17] : [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 104: f0 -> [17] : [ 0>=free_23 && free_22>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 105: f0 -> [17] : [ free_26>=2 && free_25>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 106: f0 -> [17] : [ 0>=free_23 && free_22>=1 && B>=A ], cost: 1+4*free_22 13.11/5.78 13.11/5.78 107: f0 -> [17] : [ free_26>=2 && free_25>=1 && B>=A ], cost: 1+4*free_25 13.11/5.78 13.11/5.78 108: f0 -> [17] : [ 0>=free_23 && free_22>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_22 13.11/5.78 13.11/5.78 109: f0 -> [17] : [ free_26>=2 && free_25>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_25 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Applied pruning (of leafs and parallel rules): 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 84: f0 -> [12] : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && 1>=1+free_22 ], cost: INF 13.11/5.78 13.11/5.78 85: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 86: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 87: f0 -> [12] : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && 1>=1+free_25 ], cost: INF 13.11/5.78 13.11/5.78 88: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 89: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 91: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 ], cost: INF 13.11/5.78 13.11/5.78 93: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 94: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 102: f0 -> [17] : [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 103: f0 -> [17] : [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 105: f0 -> [17] : [ free_26>=2 && free_25>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 108: f0 -> [17] : [ 0>=free_23 && free_22>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_22 13.11/5.78 13.11/5.78 109: f0 -> [17] : [ free_26>=2 && free_25>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_25 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 ### Computing asymptotic complexity ### 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Fully simplified ITS problem 13.11/5.78 13.11/5.78 Start location: f0 13.11/5.78 13.11/5.78 53: f0 -> [11] : C'=0, G'=0, H'=free_20, Q_1'=0, R'=free_19, X'=1, [ 0>=free_19 ], cost: INF 13.11/5.78 13.11/5.78 54: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ free_19>=1 ], cost: INF 13.11/5.78 13.11/5.78 55: f0 -> [11] : C'=free_19, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ A>=1+B && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 56: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_18, T'=free_17, U'=0, V'=0, W'=0, X'=1, [ B>=A && free_19>=2 ], cost: INF 13.11/5.78 13.11/5.78 57: f0 -> [11] : C'=free_19, D'=free, E'=0, F'=1, G'=0, H'=free_20, Q_1'=0, R'=free_19, S'=free_12, T'=free_11, U'=free_13, V'=free_13, W'=free_13, X'=1, [ 0>=1+free_13 && free_19>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 84: f0 -> [12] : C'=1, G'=0, H'=free_22, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && 1>=1+free_22 ], cost: INF 13.11/5.78 13.11/5.78 85: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 86: f0 -> [14] : C'=1, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 87: f0 -> [12] : C'=1, G'=0, H'=free_25, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && 1>=1+free_25 ], cost: INF 13.11/5.78 13.11/5.78 88: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 89: f0 -> [14] : C'=1, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && free_2>=1 && B>=A ], cost: INF 13.11/5.78 13.11/5.78 91: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=0, M'=0, N'=0, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 ], cost: INF 13.11/5.78 13.11/5.78 93: f0 -> [12] : C'=1+free_25, G'=0, H'=free_25, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_24, X'=free_26, [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 94: f0 -> [12] : C'=1+free_22, G'=0, H'=free_22, Q'=free_3, J'=free_1, K'=free_4, L'=free_2, M'=free_2, N'=free_2, Q_1'=0, R'=free_21, X'=free_23, [ 0>=free_23 && free_22>=1 && free_2>=1 && A>=1+B ], cost: INF 13.11/5.78 13.11/5.78 102: f0 -> [17] : [ 0>=free_23 && free_22>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_22 13.11/5.78 13.11/5.78 103: f0 -> [17] : [ free_26>=2 && free_25>=1 && 0>=1+free_2 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 105: f0 -> [17] : [ free_26>=2 && free_25>=1 && free_2>=1 && A>=1+B ], cost: 1+3*free_25 13.11/5.78 13.11/5.78 108: f0 -> [17] : [ 0>=free_23 && free_22>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_22 13.11/5.78 13.11/5.78 109: f0 -> [17] : [ free_26>=2 && free_25>=1 && B>=A && 0>=1+free_10 ], cost: 1+5*free_25 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Computing asymptotic complexity for rule 53 13.11/5.78 13.11/5.78 Resulting cost INF has complexity: Nonterm 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Found new complexity Nonterm. 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 Obtained the following overall complexity (w.r.t. the length of the input n): 13.11/5.78 13.11/5.78 Complexity: Nonterm 13.11/5.78 13.11/5.78 Cpx degree: Nonterm 13.11/5.78 13.11/5.78 Solved cost: INF 13.11/5.78 13.11/5.78 Rule cost: INF 13.11/5.78 13.11/5.78 Rule guard: [ 0>=free_19 ] 13.11/5.78 13.11/5.78 13.11/5.78 13.11/5.78 NO 13.11/5.78 13.11/5.78 13.11/5.78 ---------------------------------------- 13.11/5.78 13.11/5.78 (2) 13.11/5.78 BOUNDS(INF, INF) 13.13/5.81 EOF