6.95/3.10 WORST_CASE(NON_POLY, ?) 7.03/3.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.03/3.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.03/3.11 7.03/3.11 7.03/3.11 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 7.03/3.11 7.03/3.11 (0) CpxIntTrs 7.03/3.11 (1) Loat Proof [FINISHED, 1420 ms] 7.03/3.11 (2) BOUNDS(INF, INF) 7.03/3.11 7.03/3.11 7.03/3.11 ---------------------------------------- 7.03/3.11 7.03/3.11 (0) 7.03/3.11 Obligation: 7.03/3.11 Complexity Int TRS consisting of the following rules: 7.03/3.11 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= B 7.03/3.11 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= 3 7.03/3.11 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 1 >= C 7.03/3.11 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE 7.03/3.11 f54(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE 7.03/3.11 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1 7.03/3.11 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, 0, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= D 7.03/3.11 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, 2, D, E + 1, F, H, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= 2 && C <= 2 7.03/3.11 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, V, W, X, Y, E, V, V, O, P, Q, R, S, T, U)) :|: V >= 1 && B >= A + 1 7.03/3.11 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f37(A, B, Z, D, E, F, G, V, W, X, Y, E, V, V, V, Q, 0, Z, Z, 0, U)) :|: B >= A + 1 && 0 >= V && Z >= 2 7.03/3.11 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f37(A, B, Z, D, E, F, G, V, W, X, Y, E, V, V, V, Q, 0, Z, Z, 0, U)) :|: B >= A + 1 && 0 >= V && 0 >= Z 7.03/3.11 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A + 1, B, 1, D, E, F, G, V, W, X, Y, E, V, V, V, Q, Q, 1, 1, 0, U)) :|: 0 >= V && B >= A + 1 7.03/3.11 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A, B, C, W, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, 0)) :|: 0 >= W 7.03/3.11 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A, B, C, W, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, 0)) :|: W >= 1 7.03/3.11 7.03/3.11 The start-symbols are:[f0_21] 7.03/3.11 7.03/3.11 7.03/3.11 ---------------------------------------- 7.03/3.11 7.03/3.11 (1) Loat Proof (FINISHED) 7.03/3.11 7.03/3.11 7.03/3.11 ### Pre-processing the ITS problem ### 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Initial linear ITS problem 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 0: f13 -> f45 : [ A>=B ], cost: 1 7.03/3.11 7.03/3.11 8: f13 -> f45 : H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, [ free_1>=1 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 9: f13 -> f37 : C'=free_5, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, [ B>=1+A && 0>=free_7 && free_5>=2 ], cost: 1 7.03/3.11 7.03/3.11 10: f13 -> f37 : C'=free_10, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, [ B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 1 7.03/3.11 7.03/3.11 11: f13 -> f13 : A'=1+A, C'=1, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, [ 0>=free_15 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 3: f52 -> f52 : [], cost: 1 7.03/3.11 7.03/3.11 4: f54 -> f57 : [], cost: 1 7.03/3.11 7.03/3.11 5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1 7.03/3.11 7.03/3.11 6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1 7.03/3.11 7.03/3.11 12: f0 -> f13 : D'=free_18, F'=0, U'=0, [ 0>=free_18 ], cost: 1 7.03/3.11 7.03/3.11 13: f0 -> f13 : D'=free_19, F'=0, U'=0, [ free_19>=1 ], cost: 1 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Removed unreachable and leaf rules: 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 0: f13 -> f45 : [ A>=B ], cost: 1 7.03/3.11 7.03/3.11 8: f13 -> f45 : H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, [ free_1>=1 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 9: f13 -> f37 : C'=free_5, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, [ B>=1+A && 0>=free_7 && free_5>=2 ], cost: 1 7.03/3.11 7.03/3.11 10: f13 -> f37 : C'=free_10, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, [ B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 1 7.03/3.11 7.03/3.11 11: f13 -> f13 : A'=1+A, C'=1, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, [ 0>=free_15 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 3: f52 -> f52 : [], cost: 1 7.03/3.11 7.03/3.11 5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1 7.03/3.11 7.03/3.11 6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1 7.03/3.11 7.03/3.11 12: f0 -> f13 : D'=free_18, F'=0, U'=0, [ 0>=free_18 ], cost: 1 7.03/3.11 7.03/3.11 13: f0 -> f13 : D'=free_19, F'=0, U'=0, [ free_19>=1 ], cost: 1 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 ### Simplification by acceleration and chaining ### 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Accelerating simple loops of location 0. 7.03/3.11 7.03/3.11 Accelerating the following rules: 7.03/3.11 7.03/3.11 11: f13 -> f13 : A'=1+A, C'=1, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, [ 0>=free_15 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Accelerated rule 11 with metering function -A+B, yielding the new rule 14. 7.03/3.11 7.03/3.11 Removing the simple loops: 11. 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Accelerating simple loops of location 2. 7.03/3.11 7.03/3.11 Accelerating the following rules: 7.03/3.11 7.03/3.11 3: f52 -> f52 : [], cost: 1 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Accelerated rule 3 with NONTERM, yielding the new rule 15. 7.03/3.11 7.03/3.11 Removing the simple loops: 3. 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Accelerated all simple loops using metering functions (where possible): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 0: f13 -> f45 : [ A>=B ], cost: 1 7.03/3.11 7.03/3.11 8: f13 -> f45 : H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, [ free_1>=1 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 9: f13 -> f37 : C'=free_5, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, [ B>=1+A && 0>=free_7 && free_5>=2 ], cost: 1 7.03/3.11 7.03/3.11 10: f13 -> f37 : C'=free_10, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, [ B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 1 7.03/3.11 7.03/3.11 14: f13 -> f13 : A'=B, C'=1, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, [ 0>=free_15 && B>=1+A ], cost: -A+B 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 15: f52 -> [8] : [], cost: INF 7.03/3.11 7.03/3.11 5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1 7.03/3.11 7.03/3.11 6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1 7.03/3.11 7.03/3.11 12: f0 -> f13 : D'=free_18, F'=0, U'=0, [ 0>=free_18 ], cost: 1 7.03/3.11 7.03/3.11 13: f0 -> f13 : D'=free_19, F'=0, U'=0, [ free_19>=1 ], cost: 1 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Chained accelerated rules (with incoming rules): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 0: f13 -> f45 : [ A>=B ], cost: 1 7.03/3.11 7.03/3.11 8: f13 -> f45 : H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, [ free_1>=1 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 9: f13 -> f37 : C'=free_5, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, [ B>=1+A && 0>=free_7 && free_5>=2 ], cost: 1 7.03/3.11 7.03/3.11 10: f13 -> f37 : C'=free_10, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, [ B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 1 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1 7.03/3.11 7.03/3.11 6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1 7.03/3.11 7.03/3.11 18: f45 -> [8] : E'=0, [ D>=1 ], cost: INF 7.03/3.11 7.03/3.11 19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: INF 7.03/3.11 7.03/3.11 12: f0 -> f13 : D'=free_18, F'=0, U'=0, [ 0>=free_18 ], cost: 1 7.03/3.11 7.03/3.11 13: f0 -> f13 : D'=free_19, F'=0, U'=0, [ free_19>=1 ], cost: 1 7.03/3.11 7.03/3.11 16: f0 -> f13 : A'=B, C'=1, D'=free_18, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 17: f0 -> f13 : A'=B, C'=1, D'=free_19, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Removed unreachable locations (and leaf rules with constant cost): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 0: f13 -> f45 : [ A>=B ], cost: 1 7.03/3.11 7.03/3.11 8: f13 -> f45 : H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, [ free_1>=1 && B>=1+A ], cost: 1 7.03/3.11 7.03/3.11 9: f13 -> f37 : C'=free_5, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, [ B>=1+A && 0>=free_7 && free_5>=2 ], cost: 1 7.03/3.11 7.03/3.11 10: f13 -> f37 : C'=free_10, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, [ B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 1 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 18: f45 -> [8] : E'=0, [ D>=1 ], cost: INF 7.03/3.11 7.03/3.11 19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: INF 7.03/3.11 7.03/3.11 12: f0 -> f13 : D'=free_18, F'=0, U'=0, [ 0>=free_18 ], cost: 1 7.03/3.11 7.03/3.11 13: f0 -> f13 : D'=free_19, F'=0, U'=0, [ free_19>=1 ], cost: 1 7.03/3.11 7.03/3.11 16: f0 -> f13 : A'=B, C'=1, D'=free_18, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 17: f0 -> f13 : A'=B, C'=1, D'=free_19, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Eliminated locations (on tree-shaped paths): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 18: f45 -> [8] : E'=0, [ D>=1 ], cost: INF 7.03/3.11 7.03/3.11 19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: INF 7.03/3.11 7.03/3.11 20: f0 -> f45 : D'=free_18, F'=0, U'=0, [ 0>=free_18 && A>=B ], cost: 2 7.03/3.11 7.03/3.11 21: f0 -> f45 : D'=free_18, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ 0>=free_18 && free_1>=1 && B>=1+A ], cost: 2 7.03/3.11 7.03/3.11 22: f0 -> f37 : C'=free_5, D'=free_18, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5>=2 ], cost: 2 7.03/3.11 7.03/3.11 23: f0 -> f37 : C'=free_10, D'=free_18, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 2 7.03/3.11 7.03/3.11 24: f0 -> f45 : D'=free_19, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: 2 7.03/3.11 7.03/3.11 25: f0 -> f45 : D'=free_19, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ free_19>=1 && free_1>=1 && B>=1+A ], cost: 2 7.03/3.11 7.03/3.11 26: f0 -> f37 : C'=free_5, D'=free_19, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_7 && free_5>=2 ], cost: 2 7.03/3.11 7.03/3.11 27: f0 -> f37 : C'=free_10, D'=free_19, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 2 7.03/3.11 7.03/3.11 28: f0 -> f45 : A'=B, C'=1, D'=free_18, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 29: f0 -> f45 : A'=B, C'=1, D'=free_19, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 30: f0 -> [9] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 31: f0 -> [9] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Applied pruning (of leafs and parallel rules): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 1: f37 -> f45 : [ C>=3 ], cost: 1 7.03/3.11 7.03/3.11 2: f37 -> f45 : [ 1>=C ], cost: 1 7.03/3.11 7.03/3.11 7: f37 -> f45 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1 7.03/3.11 7.03/3.11 18: f45 -> [8] : E'=0, [ D>=1 ], cost: INF 7.03/3.11 7.03/3.11 19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: INF 7.03/3.11 7.03/3.11 21: f0 -> f45 : D'=free_18, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ 0>=free_18 && free_1>=1 && B>=1+A ], cost: 2 7.03/3.11 7.03/3.11 22: f0 -> f37 : C'=free_5, D'=free_18, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5>=2 ], cost: 2 7.03/3.11 7.03/3.11 23: f0 -> f37 : C'=free_10, D'=free_18, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 2 7.03/3.11 7.03/3.11 24: f0 -> f45 : D'=free_19, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: 2 7.03/3.11 7.03/3.11 25: f0 -> f45 : D'=free_19, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ free_19>=1 && free_1>=1 && B>=1+A ], cost: 2 7.03/3.11 7.03/3.11 26: f0 -> f37 : C'=free_5, D'=free_19, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_7 && free_5>=2 ], cost: 2 7.03/3.11 7.03/3.11 27: f0 -> f37 : C'=free_10, D'=free_19, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: 2 7.03/3.11 7.03/3.11 28: f0 -> f45 : A'=B, C'=1, D'=free_18, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 29: f0 -> f45 : A'=B, C'=1, D'=free_19, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 30: f0 -> [9] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 31: f0 -> [9] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Eliminated locations (on tree-shaped paths): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 30: f0 -> [9] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 31: f0 -> [9] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ 0>=free_18 && free_1>=1 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 39: f0 -> [8] : D'=free_19, E'=0, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: INF 7.03/3.11 7.03/3.11 40: f0 -> [8] : D'=free_19, E'=0, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ free_19>=1 && free_1>=1 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 42: f0 -> [8] : A'=B, C'=1, D'=free_19, E'=0, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 43: f0 -> [8] : C'=free_5, D'=free_18, E'=0, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5>=3 ], cost: INF 7.03/3.11 7.03/3.11 44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_7, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5==2 ], cost: INF 7.03/3.11 7.03/3.11 45: f0 -> [8] : C'=free_10, D'=free_18, E'=0, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: INF 7.03/3.11 7.03/3.11 46: f0 -> [8] : C'=free_5, D'=free_19, E'=0, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_7 && free_5>=3 ], cost: INF 7.03/3.11 7.03/3.11 47: f0 -> [8] : C'=2, D'=free_19, E'=0, F'=0, G'=free_7, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_7 && free_5==2 ], cost: INF 7.03/3.11 7.03/3.11 48: f0 -> [8] : C'=free_10, D'=free_19, E'=0, F'=0, H'=free_12, Q'=free_13, J'=free_9, K'=free_11, L'=E, M'=free_12, N'=free_12, O'=free_12, P'=Q_1, Q_1'=0, R'=free_10, S'=free_10, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_12 && 0>=free_10 ], cost: INF 7.03/3.11 7.03/3.11 49: f0 -> [10] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 50: f0 -> [10] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Applied pruning (of leafs and parallel rules): 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 30: f0 -> [9] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 31: f0 -> [9] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 1-A+B 7.03/3.11 7.03/3.11 38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ 0>=free_18 && free_1>=1 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 39: f0 -> [8] : D'=free_19, E'=0, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: INF 7.03/3.11 7.03/3.11 41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 43: f0 -> [8] : C'=free_5, D'=free_18, E'=0, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5>=3 ], cost: INF 7.03/3.11 7.03/3.11 44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_7, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5==2 ], cost: INF 7.03/3.11 7.03/3.11 49: f0 -> [10] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 50: f0 -> [10] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 ### Computing asymptotic complexity ### 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Fully simplified ITS problem 7.03/3.11 7.03/3.11 Start location: f0 7.03/3.11 7.03/3.11 38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free_1, Q'=free_2, J'=free_3, K'=free, L'=E, M'=free_1, N'=free_1, U'=0, [ 0>=free_18 && free_1>=1 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 39: f0 -> [8] : D'=free_19, E'=0, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: INF 7.03/3.11 7.03/3.11 41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_15, Q'=free_16, J'=free_17, K'=free_14, L'=E, M'=free_15, N'=free_15, O'=free_15, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: INF 7.03/3.11 7.03/3.11 43: f0 -> [8] : C'=free_5, D'=free_18, E'=0, F'=0, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5>=3 ], cost: INF 7.03/3.11 7.03/3.11 44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_7, H'=free_7, Q'=free_8, J'=free_4, K'=free_6, L'=E, M'=free_7, N'=free_7, O'=free_7, P'=Q_1, Q_1'=0, R'=free_5, S'=free_5, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_7 && free_5==2 ], cost: INF 7.03/3.11 7.03/3.11 49: f0 -> [10] : [ 0>=free_18 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 50: f0 -> [10] : [ free_19>=1 && 0>=free_15 && B>=1+A ], cost: 2-A+B 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Computing asymptotic complexity for rule 38 7.03/3.11 7.03/3.11 Resulting cost INF has complexity: Nonterm 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Found new complexity Nonterm. 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 Obtained the following overall complexity (w.r.t. the length of the input n): 7.03/3.11 7.03/3.11 Complexity: Nonterm 7.03/3.11 7.03/3.11 Cpx degree: Nonterm 7.03/3.11 7.03/3.11 Solved cost: INF 7.03/3.11 7.03/3.11 Rule cost: INF 7.03/3.11 7.03/3.11 Rule guard: [ 0>=free_18 && free_1>=1 && B>=1+A ] 7.03/3.11 7.03/3.11 7.03/3.11 7.03/3.11 NO 7.03/3.11 7.03/3.11 7.03/3.11 ---------------------------------------- 7.03/3.11 7.03/3.11 (2) 7.03/3.11 BOUNDS(INF, INF) 7.05/3.13 EOF