5.08/2.32 WORST_CASE(NON_POLY, ?) 5.08/2.33 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 5.08/2.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.08/2.33 5.08/2.33 5.08/2.33 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 5.08/2.33 5.08/2.33 (0) CpxIntTrs 5.08/2.33 (1) Loat Proof [FINISHED, 624 ms] 5.08/2.33 (2) BOUNDS(INF, INF) 5.08/2.33 5.08/2.33 5.08/2.33 ---------------------------------------- 5.08/2.33 5.08/2.33 (0) 5.08/2.33 Obligation: 5.08/2.33 Complexity Int TRS consisting of the following rules: 5.08/2.33 f51(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: TRUE 5.08/2.33 f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f56(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: TRUE 5.08/2.33 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: A >= B 5.08/2.33 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: E >= 3 5.08/2.33 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: 1 >= E 5.08/2.33 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, 2, G, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: E >= 2 && E <= 2 5.08/2.33 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, W, X, Y, Z, D, W, W, W, O, P, Q, R, S, T, U, V)) :|: W >= 1 && B >= A + 1 5.08/2.33 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f37(A, B, C, D, A1, F, W, X, Y, Z, D, W, W, W, W, Q, 0, A1, A1, A1, 0, V)) :|: B >= A + 1 && 0 >= W && A1 >= 2 5.08/2.33 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f37(A, B, C, D, A1, F, W, X, Y, Z, D, W, W, W, W, Q, 0, A1, A1, A1, 0, V)) :|: B >= A + 1 && 0 >= W && 0 >= A1 5.08/2.33 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f11(A + 1, B, C, D, 1, F, W, X, Y, Z, D, W, W, W, W, Q, Q, 1, 1, 1, 0, V)) :|: 0 >= W && B >= A + 1 5.08/2.33 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f11(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0)) :|: TRUE 5.08/2.33 5.08/2.33 The start-symbols are:[f0_22] 5.08/2.33 5.08/2.33 5.08/2.33 ---------------------------------------- 5.08/2.33 5.08/2.33 (1) Loat Proof (FINISHED) 5.08/2.33 5.08/2.33 5.08/2.33 ### Pre-processing the ITS problem ### 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Initial linear ITS problem 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 0: f51 -> f51 : [], cost: 1 5.08/2.33 5.08/2.33 1: f53 -> f56 : A1'=B, B'=C, C'=D, D'=E, E'=F, F'=G, G'=H, H'=Q, Q'=J, J'=K, K'=L, L'=M, M'=N, N'=O, O'=P, P'=Q_1, Q_1'=R, R'=S, S'=T, T'=U, U'=V, [], cost: 1 5.08/2.33 5.08/2.33 2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1 5.08/2.33 5.08/2.33 6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1 5.08/2.33 5.08/2.33 8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1 5.08/2.33 5.08/2.33 9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1 5.08/2.33 5.08/2.33 4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1 5.08/2.33 5.08/2.33 5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1 5.08/2.33 5.08/2.33 10: f0 -> f11 : C'=0, V'=0, [], cost: 1 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Removed unreachable and leaf rules: 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 0: f51 -> f51 : [], cost: 1 5.08/2.33 5.08/2.33 2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1 5.08/2.33 5.08/2.33 6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1 5.08/2.33 5.08/2.33 8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1 5.08/2.33 5.08/2.33 9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1 5.08/2.33 5.08/2.33 4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1 5.08/2.33 5.08/2.33 5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1 5.08/2.33 5.08/2.33 10: f0 -> f11 : C'=0, V'=0, [], cost: 1 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 ### Simplification by acceleration and chaining ### 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Accelerating simple loops of location 0. 5.08/2.33 5.08/2.33 Accelerating the following rules: 5.08/2.33 5.08/2.33 0: f51 -> f51 : [], cost: 1 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Accelerated rule 0 with NONTERM, yielding the new rule 11. 5.08/2.33 5.08/2.33 Removing the simple loops: 0. 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Accelerating simple loops of location 2. 5.08/2.33 5.08/2.33 Accelerating the following rules: 5.08/2.33 5.08/2.33 9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Accelerated rule 9 with metering function B-A, yielding the new rule 12. 5.08/2.33 5.08/2.33 Removing the simple loops: 9. 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Accelerated all simple loops using metering functions (where possible): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 11: f51 -> [6] : [], cost: INF 5.08/2.33 5.08/2.33 2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1 5.08/2.33 5.08/2.33 6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1 5.08/2.33 5.08/2.33 8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1 5.08/2.33 5.08/2.33 12: f11 -> f11 : A'=B, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: B-A 5.08/2.33 5.08/2.33 3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1 5.08/2.33 5.08/2.33 4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1 5.08/2.33 5.08/2.33 5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1 5.08/2.33 5.08/2.33 10: f0 -> f11 : C'=0, V'=0, [], cost: 1 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Chained accelerated rules (with incoming rules): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1 5.08/2.33 5.08/2.33 6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1 5.08/2.33 5.08/2.33 7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1 5.08/2.33 5.08/2.33 8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1 5.08/2.33 5.08/2.33 13: f11 -> [6] : C'=0, D'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 17: f11 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1 5.08/2.33 5.08/2.33 4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1 5.08/2.33 5.08/2.33 5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1 5.08/2.33 5.08/2.33 14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF 5.08/2.33 5.08/2.33 15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF 5.08/2.33 5.08/2.33 16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF 5.08/2.33 5.08/2.33 10: f0 -> f11 : C'=0, V'=0, [], cost: 1 5.08/2.33 5.08/2.33 18: f0 -> f11 : A'=B, C'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Removed unreachable locations (and leaf rules with constant cost): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1 5.08/2.33 5.08/2.33 8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1 5.08/2.33 5.08/2.33 13: f11 -> [6] : C'=0, D'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 17: f11 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF 5.08/2.33 5.08/2.33 15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF 5.08/2.33 5.08/2.33 16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF 5.08/2.33 5.08/2.33 10: f0 -> f11 : C'=0, V'=0, [], cost: 1 5.08/2.33 5.08/2.33 18: f0 -> f11 : A'=B, C'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Eliminated locations (on tree-shaped paths): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF 5.08/2.33 5.08/2.33 15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF 5.08/2.33 5.08/2.33 16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF 5.08/2.33 5.08/2.33 19: f0 -> f37 : C'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 2 5.08/2.33 5.08/2.33 20: f0 -> f37 : C'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 2 5.08/2.33 5.08/2.33 21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Eliminated locations (on tree-shaped paths): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF 5.08/2.33 5.08/2.33 26: f0 -> [6] : C'=0, D'=0, E'=2, F'=free_4, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7==2 ], cost: INF 5.08/2.33 5.08/2.33 27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Applied pruning (of leafs and parallel rules): 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF 5.08/2.33 5.08/2.33 27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 ### Computing asymptotic complexity ### 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Fully simplified ITS problem 5.08/2.33 5.08/2.33 Start location: f0 5.08/2.33 5.08/2.33 21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF 5.08/2.33 5.08/2.33 22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF 5.08/2.33 5.08/2.33 24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A 5.08/2.33 5.08/2.33 25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF 5.08/2.33 5.08/2.33 27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Computing asymptotic complexity for rule 21 5.08/2.33 5.08/2.33 Resulting cost INF has complexity: Nonterm 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Found new complexity Nonterm. 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 Obtained the following overall complexity (w.r.t. the length of the input n): 5.08/2.33 5.08/2.33 Complexity: Nonterm 5.08/2.33 5.08/2.33 Cpx degree: Nonterm 5.08/2.33 5.08/2.33 Solved cost: INF 5.08/2.33 5.08/2.33 Rule cost: INF 5.08/2.33 5.08/2.33 Rule guard: [ A>=B ] 5.08/2.33 5.08/2.33 5.08/2.33 5.08/2.33 NO 5.08/2.33 5.08/2.33 5.08/2.33 ---------------------------------------- 5.08/2.33 5.08/2.33 (2) 5.08/2.33 BOUNDS(INF, INF) 5.08/2.36 EOF