13.07/4.84 WORST_CASE(NON_POLY, ?) 13.07/4.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 13.07/4.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.07/4.85 13.07/4.85 13.07/4.85 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 13.07/4.85 13.07/4.85 (0) CpxIntTrs 13.07/4.85 (1) Loat Proof [FINISHED, 3125 ms] 13.07/4.85 (2) BOUNDS(INF, INF) 13.07/4.85 13.07/4.85 13.07/4.85 ---------------------------------------- 13.07/4.85 13.07/4.85 (0) 13.07/4.85 Obligation: 13.07/4.85 Complexity Int TRS consisting of the following rules: 13.07/4.85 f63(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= 1 + B 13.07/4.85 f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, 10, 20, 1, 20, 0, 0, H, I, J, K)) :|: TRUE 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, 1, H, I, J, K)) :|: D >= E && G >= 0 && G <= 0 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, 1, H, I, J, K)) :|: D + 1 >= E && E >= 2 + D && G >= 0 && G <= 0 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, D + 1, F, 1, H, I, J, K)) :|: E >= D + 1 && E <= D + 1 && G >= 0 && G <= 0 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, D + 1, F, 1, N, I, J, K)) :|: L >= M + 1 && E >= D + 1 && E <= D + 1 && G >= 0 && G <= 0 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(E, B, C, D, E, F, 0, N, L, D + 1, M)) :|: E >= 2 + D && G >= 0 && G <= 0 13.07/4.85 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= F + 1 13.07/4.85 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: F >= 1 13.07/4.85 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f43(A, B, C, D, E, 0, G, H, I, J + 1, K)) :|: F >= 0 && F <= 0 13.07/4.85 f43(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f43(A, B, C, D, E, F, G, H, I, J + 1, K)) :|: K >= N + 1 13.07/4.85 f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f48(A - 1, B, C, D, E, F, G, H, I, J, K)) :|: TRUE 13.07/4.85 f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= F + 1 13.07/4.85 f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, F, G, H, I, J, K)) :|: F >= 1 13.07/4.85 f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, 0, G, N, I, J, K)) :|: F >= 0 && F <= 0 13.07/4.85 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f63(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= A + 1 13.07/4.85 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f63(A, B, C, D, A - 1, F, G, H, I, J, K)) :|: A >= B 13.07/4.85 f63(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, J, E, F, G, H, I, J, K)) :|: B >= A 13.07/4.85 f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= J 13.07/4.85 f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, C, D, E, 1, G, H, I, J, K)) :|: J >= A + 1 13.07/4.85 f43(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f48(A - 1, B, C, D, E, F, G, H, I, J, K)) :|: TRUE 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= G + 1 13.07/4.85 f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: G >= 1 13.07/4.85 13.07/4.85 The start-symbols are:[f0_11] 13.07/4.85 13.07/4.85 13.07/4.85 ---------------------------------------- 13.07/4.85 13.07/4.85 (1) Loat Proof (FINISHED) 13.07/4.85 13.07/4.85 13.07/4.85 ### Pre-processing the ITS problem ### 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Initial linear ITS problem 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1 13.07/4.85 13.07/4.85 3: f11 -> f11 : G'=1, [ 1+D>=E && E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 21: f11 -> f69 : [ 0>=1+G ], cost: 1 13.07/4.85 13.07/4.85 22: f11 -> f69 : [ G>=1 ], cost: 1 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 11: f48 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Removed unreachable and leaf rules: 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1 13.07/4.85 13.07/4.85 3: f11 -> f11 : G'=1, [ 1+D>=E && E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 11: f48 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Removed rules with unsatisfiable guard: 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1 13.07/4.85 13.07/4.85 4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 11: f48 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Simplified all rules, resulting in: 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1 13.07/4.85 13.07/4.85 4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 10: f43 -> f43 : J'=1+J, [], cost: 1 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 11: f48 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 ### Simplification by acceleration and chaining ### 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerating simple loops of location 2. 13.07/4.85 13.07/4.85 Accelerating the following rules: 13.07/4.85 13.07/4.85 2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1 13.07/4.85 13.07/4.85 4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerated rule 2 with metering function 1-G, yielding the new rule 23. 13.07/4.85 13.07/4.85 Accelerated rule 4 with metering function 1-G, yielding the new rule 24. 13.07/4.85 13.07/4.85 Accelerated rule 5 with metering function 1-G, yielding the new rule 25. 13.07/4.85 13.07/4.85 Removing the simple loops: 2 4 5. 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerating simple loops of location 4. 13.07/4.85 13.07/4.85 Accelerating the following rules: 13.07/4.85 13.07/4.85 10: f43 -> f43 : J'=1+J, [], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerated rule 10 with NONTERM, yielding the new rule 26. 13.07/4.85 13.07/4.85 Removing the simple loops: 10. 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerating simple loops of location 5. 13.07/4.85 13.07/4.85 Accelerating the following rules: 13.07/4.85 13.07/4.85 11: f48 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerated rule 11 with NONTERM, yielding the new rule 27. 13.07/4.85 13.07/4.85 Removing the simple loops: 11. 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Accelerated all simple loops using metering functions (where possible): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 23: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1-G 13.07/4.85 13.07/4.85 24: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1-G 13.07/4.85 13.07/4.85 25: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1-G 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 26: f43 -> [10] : [], cost: INF 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 27: f48 -> [11] : [], cost: INF 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Chained accelerated rules (with incoming rules): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 28: f63 -> f11 : G'=1, [ A>=1+B && D>=E && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 32: f63 -> f11 : E'=1+D, G'=1, H'=free_2, [ A>=1+B && E==1+D && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 33: f63 -> f11 : D'=J, E'=1+J, G'=1, H'=free_2, [ B>=A && E==1+J && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 7: f40 -> f59 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 8: f40 -> f59 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 20: f43 -> f48 : A'=-1+A, [], cost: 1 13.07/4.85 13.07/4.85 35: f43 -> [11] : A'=-1+A, [], cost: INF 13.07/4.85 13.07/4.85 18: f48 -> f54 : [ A>=J ], cost: 1 13.07/4.85 13.07/4.85 19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1 13.07/4.85 13.07/4.85 12: f54 -> f40 : [ 0>=1+F ], cost: 1 13.07/4.85 13.07/4.85 13: f54 -> f40 : [ F>=1 ], cost: 1 13.07/4.85 13.07/4.85 14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1 13.07/4.85 13.07/4.85 15: f59 -> f63 : [ B>=1+A ], cost: 1 13.07/4.85 13.07/4.85 16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Eliminated locations (on tree-shaped paths): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 28: f63 -> f11 : G'=1, [ A>=1+B && D>=E && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 32: f63 -> f11 : E'=1+D, G'=1, H'=free_2, [ A>=1+B && E==1+D && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 33: f63 -> f11 : D'=J, E'=1+J, G'=1, H'=free_2, [ B>=A && E==1+J && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 36: f40 -> f48 : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: 2 13.07/4.85 13.07/4.85 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 38: f40 -> f63 : [ 0>=1+F && B>=1+A ], cost: 2 13.07/4.85 13.07/4.85 39: f40 -> f63 : E'=-1+A, [ 0>=1+F && A>=B ], cost: 2 13.07/4.85 13.07/4.85 40: f40 -> f63 : [ F>=1 && B>=1+A ], cost: 2 13.07/4.85 13.07/4.85 41: f40 -> f63 : E'=-1+A, [ F>=1 && A>=B ], cost: 2 13.07/4.85 13.07/4.85 42: f48 -> f40 : [ A>=J && 0>=1+F ], cost: 2 13.07/4.85 13.07/4.85 43: f48 -> f40 : [ A>=J && F>=1 ], cost: 2 13.07/4.85 13.07/4.85 44: f48 -> f40 : F'=0, H'=free_7, [ A>=J && F==0 ], cost: 2 13.07/4.85 13.07/4.85 45: f48 -> f40 : F'=1, [ J>=1+A ], cost: 2 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Applied pruning (of leafs and parallel rules): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 0: f63 -> f11 : [ A>=1+B ], cost: 1 13.07/4.85 13.07/4.85 17: f63 -> f11 : D'=J, [ B>=A ], cost: 1 13.07/4.85 13.07/4.85 29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 36: f40 -> f48 : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: 2 13.07/4.85 13.07/4.85 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 38: f40 -> f63 : [ 0>=1+F && B>=1+A ], cost: 2 13.07/4.85 13.07/4.85 39: f40 -> f63 : E'=-1+A, [ 0>=1+F && A>=B ], cost: 2 13.07/4.85 13.07/4.85 40: f40 -> f63 : [ F>=1 && B>=1+A ], cost: 2 13.07/4.85 13.07/4.85 41: f40 -> f63 : E'=-1+A, [ F>=1 && A>=B ], cost: 2 13.07/4.85 13.07/4.85 42: f48 -> f40 : [ A>=J && 0>=1+F ], cost: 2 13.07/4.85 13.07/4.85 43: f48 -> f40 : [ A>=J && F>=1 ], cost: 2 13.07/4.85 13.07/4.85 44: f48 -> f40 : F'=0, H'=free_7, [ A>=J && F==0 ], cost: 2 13.07/4.85 13.07/4.85 45: f48 -> f40 : F'=1, [ J>=1+A ], cost: 2 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Eliminated locations (on tree-shaped paths): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3 13.07/4.85 13.07/4.85 47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 48: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && B>=1+A && E==1+J && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3 13.07/4.85 13.07/4.85 50: f40 -> f11 : D'=J, E'=-1+A, [ 0>=1+F && A>=B && B>=A ], cost: 3 13.07/4.85 13.07/4.85 51: f40 -> f11 : D'=J, E'=-1+A, G'=1, [ 0>=1+F && A>=B && B>=A && J>=-1+A && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 52: f40 -> f11 : E'=1+D, G'=1, [ 0>=1+F && A>=1+B && -1+A==1+D && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 54: f40 -> f11 : D'=J, [ F>=1 && B>=1+A ], cost: 3 13.07/4.85 13.07/4.85 55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 56: f40 -> f11 : D'=J, E'=1+J, G'=1, [ F>=1 && B>=1+A && E==1+J && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 57: f40 -> f11 : E'=-1+A, [ F>=1 && A>=1+B ], cost: 3 13.07/4.85 13.07/4.85 58: f40 -> f11 : D'=J, E'=-1+A, [ F>=1 && A>=B && B>=A ], cost: 3 13.07/4.85 13.07/4.85 59: f40 -> f11 : D'=J, E'=-1+A, G'=1, [ F>=1 && A>=B && B>=A && J>=-1+A && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 60: f40 -> f11 : E'=1+D, G'=1, [ F>=1 && A>=1+B && -1+A==1+D && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 61: f40 -> f11 : D'=J, E'=1+J, G'=1, [ F>=1 && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G 13.07/4.85 13.07/4.85 62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4 13.07/4.85 13.07/4.85 63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4 13.07/4.85 13.07/4.85 13.07/4.85 13.07/4.85 Applied pruning (of leafs and parallel rules): 13.07/4.85 13.07/4.85 Start location: f0 13.07/4.85 13.07/4.85 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.85 13.07/4.85 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.85 13.07/4.85 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.85 13.07/4.85 46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3 13.07/4.85 13.07/4.85 47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3 13.07/4.86 13.07/4.86 53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4 13.07/4.86 13.07/4.86 63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerating simple loops of location 3. 13.07/4.86 13.07/4.86 Accelerating the following rules: 13.07/4.86 13.07/4.86 62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4 13.07/4.86 13.07/4.86 63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerated rule 62 with metering function meter (where 2*meter==-1-J+A), yielding the new rule 64. 13.07/4.86 13.07/4.86 Accelerated rule 63 with metering function 1-F, yielding the new rule 65. 13.07/4.86 13.07/4.86 Nested simple loops 63 (outer loop) and 64 (inner loop) with metering function -F, resulting in the new rules: 66. 13.07/4.86 13.07/4.86 Removing the simple loops: 62 63. 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerated all simple loops using metering functions (where possible): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.86 13.07/4.86 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.86 13.07/4.86 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.86 13.07/4.86 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.86 13.07/4.86 46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3 13.07/4.86 13.07/4.86 47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3 13.07/4.86 13.07/4.86 53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 64: f40 -> f40 : A'=-meter+A, F'=0, H'=free_7, J'=meter+J, [ F==0 && -1+A>=1+J && 2*meter==-1-J+A && meter>=1 ], cost: 4*meter 13.07/4.86 13.07/4.86 65: f40 -> f40 : A'=-1+F+A, F'=1, J'=1-F+J, [ F==0 && 1+J>=A ], cost: 4-4*F 13.07/4.86 13.07/4.86 66: f40 -> f40 : A'=F+F*meter+A, F'=1, H'=free_7, J'=-F+J-F*meter, [ F==0 && -1+A>=1+J && 2*meter==-1-J+A && meter>=1 && -F>=1 ], cost: -4*F-4*F*meter 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Chained accelerated rules (with incoming rules): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.86 13.07/4.86 6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1 13.07/4.86 13.07/4.86 67: f11 -> f40 : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=1+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter 13.07/4.86 13.07/4.86 68: f11 -> f40 : A'=-1+F+E, F'=1, G'=0, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F 13.07/4.86 13.07/4.86 34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.86 13.07/4.86 37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF 13.07/4.86 13.07/4.86 46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3 13.07/4.86 13.07/4.86 47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3 13.07/4.86 13.07/4.86 53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Eliminated locations (on tree-shaped paths): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.86 13.07/4.86 69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 71: f11 -> f11 : A'=E, D'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: 4 13.07/4.86 13.07/4.86 72: f11 -> f11 : A'=E, E'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B ], cost: 4 13.07/4.86 13.07/4.86 73: f11 -> f11 : A'=E, D'=1+D, E'=2+D, G'=1, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ G==0 && 0>=1+F && E>=B && B>=E && -1+E==2+D ], cost: 5 13.07/4.86 13.07/4.86 74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 76: f11 -> f11 : A'=-1+F+E, D'=2-F+D, F'=1, G'=1, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E ], cost: 9-4*F 13.07/4.86 13.07/4.86 77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter 13.07/4.86 13.07/4.86 78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerating simple loops of location 2. 13.07/4.86 13.07/4.86 Simplified some of the simple loops (and removed duplicate rules). 13.07/4.86 13.07/4.86 Accelerating the following rules: 13.07/4.86 13.07/4.86 71: f11 -> f11 : A'=E, D'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: 4 13.07/4.86 13.07/4.86 72: f11 -> f11 : A'=E, E'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B ], cost: 4 13.07/4.86 13.07/4.86 73: f11 -> f11 : A'=E, D'=1+D, E'=2+D, G'=1, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ G==0 && 0>=1+F && -E+B==0 && -1+E==2+D ], cost: 5 13.07/4.86 13.07/4.86 76: f11 -> f11 : A'=-1+F+E, D'=2-F+D, F'=1, G'=1, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E ], cost: 9-4*F 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerated rule 71 with metering function -1-D+E, yielding the new rule 79. 13.07/4.86 13.07/4.86 Accelerated rule 72 with backward acceleration, yielding the new rule 80. 13.07/4.86 13.07/4.86 Accelerated rule 72 with backward acceleration, yielding the new rule 81. 13.07/4.86 13.07/4.86 Accelerated rule 73 with metering function meter_2 (where 4*meter_2==-3-G-D+2*E-B), yielding the new rule 82. 13.07/4.86 13.07/4.86 Accelerated rule 76 with metering function meter_3 (where 4*meter_3==-2-F-G-D+E), yielding the new rule 83. 13.07/4.86 13.07/4.86 Nested simple loops 73 (outer loop) and 81 (inner loop) with metering function meter_4 (where 2*meter_4==-3-G-D+B), resulting in the new rules: 84. 13.07/4.86 13.07/4.86 Removing the simple loops: 71 72 73 76. 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Accelerated all simple loops using metering functions (where possible): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.86 13.07/4.86 69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter 13.07/4.86 13.07/4.86 78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F 13.07/4.86 13.07/4.86 79: f11 -> f11 : A'=E, D'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=-1+E, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: -4-4*D+4*E 13.07/4.86 13.07/4.86 80: f11 -> f11 : A'=2+D, E'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && 2+D>=1+B ], cost: -4-4*D+4*E 13.07/4.86 13.07/4.86 81: f11 -> f11 : A'=1+B, E'=B, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && 1+B>=2+D ], cost: 4*E-4*B 13.07/4.86 13.07/4.86 82: f11 -> f11 : A'=D+meter_2, D'=D+meter_2, E'=1+D+meter_2, G'=1, H'=free_5, Q'=free_3, J'=D+meter_2, K'=free_4, [ G==0 && 0>=1+F && -E+B==0 && -1+E==2+D && 4*meter_2==-3-G-D+2*E-B && meter_2>=1 ], cost: 5*meter_2 13.07/4.86 13.07/4.86 83: f11 -> f11 : A'=E, D'=D+meter_3, F'=1, G'=1, H'=free_5, Q'=free_3, J'=D+meter_3, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E && 4*meter_3==-2-F-G-D+E && meter_3>=1 ], cost: 5*meter_3 13.07/4.86 13.07/4.86 84: f11 -> f11 : A'=B, D'=D+meter_4, E'=1+D+meter_4, G'=1, H'=free_5, Q'=free_3, J'=D+meter_4, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && -1+B==2+D && 2*meter_4==-3-G-D+B && meter_4>=1 ], cost: -4*meter_4*B+7*meter_4+2*meter_4^2+4*D*meter_4 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Chained accelerated rules (with incoming rules): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1 13.07/4.86 13.07/4.86 69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF 13.07/4.86 13.07/4.86 74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF 13.07/4.86 13.07/4.86 77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter 13.07/4.86 13.07/4.86 78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Eliminated locations (on tree-shaped paths): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 85: f0 -> [10] : A'=20, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF 13.07/4.86 13.07/4.86 86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Applied pruning (of leafs and parallel rules): 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 85: f0 -> [10] : A'=20, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF 13.07/4.86 13.07/4.86 86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 ### Computing asymptotic complexity ### 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Fully simplified ITS problem 13.07/4.86 13.07/4.86 Start location: f0 13.07/4.86 13.07/4.86 86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Computing asymptotic complexity for rule 86 13.07/4.86 13.07/4.86 Resulting cost INF has complexity: Nonterm 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Found new complexity Nonterm. 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 Obtained the following overall complexity (w.r.t. the length of the input n): 13.07/4.86 13.07/4.86 Complexity: Nonterm 13.07/4.86 13.07/4.86 Cpx degree: Nonterm 13.07/4.86 13.07/4.86 Solved cost: INF 13.07/4.86 13.07/4.86 Rule cost: INF 13.07/4.86 13.07/4.86 Rule guard: [] 13.07/4.86 13.07/4.86 13.07/4.86 13.07/4.86 NO 13.07/4.86 13.07/4.86 13.07/4.86 ---------------------------------------- 13.07/4.86 13.07/4.86 (2) 13.07/4.86 BOUNDS(INF, INF) 13.19/4.88 EOF