/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 2677 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && 3 >= P && P >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && P >= 5 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, 3, 4, 1, 0, 3, 4, 2, M, N)) :|: TRUE f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 3, M, N)) :|: 7 >= P && P >= 1 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 6, M, N)) :|: 7 >= P && P >= 1 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(1, C, C, E, E, P, 2, 0, 1, P, 2, 4, M, N)) :|: P >= 1 && 7 >= P f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, C, C, E, E, O, 7, 1, P, O, 7, 4, M, N)) :|: 7 >= O && 1 >= P && P >= 0 && O >= 1 && H >= 1 && H <= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 1, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H >= 1 && H <= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 1, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H >= 1 && H <= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 2, M, N)) :|: M >= E + 2 && N >= C + 2 && M >= 1 && N >= 1 && 7 >= P && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 7, M, N)) :|: E + 1 >= M && C + 1 >= N && 7 >= P && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 The start-symbols are:[f0_14] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f0 0: f0 -> f1 : [], cost: 1 1: f1 -> f7 : A'=1, B'=C, D'=E, F'=free, G'=free_1, H'=0, Q'=1, J'=free, K'=free_1, L'=7, [ 7>=free_1 && 7>=free && 3>=free_1 && free_1>=1 && free>=1 ], cost: 1 2: f1 -> f7 : A'=1, B'=C, D'=E, F'=free_2, G'=free_3, H'=0, Q'=1, J'=free_2, K'=free_3, L'=7, [ 7>=free_3 && 7>=free_2 && free_3>=5 && free_2>=1 ], cost: 1 3: f1 -> f7 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_4, G'=4, H'=1, Q'=1, J'=free_4, K'=4, L'=7, [ 7>=free_4 && free_4>=1 ], cost: 1 4: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 7>=free_5 && 3>=free_5 && free_5>=1 ], cost: 1 5: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 1 6: f1 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 1 7: f2 -> f7 : A'=1, B'=C, D'=E, F'=free_7, G'=free_8, Q'=1, J'=free_7, K'=free_8, L'=7, [ 7>=free_8 && 7>=free_7 && 3>=free_8 && free_8>=1 && free_7>=1 ], cost: 1 8: f2 -> f7 : A'=1, B'=C, D'=E, F'=free_9, G'=free_10, Q'=1, J'=free_9, K'=free_10, L'=7, [ 7>=free_10 && 7>=free_9 && free_10>=5 && free_9>=1 ], cost: 1 9: f2 -> f7 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_11, G'=4, H'=1, Q'=1, J'=free_11, K'=4, L'=7, [ 7>=free_11 && free_11>=1 ], cost: 1 10: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_12, G'=free_13, Q'=0, J'=free_12, K'=free_13, L'=3, [ 7>=free_13 && 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 ], cost: 1 11: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_14, G'=free_15, Q'=0, J'=free_14, K'=free_15, L'=3, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 ], cost: 1 12: f2 -> f3 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_16, G'=4, H'=1, Q'=0, J'=free_16, K'=4, L'=3, [ 7>=free_16 && free_16>=1 ], cost: 1 13: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_17, G'=free_18, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_18 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 1 14: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_19, G'=free_20, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 1 15: f3 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_21 && free_21>=1 ], cost: 1 16: f6 -> f4 : A'=1, B'=C, D'=E, F'=free_22, G'=2, H'=0, Q'=1, J'=free_22, K'=2, L'=4, [ free_22>=1 && 7>=free_22 ], cost: 1 17: f6 -> f4 : A'=free_23, B'=C, D'=E, F'=free_24, G'=7, H'=1, Q'=free_23, J'=free_24, K'=7, L'=4, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 ], cost: 1 18: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_26 && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 && H==1 ], cost: 1 19: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 && H==1 ], cost: 1 20: f4 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 1 21: f4 -> f7 : A'=0, B'=C, D'=E, F'=free_30, G'=free_31, Q'=0, J'=free_30, K'=free_31, L'=7, [ E>=M && C>=N && 7>=free_31 && 7>=free_30 && 3>=free_31 && free_31>=1 && free_30>=1 ], cost: 1 22: f4 -> f7 : A'=0, B'=C, D'=E, F'=free_32, G'=free_33, Q'=0, J'=free_32, K'=free_33, L'=7, [ E>=M && C>=N && 7>=free_33 && 7>=free_32 && free_33>=5 && free_32>=1 ], cost: 1 23: f4 -> f7 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_34, G'=4, H'=1, Q'=0, J'=free_34, K'=4, L'=7, [ 1+E>=M && 1+C>=N && 7>=free_34 && free_34>=1 ], cost: 1 24: f4 -> f7 : A'=1, B'=C, D'=E, F'=free_35, G'=free_36, Q'=1, J'=free_35, K'=free_36, L'=7, [ 7>=free_36 && 7>=free_35 && 3>=free_36 && free_36>=1 && free_35>=1 ], cost: 1 25: f4 -> f7 : A'=1, B'=C, D'=E, F'=free_37, G'=free_38, Q'=1, J'=free_37, K'=free_38, L'=7, [ 7>=free_38 && 7>=free_37 && free_38>=5 && free_37>=1 ], cost: 1 26: f4 -> f7 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_39, G'=4, H'=1, Q'=1, J'=free_39, K'=4, L'=7, [ 7>=free_39 && free_39>=1 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: f0 -> f1 : [], cost: 1 Removed unreachable and leaf rules: Start location: f0 0: f0 -> f1 : [], cost: 1 4: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 7>=free_5 && 3>=free_5 && free_5>=1 ], cost: 1 5: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 1 6: f1 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 1 10: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_12, G'=free_13, Q'=0, J'=free_12, K'=free_13, L'=3, [ 7>=free_13 && 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 ], cost: 1 11: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_14, G'=free_15, Q'=0, J'=free_14, K'=free_15, L'=3, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 ], cost: 1 12: f2 -> f3 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_16, G'=4, H'=1, Q'=0, J'=free_16, K'=4, L'=3, [ 7>=free_16 && free_16>=1 ], cost: 1 13: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_17, G'=free_18, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_18 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 1 14: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_19, G'=free_20, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 1 15: f3 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_21 && free_21>=1 ], cost: 1 16: f6 -> f4 : A'=1, B'=C, D'=E, F'=free_22, G'=2, H'=0, Q'=1, J'=free_22, K'=2, L'=4, [ free_22>=1 && 7>=free_22 ], cost: 1 17: f6 -> f4 : A'=free_23, B'=C, D'=E, F'=free_24, G'=7, H'=1, Q'=free_23, J'=free_24, K'=7, L'=4, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 ], cost: 1 18: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_26 && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 && H==1 ], cost: 1 19: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 && H==1 ], cost: 1 20: f4 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 1 Simplified all rules, resulting in: Start location: f0 0: f0 -> f1 : [], cost: 1 4: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 3>=free_5 && free_5>=1 ], cost: 1 5: f1 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 1 6: f1 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 1 10: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_12, G'=free_13, Q'=0, J'=free_12, K'=free_13, L'=3, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 ], cost: 1 11: f2 -> f3 : A'=0, B'=C, D'=E, F'=free_14, G'=free_15, Q'=0, J'=free_14, K'=free_15, L'=3, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 ], cost: 1 12: f2 -> f3 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_16, G'=4, H'=1, Q'=0, J'=free_16, K'=4, L'=3, [ 7>=free_16 && free_16>=1 ], cost: 1 13: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_17, G'=free_18, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 1 14: f3 -> f6 : A'=1, B'=C, D'=E, F'=free_19, G'=free_20, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 1 15: f3 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_21 && free_21>=1 ], cost: 1 16: f6 -> f4 : A'=1, B'=C, D'=E, F'=free_22, G'=2, H'=0, Q'=1, J'=free_22, K'=2, L'=4, [ free_22>=1 && 7>=free_22 ], cost: 1 17: f6 -> f4 : A'=free_23, B'=C, D'=E, F'=free_24, G'=7, H'=1, Q'=free_23, J'=free_24, K'=7, L'=4, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 ], cost: 1 18: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 && H==1 ], cost: 1 19: f4 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 && H==1 ], cost: 1 20: f4 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: f0 27: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 3>=free_5 && free_5>=1 ], cost: 2 28: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 2 29: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 2 30: f2 -> f6 : A'=1, B'=C, D'=E, F'=free_17, G'=free_18, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 2 31: f2 -> f6 : A'=1, B'=C, D'=E, F'=free_19, G'=free_20, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 2 32: f2 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_21 && free_21>=1 ], cost: 2 33: f2 -> f6 : A'=1, B'=C, D'=E, F'=free_17, G'=free_18, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 2 34: f2 -> f6 : A'=1, B'=C, D'=E, F'=free_19, G'=free_20, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 2 35: f2 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_21 && free_21>=1 ], cost: 2 36: f2 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_17, G'=free_18, H'=1, Q'=1, J'=free_17, K'=free_18, L'=6, [ 7>=free_16 && free_16>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 ], cost: 2 37: f2 -> f6 : A'=1, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_19, G'=free_20, H'=1, Q'=1, J'=free_19, K'=free_20, L'=6, [ 7>=free_16 && free_16>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 ], cost: 2 38: f2 -> f6 : A'=1, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_21, G'=4, H'=1, Q'=1, J'=free_21, K'=4, L'=6, [ 7>=free_16 && free_16>=1 && 7>=free_21 && free_21>=1 ], cost: 2 39: f6 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ free_22>=1 && 7>=free_22 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 2 40: f6 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 2 41: f6 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 2 42: f6 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: f0 27: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 3>=free_5 && free_5>=1 ], cost: 2 28: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 2 29: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 2 43: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && free_22>=1 && 7>=free_22 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 44: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 45: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 46: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 47: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && free_22>=1 && 7>=free_22 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 48: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 49: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 50: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 51: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_21 && free_21>=1 && free_22>=1 && 7>=free_22 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 52: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 53: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 54: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_12 && 3>=free_13 && free_13>=1 && free_12>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 55: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && free_22>=1 && 7>=free_22 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 56: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 57: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 58: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 59: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && free_22>=1 && 7>=free_22 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 60: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 61: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 62: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 63: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_21 && free_21>=1 && free_22>=1 && 7>=free_22 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 64: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 65: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 66: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_15 && 7>=free_14 && free_15>=5 && free_14>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 67: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && free_22>=1 && 7>=free_22 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 68: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 69: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 70: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_17 && 3>=free_18 && free_18>=1 && free_17>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 71: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && free_22>=1 && 7>=free_22 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 72: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 73: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 74: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_20 && 7>=free_19 && free_20>=5 && free_19>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 75: f2 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_21 && free_21>=1 && free_22>=1 && 7>=free_22 && M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 76: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 77: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 78: f2 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ 7>=free_16 && free_16>=1 && 7>=free_21 && free_21>=1 && 7>=free_24 && 1>=free_23 && free_23>=0 && free_24>=1 && M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 59: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 60: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 61: f2 -> f2 : A'=0, B'=C, D'=E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 62: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 72: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 73: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 74: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 76: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 77: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 78: f2 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 Found no metering function for rule 59. Accelerated rule 60 with NONTERM, yielding the new rule 79. Accelerated rule 61 with NONTERM, yielding the new rule 80. Found no metering function for rule 62. Found no metering function for rule 72. Found no metering function for rule 73. Found no metering function for rule 74. Found no metering function for rule 76. Found no metering function for rule 77. Found no metering function for rule 78. Removing the simple loops: 60 61. Accelerated all simple loops using metering functions (where possible): Start location: f0 27: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 3>=free_5 && free_5>=1 ], cost: 2 28: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 2 29: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 2 59: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 62: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ H==1 && M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 72: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 73: f2 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 74: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 76: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 4 77: f2 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 4 78: f2 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 4 79: f2 -> [7] : [ H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: NONTERM 80: f2 -> [7] : [ H==1 && M>=1 && M>=1+E && N>=1 && N>=1+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: f0 27: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_5, H'=0, Q'=0, J'=3, K'=free_5, L'=2, [ 3>=free_5 && free_5>=1 ], cost: 2 28: f0 -> f2 : A'=0, B'=C, D'=E, F'=3, G'=free_6, H'=0, Q'=0, J'=3, K'=free_6, L'=2, [ 7>=free_6 && free_6>=5 ], cost: 2 29: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [], cost: 2 81: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 82: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=2+E && N>=2+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 83: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 84: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 85: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 86: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 87: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 88: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 89: f0 -> f2 : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 90: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 91: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 92: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=3+E && N>=3+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 93: f0 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 94: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 95: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 96: f0 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_25, G'=free_26, H'=1, Q'=0, J'=free_25, K'=free_26, L'=2, [ M>=1 && M>=4+E && N>=1 && N>=4+C && 7>=free_25 && 3>=free_26 && free_26>=1 && free_25>=1 ], cost: 6 97: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 98: f0 -> f2 : A'=0, B'=2+C, C'=2+C, D'=2+E, E'=2+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=3+E && N>=1 && N>=3+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 99: f0 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_27, G'=free_28, H'=1, Q'=0, J'=free_27, K'=free_28, L'=2, [ M>=1 && M>=4+E && N>=1 && N>=4+C && 7>=free_28 && 7>=free_27 && free_28>=5 && free_27>=1 ], cost: 6 100: f0 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 101: f0 -> f2 : A'=0, B'=3+C, C'=3+C, D'=3+E, E'=3+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=4+E && N>=4+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 102: f0 -> f2 : A'=0, B'=4+C, C'=4+C, D'=4+E, E'=4+E, F'=free_29, G'=4, H'=1, Q'=0, J'=free_29, K'=4, L'=2, [ M>=5+E && N>=5+C && M>=1 && N>=1 && 7>=free_29 && free_29>=1 ], cost: 6 103: f0 -> [7] : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C ], cost: NONTERM 104: f0 -> [7] : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: f0 103: f0 -> [7] : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C ], cost: NONTERM 104: f0 -> [7] : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f0 104: f0 -> [7] : A'=0, B'=1+C, C'=1+C, D'=1+E, E'=1+E, F'=3, G'=4, H'=1, Q'=0, J'=3, K'=4, L'=2, [ M>=1 && M>=2+E && N>=1 && N>=2+C ], cost: NONTERM Computing asymptotic complexity for rule 104 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ M>=1 && M>=2+E && N>=1 && N>=2+C ] NO ---------------------------------------- (2) BOUNDS(INF, INF)