/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 12.8 s] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f2(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= B f75(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D + 1 f75(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1 + C f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f15(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= C f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= A f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f24(A, B, C, D, E, V, W, V + W, 0, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= 1 + D f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f15(A, B, C, D + 1, E, V, W, V + W, X, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= X + 1 && A >= 1 + D f15(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f15(A, B, C, D + 1, E, V, W, V + W, X, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: X >= 1 && A >= 1 + D f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f75(A, B, C, C, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D && C <= D f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f28(A, B, C, D, E + 1, F, G, H, I, E, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D + 1 f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f28(A, B, C, D, E + 1, F, G, H, I, E, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1 + C f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, V, W, M, N, O, P, Q, R, S, T, U)) :|: 29 >= J f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, V, W, M, N, O, P, Q, R, S, T, U)) :|: J >= 31 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f32(A, B, C, D, E, F, G, H, I, 30, V, W, M, N, O, P, Q, R, S, T, U)) :|: J >= 30 && J <= 30 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B, C, D, E, F, G, H, I, J, V, L, W, W, 1, 1, 0, R, S, T, U)) :|: K >= 0 f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B, C, D, E, F, G, H, I, J, V, L, M, -(W), 1, 1, 0, W, S, T, U)) :|: 0 >= K + 1 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= B + 1 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f68(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, V, W, U)) :|: B >= C f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f60(A, B, C, D, E, F, G, H, I, J, V, W, M, N, X, Z, A1, R, B1, C1, U)) :|: B >= C && 0 >= Y + 1 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f60(A, B, C, D, E, F, G, H, I, J, V, W, M, N, X, Z, A1, R, B1, C1, U)) :|: B >= C && Y >= 1 f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, V, T, U + 1)) :|: A >= U f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, S, T, U)) :|: B >= C && L >= 0 && L <= 0 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= L + 1 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: L >= 1 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, S, T, U)) :|: C >= B + 1 && L >= 0 && L <= 0 f75(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f10(A, B, C + 1, C, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D && C <= D f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B - 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: U >= 1 + A f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= 1 + A f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: B >= 1 + A start(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE The start-symbols are:[start_21] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: f2 -> f2 : B'=1+B, [ A>=B ], cost: 1 28: f2 -> f10 : [ B>=1+A ], cost: 1 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 27: f10 -> f1 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, E'=H, F'=Q, G'=J, H'=K, Q'=L, J'=M, K'=N, L'=O, M'=P, N'=Q_1, O'=R, P'=S, Q_1'=T, R'=U, [ C>=1+A ], cost: 1 4: f15 -> f24 : [ D>=A ], cost: 1 5: f15 -> f24 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 6: f15 -> f15 : D'=1+D, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: 1 7: f15 -> f15 : D'=1+D, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: 1 8: f24 -> f75 : D'=C, [ C==D ], cost: 1 9: f24 -> f28 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 10: f24 -> f28 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 11: f28 -> f32 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 12: f28 -> f32 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 13: f28 -> f32 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 14: f32 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 15: f32 -> f42 : K'=free_16, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 0>=1+K ], cost: 1 16: f42 -> f68 : [ C>=1+B ], cost: 1 17: f42 -> f68 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 1 18: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && 0>=1+free_20 ], cost: 1 19: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && free_28>=1 ], cost: 1 20: f60 -> f60 : S'=free_36, U'=1+U, [ A>=U ], cost: 1 26: f60 -> f42 : B'=-1+B, [ U>=1+A ], cost: 1 21: f68 -> f75 : L'=0, [ B>=C && L==0 ], cost: 1 22: f68 -> f75 : [ 0>=1+L ], cost: 1 23: f68 -> f75 : [ L>=1 ], cost: 1 24: f68 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 1 29: start -> f2 : [], cost: 1 Removed unreachable and leaf rules: Start location: start 0: f2 -> f2 : B'=1+B, [ A>=B ], cost: 1 28: f2 -> f10 : [ B>=1+A ], cost: 1 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 4: f15 -> f24 : [ D>=A ], cost: 1 5: f15 -> f24 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 6: f15 -> f15 : D'=1+D, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: 1 7: f15 -> f15 : D'=1+D, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: 1 8: f24 -> f75 : D'=C, [ C==D ], cost: 1 9: f24 -> f28 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 10: f24 -> f28 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 11: f28 -> f32 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 12: f28 -> f32 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 13: f28 -> f32 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 14: f32 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 15: f32 -> f42 : K'=free_16, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 0>=1+K ], cost: 1 16: f42 -> f68 : [ C>=1+B ], cost: 1 17: f42 -> f68 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 1 18: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && 0>=1+free_20 ], cost: 1 19: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && free_28>=1 ], cost: 1 20: f60 -> f60 : S'=free_36, U'=1+U, [ A>=U ], cost: 1 26: f60 -> f42 : B'=-1+B, [ U>=1+A ], cost: 1 21: f68 -> f75 : L'=0, [ B>=C && L==0 ], cost: 1 22: f68 -> f75 : [ 0>=1+L ], cost: 1 23: f68 -> f75 : [ L>=1 ], cost: 1 24: f68 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 1 29: start -> f2 : [], cost: 1 Simplified all rules, resulting in: Start location: start 0: f2 -> f2 : B'=1+B, [ A>=B ], cost: 1 28: f2 -> f10 : [ B>=1+A ], cost: 1 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 4: f15 -> f24 : [ D>=A ], cost: 1 5: f15 -> f24 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 6: f15 -> f15 : D'=1+D, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: 1 7: f15 -> f15 : D'=1+D, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: 1 8: f24 -> f75 : D'=C, [ C==D ], cost: 1 9: f24 -> f28 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 10: f24 -> f28 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 11: f28 -> f32 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 12: f28 -> f32 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 13: f28 -> f32 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 14: f32 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 15: f32 -> f42 : K'=free_16, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 0>=1+K ], cost: 1 16: f42 -> f68 : [ C>=1+B ], cost: 1 17: f42 -> f68 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 1 18: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C ], cost: 1 19: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C ], cost: 1 20: f60 -> f60 : S'=free_36, U'=1+U, [ A>=U ], cost: 1 26: f60 -> f42 : B'=-1+B, [ U>=1+A ], cost: 1 21: f68 -> f75 : L'=0, [ B>=C && L==0 ], cost: 1 22: f68 -> f75 : [ 0>=1+L ], cost: 1 23: f68 -> f75 : [ L>=1 ], cost: 1 24: f68 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 1 29: start -> f2 : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: f2 -> f2 : B'=1+B, [ A>=B ], cost: 1 Accelerated rule 0 with metering function 1-B+A, yielding the new rule 30. Removing the simple loops: 0. Accelerating simple loops of location 3. Accelerating the following rules: 6: f15 -> f15 : D'=1+D, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: 1 7: f15 -> f15 : D'=1+D, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: 1 Accelerated rule 6 with metering function -D+A, yielding the new rule 31. Accelerated rule 7 with metering function -D+A, yielding the new rule 32. Removing the simple loops: 6 7. Accelerating simple loops of location 8. Accelerating the following rules: 20: f60 -> f60 : S'=free_36, U'=1+U, [ A>=U ], cost: 1 Accelerated rule 20 with metering function 1+A-U, yielding the new rule 33. Removing the simple loops: 20. Accelerated all simple loops using metering functions (where possible): Start location: start 28: f2 -> f10 : [ B>=1+A ], cost: 1 30: f2 -> f2 : B'=1+A, [ A>=B ], cost: 1-B+A 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 4: f15 -> f24 : [ D>=A ], cost: 1 5: f15 -> f24 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 31: f15 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: -D+A 32: f15 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: -D+A 8: f24 -> f75 : D'=C, [ C==D ], cost: 1 9: f24 -> f28 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 10: f24 -> f28 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 11: f28 -> f32 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 12: f28 -> f32 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 13: f28 -> f32 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 14: f32 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 15: f32 -> f42 : K'=free_16, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 0>=1+K ], cost: 1 16: f42 -> f68 : [ C>=1+B ], cost: 1 17: f42 -> f68 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 1 18: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C ], cost: 1 19: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C ], cost: 1 26: f60 -> f42 : B'=-1+B, [ U>=1+A ], cost: 1 33: f60 -> f60 : S'=free_36, U'=1+A, [ A>=U ], cost: 1+A-U 21: f68 -> f75 : L'=0, [ B>=C && L==0 ], cost: 1 22: f68 -> f75 : [ 0>=1+L ], cost: 1 23: f68 -> f75 : [ L>=1 ], cost: 1 24: f68 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 1 29: start -> f2 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 28: f2 -> f10 : [ B>=1+A ], cost: 1 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 4: f15 -> f24 : [ D>=A ], cost: 1 5: f15 -> f24 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 8: f24 -> f75 : D'=C, [ C==D ], cost: 1 9: f24 -> f28 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 10: f24 -> f28 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 11: f28 -> f32 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 12: f28 -> f32 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 13: f28 -> f32 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 14: f32 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 15: f32 -> f42 : K'=free_16, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 0>=1+K ], cost: 1 16: f42 -> f68 : [ C>=1+B ], cost: 1 17: f42 -> f68 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 1 18: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C ], cost: 1 19: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C ], cost: 1 41: f42 -> f60 : K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ B>=C && A>=U ], cost: 2+A-U 42: f42 -> f60 : K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ B>=C && A>=U ], cost: 2+A-U 26: f60 -> f42 : B'=-1+B, [ U>=1+A ], cost: 1 21: f68 -> f75 : L'=0, [ B>=C && L==0 ], cost: 1 22: f68 -> f75 : [ 0>=1+L ], cost: 1 23: f68 -> f75 : [ L>=1 ], cost: 1 24: f68 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 1 29: start -> f2 : [], cost: 1 34: start -> f2 : B'=1+A, [ A>=B ], cost: 2-B+A Eliminated locations (on tree-shaped paths): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 2: f75 -> f15 : [ D>=1+C ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 46: f15 -> f28 : E'=1+E, J'=E, [ D>=A && C>=1+D ], cost: 2 47: f15 -> f28 : E'=1+E, J'=E, [ D>=A && D>=1+C ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 49: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && C>=1+D ], cost: 2 50: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && D>=1+C ], cost: 2 51: f28 -> f42 : K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ 29>=J && free_8>=0 ], cost: 2 52: f28 -> f42 : K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 29>=J && 0>=1+free_8 ], cost: 2 53: f28 -> f42 : K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ J>=31 && free_10>=0 ], cost: 2 54: f28 -> f42 : K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J>=31 && 0>=1+free_10 ], cost: 2 55: f28 -> f42 : J'=30, K'=free_14, L'=free_13, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ J==30 && free_12>=0 ], cost: 2 56: f28 -> f42 : J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J==30 && 0>=1+free_12 ], cost: 2 57: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && U>=1+A ], cost: 2 58: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && U>=1+A ], cost: 2 59: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 60: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Applied pruning (of leafs and parallel rules): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 46: f15 -> f28 : E'=1+E, J'=E, [ D>=A && C>=1+D ], cost: 2 47: f15 -> f28 : E'=1+E, J'=E, [ D>=A && D>=1+C ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 49: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && C>=1+D ], cost: 2 50: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && D>=1+C ], cost: 2 51: f28 -> f42 : K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ 29>=J && free_8>=0 ], cost: 2 52: f28 -> f42 : K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 29>=J && 0>=1+free_8 ], cost: 2 53: f28 -> f42 : K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ J>=31 && free_10>=0 ], cost: 2 54: f28 -> f42 : K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J>=31 && 0>=1+free_10 ], cost: 2 56: f28 -> f42 : J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J==30 && 0>=1+free_12 ], cost: 2 57: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && U>=1+A ], cost: 2 58: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && U>=1+A ], cost: 2 59: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 60: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Accelerating simple loops of location 7. Accelerating the following rules: 57: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && U>=1+A ], cost: 2 58: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && U>=1+A ], cost: 2 59: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 60: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U Accelerated rule 57 with metering function 1+B-C, yielding the new rule 65. Accelerated rule 58 with metering function 1+B-C, yielding the new rule 66. Found no metering function for rule 59. Found no metering function for rule 60. Removing the simple loops: 57 58. Accelerated all simple loops using metering functions (where possible): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 46: f15 -> f28 : E'=1+E, J'=E, [ D>=A && C>=1+D ], cost: 2 47: f15 -> f28 : E'=1+E, J'=E, [ D>=A && D>=1+C ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 49: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && C>=1+D ], cost: 2 50: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && D>=1+C ], cost: 2 51: f28 -> f42 : K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ 29>=J && free_8>=0 ], cost: 2 52: f28 -> f42 : K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 29>=J && 0>=1+free_8 ], cost: 2 53: f28 -> f42 : K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ J>=31 && free_10>=0 ], cost: 2 54: f28 -> f42 : K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J>=31 && 0>=1+free_10 ], cost: 2 56: f28 -> f42 : J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J==30 && 0>=1+free_12 ], cost: 2 59: f42 -> f42 : B'=-1+B, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 60: f42 -> f42 : B'=-1+B, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ B>=C && A>=U ], cost: 3+A-U 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 65: f42 -> f42 : B'=-1+C, K'=free_21, L'=free_24, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ B>=C && U>=1+A ], cost: 2+2*B-2*C 66: f42 -> f42 : B'=-1+C, K'=free_29, L'=free_32, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=C && U>=1+A ], cost: 2+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Chained accelerated rules (with incoming rules): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 46: f15 -> f28 : E'=1+E, J'=E, [ D>=A && C>=1+D ], cost: 2 47: f15 -> f28 : E'=1+E, J'=E, [ D>=A && D>=1+C ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 49: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && C>=1+D ], cost: 2 50: f15 -> f28 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, [ A>=1+D && D>=1+C ], cost: 2 51: f28 -> f42 : K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ 29>=J && free_8>=0 ], cost: 2 52: f28 -> f42 : K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ 29>=J && 0>=1+free_8 ], cost: 2 53: f28 -> f42 : K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ J>=31 && free_10>=0 ], cost: 2 54: f28 -> f42 : K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J>=31 && 0>=1+free_10 ], cost: 2 56: f28 -> f42 : J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ J==30 && 0>=1+free_12 ], cost: 2 67: f28 -> f42 : B'=-1+B, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ 29>=J && B>=C && A>=U ], cost: 5+A-U 68: f28 -> f42 : B'=-1+B, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ 29>=J && B>=C && A>=U ], cost: 5+A-U 69: f28 -> f42 : B'=-1+B, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ J>=31 && B>=C && A>=U ], cost: 5+A-U 70: f28 -> f42 : B'=-1+B, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ J>=31 && B>=C && A>=U ], cost: 5+A-U 71: f28 -> f42 : B'=-1+B, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ J==30 && B>=C && A>=U ], cost: 5+A-U 72: f28 -> f42 : B'=-1+B, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ 29>=J && B>=C && A>=U ], cost: 5+A-U 73: f28 -> f42 : B'=-1+B, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ 29>=J && B>=C && A>=U ], cost: 5+A-U 74: f28 -> f42 : B'=-1+B, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ J>=31 && B>=C && A>=U ], cost: 5+A-U 75: f28 -> f42 : B'=-1+B, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ J>=31 && B>=C && A>=U ], cost: 5+A-U 76: f28 -> f42 : B'=-1+B, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ J==30 && B>=C && A>=U ], cost: 5+A-U 77: f28 -> f42 : B'=-1+C, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ 29>=J && B>=C && U>=1+A ], cost: 4+2*B-2*C 78: f28 -> f42 : B'=-1+C, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ 29>=J && B>=C && U>=1+A ], cost: 4+2*B-2*C 79: f28 -> f42 : B'=-1+C, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ J>=31 && B>=C && U>=1+A ], cost: 4+2*B-2*C 80: f28 -> f42 : B'=-1+C, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ J>=31 && B>=C && U>=1+A ], cost: 4+2*B-2*C 81: f28 -> f42 : B'=-1+C, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ J==30 && B>=C && U>=1+A ], cost: 4+2*B-2*C 82: f28 -> f42 : B'=-1+C, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ 29>=J && B>=C && U>=1+A ], cost: 4+2*B-2*C 83: f28 -> f42 : B'=-1+C, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ 29>=J && B>=C && U>=1+A ], cost: 4+2*B-2*C 84: f28 -> f42 : B'=-1+C, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ J>=31 && B>=C && U>=1+A ], cost: 4+2*B-2*C 85: f28 -> f42 : B'=-1+C, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ J>=31 && B>=C && U>=1+A ], cost: 4+2*B-2*C 86: f28 -> f42 : B'=-1+C, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ J==30 && B>=C && U>=1+A ], cost: 4+2*B-2*C 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Eliminated locations (on tree-shaped paths): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 87: f15 -> f42 : E'=1+E, J'=E, K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ D>=A && C>=1+D && 29>=E && free_8>=0 ], cost: 4 88: f15 -> f42 : E'=1+E, J'=E, K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && C>=1+D && 29>=E && 0>=1+free_8 ], cost: 4 89: f15 -> f42 : E'=1+E, J'=E, K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ D>=A && C>=1+D && E>=31 && free_10>=0 ], cost: 4 90: f15 -> f42 : E'=1+E, J'=E, K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && C>=1+D && E>=31 && 0>=1+free_10 ], cost: 4 91: f15 -> f42 : E'=1+E, J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && C>=1+D && E==30 && 0>=1+free_12 ], cost: 4 92: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ D>=A && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 93: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 94: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ D>=A && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 95: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 96: f15 -> f42 : B'=-1+B, E'=1+E, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && C>=1+D && E==30 && B>=C && A>=U ], cost: 7+A-U 97: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ D>=A && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 98: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 99: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ D>=A && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 100: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 101: f15 -> f42 : B'=-1+B, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && C>=1+D && E==30 && B>=C && A>=U ], cost: 7+A-U 102: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 103: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 104: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 105: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 106: f15 -> f42 : B'=-1+C, E'=1+E, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 107: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 108: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 109: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 110: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 111: f15 -> f42 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 112: f15 -> f42 : E'=1+E, J'=E, K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ D>=A && D>=1+C && 29>=E && free_8>=0 ], cost: 4 113: f15 -> f42 : E'=1+E, J'=E, K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && D>=1+C && 29>=E && 0>=1+free_8 ], cost: 4 114: f15 -> f42 : E'=1+E, J'=E, K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ D>=A && D>=1+C && E>=31 && free_10>=0 ], cost: 4 115: f15 -> f42 : E'=1+E, J'=E, K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && D>=1+C && E>=31 && 0>=1+free_10 ], cost: 4 116: f15 -> f42 : E'=1+E, J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ D>=A && D>=1+C && E==30 && 0>=1+free_12 ], cost: 4 117: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ D>=A && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 118: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 119: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ D>=A && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 120: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 121: f15 -> f42 : B'=-1+B, E'=1+E, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ D>=A && D>=1+C && E==30 && B>=C && A>=U ], cost: 7+A-U 122: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ D>=A && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 123: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 124: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ D>=A && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 125: f15 -> f42 : B'=-1+B, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 126: f15 -> f42 : B'=-1+B, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ D>=A && D>=1+C && E==30 && B>=C && A>=U ], cost: 7+A-U 127: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 128: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 129: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 130: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 131: f15 -> f42 : B'=-1+C, E'=1+E, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ D>=A && D>=1+C && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 132: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ D>=A && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 133: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 134: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ D>=A && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 135: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 136: f15 -> f42 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && D>=1+C && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 137: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ A>=1+D && C>=1+D && 29>=E && free_8>=0 ], cost: 4 138: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && C>=1+D && 29>=E && 0>=1+free_8 ], cost: 4 139: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ A>=1+D && C>=1+D && E>=31 && free_10>=0 ], cost: 4 140: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && C>=1+D && E>=31 && 0>=1+free_10 ], cost: 4 141: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && C>=1+D && E==30 && 0>=1+free_12 ], cost: 4 142: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 143: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 144: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 145: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 146: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && C>=1+D && E==30 && B>=C && A>=U ], cost: 7+A-U 147: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 148: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && C>=1+D && 29>=E && B>=C && A>=U ], cost: 7+A-U 149: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 150: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && C>=1+D && E>=31 && B>=C && A>=U ], cost: 7+A-U 151: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && C>=1+D && E==30 && B>=C && A>=U ], cost: 7+A-U 152: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 153: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 154: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 155: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 156: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 157: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 158: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 159: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 160: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 161: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 162: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_14, L'=free_9, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ A>=1+D && D>=1+C && 29>=E && free_8>=0 ], cost: 4 163: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_16, L'=free_9, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && D>=1+C && 29>=E && 0>=1+free_8 ], cost: 4 164: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_14, L'=free_11, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ A>=1+D && D>=1+C && E>=31 && free_10>=0 ], cost: 4 165: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_16, L'=free_11, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && D>=1+C && E>=31 && 0>=1+free_10 ], cost: 4 166: f15 -> f42 : E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_16, L'=free_13, N'=-free_17, O'=1, P'=1, Q_1'=0, R'=free_17, [ A>=1+D && D>=1+C && E==30 && 0>=1+free_12 ], cost: 4 167: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 168: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 169: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 170: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 171: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_36, T'=free_22, U'=1+A, [ A>=1+D && D>=1+C && E==30 && B>=C && A>=U ], cost: 7+A-U 172: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 173: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && D>=1+C && 29>=E && B>=C && A>=U ], cost: 7+A-U 174: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 175: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && D>=1+C && E>=31 && B>=C && A>=U ], cost: 7+A-U 176: f15 -> f42 : B'=-1+B, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_36, T'=free_30, U'=1+A, [ A>=1+D && D>=1+C && E==30 && B>=C && A>=U ], cost: 7+A-U 177: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ A>=1+D && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 178: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 179: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ A>=1+D && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 180: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 181: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && D>=1+C && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 182: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 183: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && D>=1+C && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 184: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 185: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && D>=1+C && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 186: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ A>=1+D && D>=1+C && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Applied pruning (of leafs and parallel rules): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 102: f15 -> f42 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 111: f15 -> f42 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 156: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 157: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 159: f15 -> f42 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 61: f42 -> f75 : [ C>=1+B && 0>=1+L ], cost: 2 62: f42 -> f75 : [ C>=1+B && L>=1 ], cost: 2 63: f42 -> f75 : L'=0, [ C>=1+B && L==0 ], cost: 2 64: f42 -> f75 : L'=0, S'=free_18, T'=free_19, [ B>=C ], cost: 2 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Eliminated locations (on tree-shaped paths): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 45: f15 -> f75 : D'=C, [ D>=A && C==D ], cost: 2 48: f15 -> f75 : D'=C, F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D && C==D ], cost: 2 187: f15 -> f75 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_24 ], cost: 8+2*B-2*C 188: f15 -> f75 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 189: f15 -> f75 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=0, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24==0 ], cost: 8+2*B-2*C 190: f15 -> f75 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 191: f15 -> f75 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32>=1 ], cost: 8+2*B-2*C 192: f15 -> f75 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=0, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 193: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_24 ], cost: 8+2*B-2*C 194: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=free_24, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 195: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=30, K'=free_21, L'=0, N'=-free_17, O'=free_26, P'=free_23, Q_1'=free_27, R'=free_17, S'=free_25, T'=free_22, [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A && free_24==0 ], cost: 8+2*B-2*C 196: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 197: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && free_32>=1 ], cost: 8+2*B-2*C 198: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=0, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 199: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 200: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && free_32>=1 ], cost: 8+2*B-2*C 201: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=0, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Applied pruning (of leafs and parallel rules): Start location: start 1: f75 -> f15 : [ C>=1+D ], cost: 1 25: f75 -> f10 : C'=1+C, D'=C, [ C==D ], cost: 1 35: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ C>=1+D && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 36: f75 -> f15 : D'=A, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ D>=1+C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 38: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ C>=1+D && free_7>=1 && A>=1+D ], cost: 1-D+A 39: f75 -> f15 : D'=A, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ D>=1+C && free_7>=1 && A>=1+D ], cost: 1-D+A 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 188: f15 -> f75 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 190: f15 -> f75 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 192: f15 -> f75 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=0, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 196: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 199: f15 -> f75 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Eliminated locations (on tree-shaped paths): Start location: start 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 207: f15 -> f15 : B'=-1+C, E'=1+E, J'=E, K'=free_21, L'=free_24, M'=free_15, N'=free_15, O'=free_26, P'=free_23, Q_1'=free_27, S'=free_25, T'=free_22, [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 9+2*B-2*C 208: f15 -> f15 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 209: f15 -> f15 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=0, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 9+2*B-2*C 210: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 211: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 212: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 && free_7>=1 ], cost: 9+2*B-D+A-2*C 213: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 214: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 215: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 && free_7>=1 ], cost: 9+2*B-D+A-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Applied pruning (of leafs and parallel rules): Start location: start 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 208: f15 -> f15 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 210: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 211: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 213: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 214: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Accelerating simple loops of location 3. Accelerating the following rules: 208: f15 -> f15 : B'=-1+C, E'=1+E, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 210: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 211: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 213: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 214: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C Accelerated rule 208 with metering function 30-E, yielding the new rule 221. Found no metering function for rule 210. Found no metering function for rule 211. Found no metering function for rule 213. Found no metering function for rule 214. Removing the simple loops: 208. Accelerated all simple loops using metering functions (where possible): Start location: start 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 210: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 211: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 213: f15 -> f15 : B'=-1+C, E'=1+E, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 9+2*B-2*C 214: f15 -> f15 : B'=-1+C, D'=A, E'=1+E, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=E, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 9+2*B-D+A-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 221: f15 -> f15 : B'=-1+C, E'=30, J'=30, K'=free_29, L'=free_32, N'=-free_17, O'=free_34, P'=free_31, Q_1'=free_35, R'=free_17, S'=free_33, T'=free_30, [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 && 30-E>=1 ], cost: 210-7*E 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Chained accelerated rules (with incoming rules): Start location: start 3: f10 -> f15 : E'=0, [ A>=C ], cost: 1 37: f10 -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=C && 0>=1+free_4 && A>=1+D ], cost: 1-D+A 40: f10 -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=C && free_7>=1 && A>=1+D ], cost: 1-D+A 222: f10 -> f15 : B'=-1+C, E'=1, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 10+2*B-2*C 223: f10 -> f15 : B'=-1+C, D'=A, E'=1, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 10+2*B-D+A-2*C 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 43: start -> f10 : [ B>=1+A ], cost: 2 44: start -> f10 : B'=1+A, [ A>=B ], cost: 3-B+A Eliminated locations (on tree-shaped paths): Start location: start 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 224: start -> f15 : E'=0, [ B>=1+A && A>=C ], cost: 3 225: start -> f15 : D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ B>=1+A && A>=C && 0>=1+free_4 && A>=1+D ], cost: 3-D+A 226: start -> f15 : D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ B>=1+A && A>=C && free_7>=1 && A>=1+D ], cost: 3-D+A 227: start -> f15 : B'=-1+C, E'=1, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 12+2*B-2*C 228: start -> f15 : B'=-1+C, D'=A, E'=1, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 12+2*B-D+A-2*C 229: start -> f15 : B'=1+A, E'=0, [ A>=B && A>=C ], cost: 4-B+A 230: start -> f15 : B'=1+A, D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=B && A>=C && 0>=1+free_4 && A>=1+D ], cost: 4-B-D+2*A 231: start -> f15 : B'=1+A, D'=A, E'=0, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ A>=B && A>=C && free_7>=1 && A>=1+D ], cost: 4-B-D+2*A 232: start -> f15 : B'=-1+C, E'=1, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ], cost: 15-B+3*A-2*C 233: start -> f15 : B'=-1+C, D'=A, E'=1, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 15-B-D+4*A-2*C Applied pruning (of leafs and parallel rules): Start location: start 202: f15 -> [16] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 203: f15 -> [16] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 204: f15 -> [16] : [ A>=1+D && C>=1+D && E==30 && B>=C && U>=1+A ], cost: 6+2*B-2*C 205: f15 -> [16] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A ], cost: 6+2*B-2*C 206: f15 -> [16] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A ], cost: 6+2*B-2*C 216: f15 -> [17] : [ D>=A && C>=1+D && 29>=E && B>=C && U>=1+A && free_24>=1 ], cost: 8+2*B-2*C 217: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 218: f15 -> [17] : [ D>=A && C>=1+D && E==30 && B>=C && U>=1+A && free_32==0 ], cost: 8+2*B-2*C 219: f15 -> [17] : [ A>=1+D && C>=1+D && 29>=E && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 220: f15 -> [17] : [ A>=1+D && C>=1+D && E>=31 && B>=C && U>=1+A && 0>=1+free_32 ], cost: 8+2*B-2*C 227: start -> f15 : B'=-1+C, E'=1, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 12+2*B-2*C 228: start -> f15 : B'=-1+C, D'=A, E'=1, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 12+2*B-D+A-2*C 230: start -> f15 : B'=1+A, D'=A, E'=0, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ A>=B && A>=C && 0>=1+free_4 && A>=1+D ], cost: 4-B-D+2*A 232: start -> f15 : B'=-1+C, E'=1, F'=free, G'=free_1, H'=free_1+free, Q'=0, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ], cost: 15-B+3*A-2*C 233: start -> f15 : B'=-1+C, D'=A, E'=1, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, J'=0, K'=free_29, L'=free_32, M'=free_15, N'=free_15, O'=free_34, P'=free_31, Q_1'=free_35, S'=free_33, T'=free_30, [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 15-B-D+4*A-2*C Eliminated locations (on tree-shaped paths): Start location: start 234: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 12+2*B-2*C 235: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 12+2*B-D+A-2*C 236: start -> [19] : [ A>=B && A>=C && 0>=1+free_4 && A>=1+D ], cost: 4-B-D+2*A 237: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ], cost: 15-B+3*A-2*C 238: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 15-B-D+4*A-2*C Applied pruning (of leafs and parallel rules): Start location: start 234: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 12+2*B-2*C 235: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 12+2*B-D+A-2*C 236: start -> [19] : [ A>=B && A>=C && 0>=1+free_4 && A>=1+D ], cost: 4-B-D+2*A 237: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ], cost: 15-B+3*A-2*C 238: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 15-B-D+4*A-2*C ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start 234: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 ], cost: 12+2*B-2*C 235: start -> [19] : [ B>=1+A && A>=C && A>=1+D && C>=1+D && B>=C && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 12+2*B-D+A-2*C 236: start -> [19] : [ A>=B && A>=C && 0>=1+free_4 && A>=1+D ], cost: 4-B-D+2*A 237: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ], cost: 15-B+3*A-2*C 238: start -> [19] : [ A>=B && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 && 0>=1+free_4 ], cost: 15-B-D+4*A-2*C Computing asymptotic complexity for rule 234 Solved the limit problem by the following transformations: Created initial limit problem: -D+C (+/+!), -free_32 (+/+!), 12+2*B-2*C (+), -D+A (+/+!), -A+U (+/+!), 1+A-C (+/+!), B-A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {B==1,D==-1-n,A==0,U==1,C==-n,free_32==-n} resulting limit problem: [solved] Solution: B / 1 D / -1-n A / 0 U / 1 C / -n free_32 / -n Resulting cost 14+2*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 14+2*n Rule cost: 12+2*B-2*C Rule guard: [ B>=1+A && A>=C && A>=1+D && C>=1+D && U>=1+A && 0>=1+free_32 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (2) BOUNDS(n^1, INF)