/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(max(4 * Arg_1, 4 * Arg_1 + nat(8 + 8 * Arg_0 + -8 * Arg_1)) + max(-4 * Arg_3, min(-4 * Arg_3 + min(-8 + -8 * Arg_0 + 8 * Arg_3, 0), -4 * Arg_3))) + nat(4 + 4 * Arg_0 + -4 * Arg_3) + max(1, 2 + Arg_0 + -1 * Arg_3) + max(2, 3 + 3 * Arg_0 + max(-3 * Arg_3, min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3))) + nat(3 + 3 * Arg_0 + -3 * Arg_1) + nat(-3 * Arg_3 + max(3 * Arg_1, 3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1))) + nat(2 * Arg_0 + -2 * Arg_3) + nat(-1 * Arg_7 + max(Arg_1 + nat(2 + 2 * Arg_0 + -2 * Arg_1), Arg_1)) + nat(1 + 2 * Arg_0 + max(-2 * Arg_3, min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3))) + nat(max(5 * Arg_1, 5 * Arg_1 + nat(10 + 10 * Arg_0 + -10 * Arg_1)) + max(min(-5 * Arg_3 + min(-10 + -10 * Arg_0 + 10 * Arg_3, 0), -5 * Arg_3), -5 * Arg_3))). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 14.1 s] (2) BOUNDS(1, nat(max(4 * Arg_1, 4 * Arg_1 + nat(8 + 8 * Arg_0 + -8 * Arg_1)) + max(-4 * Arg_3, min(-4 * Arg_3 + min(-8 + -8 * Arg_0 + 8 * Arg_3, 0), -4 * Arg_3))) + nat(4 + 4 * Arg_0 + -4 * Arg_3) + max(1, 2 + Arg_0 + -1 * Arg_3) + max(2, 3 + 3 * Arg_0 + max(-3 * Arg_3, min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3))) + nat(3 + 3 * Arg_0 + -3 * Arg_1) + nat(-3 * Arg_3 + max(3 * Arg_1, 3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1))) + nat(2 * Arg_0 + -2 * Arg_3) + nat(-1 * Arg_7 + max(Arg_1 + nat(2 + 2 * Arg_0 + -2 * Arg_1), Arg_1)) + nat(1 + 2 * Arg_0 + max(-2 * Arg_3, min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3))) + nat(max(5 * Arg_1, 5 * Arg_1 + nat(10 + 10 * Arg_0 + -10 * Arg_1)) + max(min(-5 * Arg_3 + min(-10 + -10 * Arg_0 + 10 * Arg_3, 0), -5 * Arg_3), -5 * Arg_3))) (3) Loat Proof [FINISHED, 18.3 s] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= L + 1 f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: L >= 1 f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE f5(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, 0, D, E, F, G, H, I, J, K)) :|: A >= B f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, C, D + 1, L, L, G, H, I, J, K)) :|: C >= L && A >= D f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, L, D + 1, L, L, G, H, I, J, K)) :|: L >= 1 + C && A >= D f23(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f26(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= D f26(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B, C, D, E, F, L, H, I, J, K)) :|: D >= B + 1 f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B, C, D, E, F, L, H + 1, I, J, K)) :|: B >= H + 1 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f44(A, B, C, D, E, F, L, H, I, J, K)) :|: A >= B f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f44(A, B, C, D, E, F, L, H + 1, I, J, K)) :|: D >= H + 1 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H + 1, L, J, K)) :|: A >= H f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B, C, D, E, F, G, H, L, J, K)) :|: A >= D + 1 f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B, C, D, E, F, G, H, L, J, K)) :|: D >= 1 + A f74(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: A >= B f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, A + 1, E, F, G, H, I, J, K)) :|: A >= D && A <= D f74(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, D + 1, E, F, G, H, I, J, K)) :|: B >= 1 + A f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: H >= 1 + A f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B + 1, C, D, E, F, G, H, M, L, K)) :|: C >= M + 1 && H >= D f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B + 1, L, D, E, F, G, H, L, M, B)) :|: L >= C && H >= D f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && K >= D + 1 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && D >= 1 + K f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, D)) :|: B >= 1 + A && D >= K && D <= K f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f26(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: H >= B f26(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, 0, D, E, F, G, H, I, J, K)) :|: B >= D f23(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K)) :|: D >= 1 + A f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: 0 >= C + 1 && D >= 1 + A f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: C >= 1 && D >= 1 + A f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, 0, D, E, F, G, H, I, J, K)) :|: D >= 1 + A && C >= 0 && C <= 0 f5(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A The start-symbols are:[f2_11] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 1+max([0, 1+Arg_0-Arg_3])+max([0, max([4*Arg_1, 4*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-4*Arg_3, -4*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3])+max([2, 2+1+3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, 1+Arg_0-Arg_3])+max([0, Arg_0-Arg_3])+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, Arg_0-Arg_3])+max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_3])+max([0, max([5*Arg_1, 5*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-5*Arg_3, -5*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3]) {O(n)}) Initial Complexity Problem: Start: f2 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8, Arg_9, Arg_10 Temp_Vars: L Locations: f1, f2, f23, f26, f40, f5, f59, f69, f71, f74, f9 Transitions: f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|: f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_3 f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 && Arg_3 <= Arg_0 f26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f40(Arg_0,Arg_1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 1+Arg_0 <= Arg_1 && Arg_3 <= Arg_1 f40(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_1 && Arg_3+1 <= Arg_10 f40(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_1 && 1+Arg_10 <= Arg_3 f40(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f69(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_3):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_1 && Arg_3 <= Arg_10 && Arg_10 <= Arg_3 f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f9(Arg_0,Arg_1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:Arg_1 <= Arg_0 f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7+1,L,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && Arg_7 <= Arg_0 f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f69(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_7 f69(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && L+1 <= 0 f69(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1 <= L f69(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 f71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f23(Arg_0,Arg_1,Arg_2,Arg_0+1,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && Arg_0 <= Arg_3 && Arg_3 <= Arg_0 f71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f74(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,L,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && Arg_3+1 <= Arg_0 f74(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f23(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:2+Arg_3 <= Arg_1 && 1+Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_1 f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f5(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1 <= Arg_2 && 1+Arg_0 <= Arg_3 f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f5(Arg_0,Arg_1+1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1+Arg_0 <= Arg_3 && Arg_2 <= 0 && 0 <= Arg_2 f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f9(Arg_0,Arg_1,Arg_2,Arg_3+1,L,L,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && L <= Arg_2 && Arg_3 <= Arg_0 f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f9(Arg_0,Arg_1,L,Arg_3+1,L,L,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1+Arg_2 <= L && Arg_3 <= Arg_0 Timebounds: Overall timebound: 1+max([0, 1+Arg_0-Arg_3])+max([0, max([4*Arg_1, 4*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-4*Arg_3, -4*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3])+max([2, 2+1+3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, 1+Arg_0-Arg_3])+max([0, Arg_0-Arg_3])+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, Arg_0-Arg_3])+max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_3])+max([0, max([5*Arg_1, 5*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-5*Arg_3, -5*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3]) {O(n)} 2: f2->f5: 1 {O(1)} 6: f23->f26: max([0, 1+3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 26: f23->f1: 1 {O(1)} 25: f26->f40: max([0, 1+Arg_0-Arg_3]) {O(n)} 21: f40->f59: max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 22: f40->f59: max([0, 1+Arg_0-Arg_3]) {O(n)} 23: f40->f69: max([0, 1+Arg_0-Arg_3]) {O(n)} 3: f5->f9: max([0, 1+Arg_0-Arg_1]) {O(n)} 30: f5->f23: 1 {O(1)} 11: f59->f59: max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 18: f59->f69: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 0: f69->f71: max([0, max([4*Arg_1, 4*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-4*Arg_3, -4*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 1: f69->f71: max([0, max([5*Arg_1, 5*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-5*Arg_3, -5*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 12: f69->f71: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 13: f71->f74: max([0, Arg_0-Arg_3]) {O(n)} 16: f71->f23: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 17: f74->f23: max([0, Arg_0-Arg_3]) {O(n)} 4: f9->f9: max([0, 1+Arg_0-Arg_3]) {O(n)} 5: f9->f9: max([0, 1+Arg_0-Arg_3]) {O(n)} 28: f9->f5: max([0, 1+Arg_0-Arg_1]) {O(n)} 29: f9->f5: max([0, 1+Arg_0-Arg_1]) {O(n)} Costbounds: Overall costbound: 1+max([0, 1+Arg_0-Arg_3])+max([0, max([4*Arg_1, 4*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-4*Arg_3, -4*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3])+max([2, 2+1+3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, 1+Arg_0-Arg_3])+max([0, Arg_0-Arg_3])+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, Arg_0-Arg_3])+max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_3])+max([0, max([5*Arg_1, 5*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-5*Arg_3, -5*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3]) {O(n)} 2: f2->f5: 1 {O(1)} 6: f23->f26: max([0, 1+3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 26: f23->f1: 1 {O(1)} 25: f26->f40: max([0, 1+Arg_0-Arg_3]) {O(n)} 21: f40->f59: max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 22: f40->f59: max([0, 1+Arg_0-Arg_3]) {O(n)} 23: f40->f69: max([0, 1+Arg_0-Arg_3]) {O(n)} 3: f5->f9: max([0, 1+Arg_0-Arg_1]) {O(n)} 30: f5->f23: 1 {O(1)} 11: f59->f59: max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 18: f59->f69: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 0: f69->f71: max([0, max([4*Arg_1, 4*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-4*Arg_3, -4*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 1: f69->f71: max([0, max([5*Arg_1, 5*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-5*Arg_3, -5*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])]) {O(n)} 12: f69->f71: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 13: f71->f74: max([0, Arg_0-Arg_3]) {O(n)} 16: f71->f23: max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 17: f74->f23: max([0, Arg_0-Arg_3]) {O(n)} 4: f9->f9: max([0, 1+Arg_0-Arg_3]) {O(n)} 5: f9->f9: max([0, 1+Arg_0-Arg_3]) {O(n)} 28: f9->f5: max([0, 1+Arg_0-Arg_1]) {O(n)} 29: f9->f5: max([0, 1+Arg_0-Arg_1]) {O(n)} Sizebounds: `Lower: 2: f2->f5, Arg_0: Arg_0 {O(n)} 2: f2->f5, Arg_1: Arg_1 {O(n)} 2: f2->f5, Arg_2: Arg_2 {O(n)} 2: f2->f5, Arg_3: Arg_3 {O(n)} 2: f2->f5, Arg_4: Arg_4 {O(n)} 2: f2->f5, Arg_5: Arg_5 {O(n)} 2: f2->f5, Arg_6: Arg_6 {O(n)} 2: f2->f5, Arg_7: Arg_7 {O(n)} 2: f2->f5, Arg_8: Arg_8 {O(n)} 2: f2->f5, Arg_9: Arg_9 {O(n)} 2: f2->f5, Arg_10: Arg_10 {O(n)} 6: f23->f26, Arg_0: Arg_0 {O(n)} 6: f23->f26, Arg_1: Arg_1 {O(n)} 6: f23->f26, Arg_2: min([0, Arg_2]) {O(n)} 6: f23->f26, Arg_3: Arg_3 {O(n)} 6: f23->f26, Arg_6: Arg_6 {O(n)} 6: f23->f26, Arg_7: Arg_7 {O(n)} 6: f23->f26, Arg_9: Arg_9 {O(n)} 6: f23->f26, Arg_10: min([Arg_3, Arg_10]) {O(n)} 26: f23->f1, Arg_0: Arg_0 {O(n)} 26: f23->f1, Arg_1: Arg_1 {O(n)} 26: f23->f1, Arg_2: min([0, Arg_2]) {O(n)} 26: f23->f1, Arg_3: min([Arg_3, -(-1-Arg_0)]) {O(n)} 26: f23->f1, Arg_6: Arg_6 {O(n)} 26: f23->f1, Arg_7: Arg_7 {O(n)} 26: f23->f1, Arg_9: Arg_9 {O(n)} 26: f23->f1, Arg_10: min([Arg_10, min([Arg_3, Arg_10])]) {O(n)} 25: f26->f40, Arg_0: Arg_0 {O(n)} 25: f26->f40, Arg_1: Arg_1 {O(n)} 25: f26->f40, Arg_2: 0 {O(1)} 25: f26->f40, Arg_3: Arg_3 {O(n)} 25: f26->f40, Arg_6: Arg_6 {O(n)} 25: f26->f40, Arg_7: Arg_7 {O(n)} 25: f26->f40, Arg_9: Arg_9 {O(n)} 25: f26->f40, Arg_10: min([Arg_3, Arg_10]) {O(n)} 21: f40->f59, Arg_0: Arg_0 {O(n)} 21: f40->f59, Arg_1: Arg_1 {O(n)} 21: f40->f59, Arg_2: 0 {O(1)} 21: f40->f59, Arg_3: Arg_3 {O(n)} 21: f40->f59, Arg_6: Arg_6 {O(n)} 21: f40->f59, Arg_7: Arg_7 {O(n)} 21: f40->f59, Arg_9: Arg_9 {O(n)} 21: f40->f59, Arg_10: min([Arg_3, Arg_10]) {O(n)} 22: f40->f59, Arg_0: Arg_0 {O(n)} 22: f40->f59, Arg_1: Arg_1 {O(n)} 22: f40->f59, Arg_2: 0 {O(1)} 22: f40->f59, Arg_3: Arg_3 {O(n)} 22: f40->f59, Arg_6: Arg_6 {O(n)} 22: f40->f59, Arg_7: Arg_7 {O(n)} 22: f40->f59, Arg_9: Arg_9 {O(n)} 22: f40->f59, Arg_10: min([Arg_3, Arg_10]) {O(n)} 23: f40->f69, Arg_0: Arg_0 {O(n)} 23: f40->f69, Arg_1: Arg_1 {O(n)} 23: f40->f69, Arg_2: 0 {O(1)} 23: f40->f69, Arg_3: Arg_3 {O(n)} 23: f40->f69, Arg_6: Arg_6 {O(n)} 23: f40->f69, Arg_7: Arg_7 {O(n)} 23: f40->f69, Arg_9: Arg_9 {O(n)} 23: f40->f69, Arg_10: Arg_3 {O(n)} 3: f5->f9, Arg_0: Arg_0 {O(n)} 3: f5->f9, Arg_1: Arg_1 {O(n)} 3: f5->f9, Arg_2: 0 {O(1)} 3: f5->f9, Arg_3: Arg_3 {O(n)} 3: f5->f9, Arg_6: Arg_6 {O(n)} 3: f5->f9, Arg_7: Arg_7 {O(n)} 3: f5->f9, Arg_8: Arg_8 {O(n)} 3: f5->f9, Arg_9: Arg_9 {O(n)} 3: f5->f9, Arg_10: Arg_10 {O(n)} 30: f5->f23, Arg_0: Arg_0 {O(n)} 30: f5->f23, Arg_1: Arg_1 {O(n)} 30: f5->f23, Arg_2: min([0, Arg_2]) {O(n)} 30: f5->f23, Arg_3: Arg_3 {O(n)} 30: f5->f23, Arg_6: Arg_6 {O(n)} 30: f5->f23, Arg_7: Arg_7 {O(n)} 30: f5->f23, Arg_8: Arg_8 {O(n)} 30: f5->f23, Arg_9: Arg_9 {O(n)} 30: f5->f23, Arg_10: Arg_10 {O(n)} 11: f59->f59, Arg_0: Arg_0 {O(n)} 11: f59->f59, Arg_1: Arg_1 {O(n)} 11: f59->f59, Arg_2: 0 {O(1)} 11: f59->f59, Arg_3: Arg_3 {O(n)} 11: f59->f59, Arg_6: Arg_6 {O(n)} 11: f59->f59, Arg_7: Arg_7 {O(n)} 11: f59->f59, Arg_9: Arg_9 {O(n)} 11: f59->f59, Arg_10: min([Arg_3, Arg_10]) {O(n)} 18: f59->f69, Arg_0: Arg_0 {O(n)} 18: f59->f69, Arg_1: Arg_1 {O(n)} 18: f59->f69, Arg_2: 0 {O(1)} 18: f59->f69, Arg_3: Arg_3 {O(n)} 18: f59->f69, Arg_6: Arg_6 {O(n)} 18: f59->f69, Arg_7: Arg_7 {O(n)} 18: f59->f69, Arg_9: Arg_9 {O(n)} 18: f59->f69, Arg_10: min([Arg_3, Arg_10]) {O(n)} 0: f69->f71, Arg_0: Arg_0 {O(n)} 0: f69->f71, Arg_1: Arg_1 {O(n)} 0: f69->f71, Arg_2: 0 {O(1)} 0: f69->f71, Arg_3: Arg_3 {O(n)} 0: f69->f71, Arg_6: Arg_6 {O(n)} 0: f69->f71, Arg_7: Arg_7 {O(n)} 0: f69->f71, Arg_9: Arg_9 {O(n)} 0: f69->f71, Arg_10: min([Arg_3, Arg_10]) {O(n)} 1: f69->f71, Arg_0: Arg_0 {O(n)} 1: f69->f71, Arg_1: Arg_1 {O(n)} 1: f69->f71, Arg_2: 0 {O(1)} 1: f69->f71, Arg_3: Arg_3 {O(n)} 1: f69->f71, Arg_6: Arg_6 {O(n)} 1: f69->f71, Arg_7: Arg_7 {O(n)} 1: f69->f71, Arg_9: Arg_9 {O(n)} 1: f69->f71, Arg_10: min([Arg_3, Arg_10]) {O(n)} 12: f69->f71, Arg_0: Arg_0 {O(n)} 12: f69->f71, Arg_1: Arg_1 {O(n)} 12: f69->f71, Arg_2: 0 {O(1)} 12: f69->f71, Arg_3: Arg_3 {O(n)} 12: f69->f71, Arg_6: Arg_6 {O(n)} 12: f69->f71, Arg_7: Arg_7 {O(n)} 12: f69->f71, Arg_9: Arg_9 {O(n)} 12: f69->f71, Arg_10: min([Arg_3, Arg_10]) {O(n)} 13: f71->f74, Arg_0: Arg_0 {O(n)} 13: f71->f74, Arg_1: Arg_1 {O(n)} 13: f71->f74, Arg_2: 0 {O(1)} 13: f71->f74, Arg_3: Arg_3 {O(n)} 13: f71->f74, Arg_6: Arg_6 {O(n)} 13: f71->f74, Arg_7: Arg_7 {O(n)} 13: f71->f74, Arg_9: Arg_9 {O(n)} 13: f71->f74, Arg_10: min([Arg_3, Arg_10]) {O(n)} 16: f71->f23, Arg_0: Arg_0 {O(n)} 16: f71->f23, Arg_1: Arg_1 {O(n)} 16: f71->f23, Arg_2: 0 {O(1)} 16: f71->f23, Arg_3: 1+Arg_0 {O(n)} 16: f71->f23, Arg_6: Arg_6 {O(n)} 16: f71->f23, Arg_7: Arg_7 {O(n)} 16: f71->f23, Arg_9: Arg_9 {O(n)} 16: f71->f23, Arg_10: min([Arg_3, Arg_10]) {O(n)} 17: f74->f23, Arg_0: Arg_0 {O(n)} 17: f74->f23, Arg_1: Arg_1 {O(n)} 17: f74->f23, Arg_2: 0 {O(1)} 17: f74->f23, Arg_3: Arg_3 {O(n)} 17: f74->f23, Arg_6: Arg_6 {O(n)} 17: f74->f23, Arg_7: Arg_7 {O(n)} 17: f74->f23, Arg_9: Arg_9 {O(n)} 17: f74->f23, Arg_10: min([Arg_3, Arg_10]) {O(n)} 4: f9->f9, Arg_0: Arg_0 {O(n)} 4: f9->f9, Arg_1: Arg_1 {O(n)} 4: f9->f9, Arg_2: 0 {O(1)} 4: f9->f9, Arg_3: Arg_3 {O(n)} 4: f9->f9, Arg_6: Arg_6 {O(n)} 4: f9->f9, Arg_7: Arg_7 {O(n)} 4: f9->f9, Arg_8: Arg_8 {O(n)} 4: f9->f9, Arg_9: Arg_9 {O(n)} 4: f9->f9, Arg_10: Arg_10 {O(n)} 5: f9->f9, Arg_0: Arg_0 {O(n)} 5: f9->f9, Arg_1: Arg_1 {O(n)} 5: f9->f9, Arg_2: 1 {O(1)} 5: f9->f9, Arg_3: Arg_3 {O(n)} 5: f9->f9, Arg_4: 1 {O(1)} 5: f9->f9, Arg_5: 1 {O(1)} 5: f9->f9, Arg_6: Arg_6 {O(n)} 5: f9->f9, Arg_7: Arg_7 {O(n)} 5: f9->f9, Arg_8: Arg_8 {O(n)} 5: f9->f9, Arg_9: Arg_9 {O(n)} 5: f9->f9, Arg_10: Arg_10 {O(n)} 28: f9->f5, Arg_0: Arg_0 {O(n)} 28: f9->f5, Arg_1: Arg_1 {O(n)} 28: f9->f5, Arg_2: 1 {O(1)} 28: f9->f5, Arg_3: Arg_3 {O(n)} 28: f9->f5, Arg_6: Arg_6 {O(n)} 28: f9->f5, Arg_7: Arg_7 {O(n)} 28: f9->f5, Arg_8: Arg_8 {O(n)} 28: f9->f5, Arg_9: Arg_9 {O(n)} 28: f9->f5, Arg_10: Arg_10 {O(n)} 29: f9->f5, Arg_0: Arg_0 {O(n)} 29: f9->f5, Arg_1: Arg_1 {O(n)} 29: f9->f5, Arg_2: 0 {O(1)} 29: f9->f5, Arg_3: Arg_3 {O(n)} 29: f9->f5, Arg_6: Arg_6 {O(n)} 29: f9->f5, Arg_7: Arg_7 {O(n)} 29: f9->f5, Arg_8: Arg_8 {O(n)} 29: f9->f5, Arg_9: Arg_9 {O(n)} 29: f9->f5, Arg_10: Arg_10 {O(n)} `Upper: 2: f2->f5, Arg_0: Arg_0 {O(n)} 2: f2->f5, Arg_1: Arg_1 {O(n)} 2: f2->f5, Arg_2: Arg_2 {O(n)} 2: f2->f5, Arg_3: Arg_3 {O(n)} 2: f2->f5, Arg_4: Arg_4 {O(n)} 2: f2->f5, Arg_5: Arg_5 {O(n)} 2: f2->f5, Arg_6: Arg_6 {O(n)} 2: f2->f5, Arg_7: Arg_7 {O(n)} 2: f2->f5, Arg_8: Arg_8 {O(n)} 2: f2->f5, Arg_9: Arg_9 {O(n)} 2: f2->f5, Arg_10: Arg_10 {O(n)} 6: f23->f26, Arg_0: Arg_0 {O(n)} 6: f23->f26, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 6: f23->f26, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 6: f23->f26, Arg_6: Arg_6 {O(n)} 6: f23->f26, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 6: f23->f26, Arg_9: Arg_9 {O(n)} 6: f23->f26, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 26: f23->f1, Arg_0: Arg_0 {O(n)} 26: f23->f1, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 26: f23->f1, Arg_3: max([Arg_3, max([1+Arg_0, Arg_3+2*max([0, 1+Arg_0-Arg_3])])]) {O(n)} 26: f23->f1, Arg_6: Arg_6 {O(n)} 26: f23->f1, Arg_7: max([Arg_7, Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])]) {O(n)} 26: f23->f1, Arg_9: Arg_9 {O(n)} 26: f23->f1, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 25: f26->f40, Arg_0: Arg_0 {O(n)} 25: f26->f40, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 25: f26->f40, Arg_2: 0 {O(1)} 25: f26->f40, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 25: f26->f40, Arg_6: Arg_6 {O(n)} 25: f26->f40, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 25: f26->f40, Arg_9: Arg_9 {O(n)} 25: f26->f40, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 21: f40->f59, Arg_0: Arg_0 {O(n)} 21: f40->f59, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 21: f40->f59, Arg_2: 0 {O(1)} 21: f40->f59, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 21: f40->f59, Arg_6: Arg_6 {O(n)} 21: f40->f59, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 21: f40->f59, Arg_9: Arg_9 {O(n)} 21: f40->f59, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 22: f40->f59, Arg_0: Arg_0 {O(n)} 22: f40->f59, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 22: f40->f59, Arg_2: 0 {O(1)} 22: f40->f59, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 22: f40->f59, Arg_6: Arg_6 {O(n)} 22: f40->f59, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 22: f40->f59, Arg_9: Arg_9 {O(n)} 22: f40->f59, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 23: f40->f69, Arg_0: Arg_0 {O(n)} 23: f40->f69, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 23: f40->f69, Arg_2: 0 {O(1)} 23: f40->f69, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 23: f40->f69, Arg_6: Arg_6 {O(n)} 23: f40->f69, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 23: f40->f69, Arg_9: Arg_9 {O(n)} 23: f40->f69, Arg_10: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 3: f5->f9, Arg_0: Arg_0 {O(n)} 3: f5->f9, Arg_1: Arg_1+2*max([0, 1+Arg_0-Arg_1]) {O(n)} 3: f5->f9, Arg_2: 0 {O(1)} 3: f5->f9, Arg_3: Arg_3+2*max([0, 1+Arg_0-Arg_3]) {O(n)} 3: f5->f9, Arg_6: Arg_6 {O(n)} 3: f5->f9, Arg_7: Arg_7 {O(n)} 3: f5->f9, Arg_8: Arg_8 {O(n)} 3: f5->f9, Arg_9: Arg_9 {O(n)} 3: f5->f9, Arg_10: Arg_10 {O(n)} 30: f5->f23, Arg_0: Arg_0 {O(n)} 30: f5->f23, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 30: f5->f23, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])]) {O(n)} 30: f5->f23, Arg_6: Arg_6 {O(n)} 30: f5->f23, Arg_7: Arg_7 {O(n)} 30: f5->f23, Arg_8: Arg_8 {O(n)} 30: f5->f23, Arg_9: Arg_9 {O(n)} 30: f5->f23, Arg_10: Arg_10 {O(n)} 11: f59->f59, Arg_0: Arg_0 {O(n)} 11: f59->f59, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 11: f59->f59, Arg_2: 0 {O(1)} 11: f59->f59, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 11: f59->f59, Arg_6: Arg_6 {O(n)} 11: f59->f59, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 11: f59->f59, Arg_9: Arg_9 {O(n)} 11: f59->f59, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 18: f59->f69, Arg_0: Arg_0 {O(n)} 18: f59->f69, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 18: f59->f69, Arg_2: 0 {O(1)} 18: f59->f69, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 18: f59->f69, Arg_6: Arg_6 {O(n)} 18: f59->f69, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 18: f59->f69, Arg_9: Arg_9 {O(n)} 18: f59->f69, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 0: f69->f71, Arg_0: Arg_0 {O(n)} 0: f69->f71, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 0: f69->f71, Arg_2: 0 {O(1)} 0: f69->f71, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 0: f69->f71, Arg_6: Arg_6 {O(n)} 0: f69->f71, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 0: f69->f71, Arg_9: Arg_9 {O(n)} 0: f69->f71, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 1: f69->f71, Arg_0: Arg_0 {O(n)} 1: f69->f71, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 1: f69->f71, Arg_2: 0 {O(1)} 1: f69->f71, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 1: f69->f71, Arg_6: Arg_6 {O(n)} 1: f69->f71, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 1: f69->f71, Arg_9: Arg_9 {O(n)} 1: f69->f71, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 12: f69->f71, Arg_0: Arg_0 {O(n)} 12: f69->f71, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 12: f69->f71, Arg_2: 0 {O(1)} 12: f69->f71, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 12: f69->f71, Arg_6: Arg_6 {O(n)} 12: f69->f71, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 12: f69->f71, Arg_9: Arg_9 {O(n)} 12: f69->f71, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 13: f71->f74, Arg_0: Arg_0 {O(n)} 13: f71->f74, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 13: f71->f74, Arg_2: 0 {O(1)} 13: f71->f74, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 13: f71->f74, Arg_6: Arg_6 {O(n)} 13: f71->f74, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 13: f71->f74, Arg_9: Arg_9 {O(n)} 13: f71->f74, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 16: f71->f23, Arg_0: Arg_0 {O(n)} 16: f71->f23, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 16: f71->f23, Arg_2: 0 {O(1)} 16: f71->f23, Arg_3: 1+Arg_0 {O(n)} 16: f71->f23, Arg_6: Arg_6 {O(n)} 16: f71->f23, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 16: f71->f23, Arg_9: Arg_9 {O(n)} 16: f71->f23, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 17: f74->f23, Arg_0: Arg_0 {O(n)} 17: f74->f23, Arg_1: max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])]) {O(n)} 17: f74->f23, Arg_2: 0 {O(1)} 17: f74->f23, Arg_3: max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3]) {O(n)} 17: f74->f23, Arg_6: Arg_6 {O(n)} 17: f74->f23, Arg_7: Arg_7+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)} 17: f74->f23, Arg_9: Arg_9 {O(n)} 17: f74->f23, Arg_10: max([Arg_10, max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])+max([0, Arg_0-Arg_3])]) {O(n)} 4: f9->f9, Arg_0: Arg_0 {O(n)} 4: f9->f9, Arg_1: Arg_1+2*max([0, 1+Arg_0-Arg_1]) {O(n)} 4: f9->f9, Arg_3: Arg_3+2*max([0, 1+Arg_0-Arg_3]) {O(n)} 4: f9->f9, Arg_6: Arg_6 {O(n)} 4: f9->f9, Arg_7: Arg_7 {O(n)} 4: f9->f9, Arg_8: Arg_8 {O(n)} 4: f9->f9, Arg_9: Arg_9 {O(n)} 4: f9->f9, Arg_10: Arg_10 {O(n)} 5: f9->f9, Arg_0: Arg_0 {O(n)} 5: f9->f9, Arg_1: Arg_1+2*max([0, 1+Arg_0-Arg_1]) {O(n)} 5: f9->f9, Arg_3: Arg_3+2*max([0, 1+Arg_0-Arg_3]) {O(n)} 5: f9->f9, Arg_6: Arg_6 {O(n)} 5: f9->f9, Arg_7: Arg_7 {O(n)} 5: f9->f9, Arg_8: Arg_8 {O(n)} 5: f9->f9, Arg_9: Arg_9 {O(n)} 5: f9->f9, Arg_10: Arg_10 {O(n)} 28: f9->f5, Arg_0: Arg_0 {O(n)} 28: f9->f5, Arg_1: Arg_1+2*max([0, 1+Arg_0-Arg_1]) {O(n)} 28: f9->f5, Arg_3: Arg_3+2*max([0, 1+Arg_0-Arg_3]) {O(n)} 28: f9->f5, Arg_6: Arg_6 {O(n)} 28: f9->f5, Arg_7: Arg_7 {O(n)} 28: f9->f5, Arg_8: Arg_8 {O(n)} 28: f9->f5, Arg_9: Arg_9 {O(n)} 28: f9->f5, Arg_10: Arg_10 {O(n)} 29: f9->f5, Arg_0: Arg_0 {O(n)} 29: f9->f5, Arg_1: Arg_1+2*max([0, 1+Arg_0-Arg_1]) {O(n)} 29: f9->f5, Arg_2: 0 {O(1)} 29: f9->f5, Arg_3: Arg_3+2*max([0, 1+Arg_0-Arg_3]) {O(n)} 29: f9->f5, Arg_6: Arg_6 {O(n)} 29: f9->f5, Arg_7: Arg_7 {O(n)} 29: f9->f5, Arg_8: Arg_8 {O(n)} 29: f9->f5, Arg_9: Arg_9 {O(n)} 29: f9->f5, Arg_10: Arg_10 {O(n)} ---------------------------------------- (2) BOUNDS(1, nat(max(4 * Arg_1, 4 * Arg_1 + nat(8 + 8 * Arg_0 + -8 * Arg_1)) + max(-4 * Arg_3, min(-4 * Arg_3 + min(-8 + -8 * Arg_0 + 8 * Arg_3, 0), -4 * Arg_3))) + nat(4 + 4 * Arg_0 + -4 * Arg_3) + max(1, 2 + Arg_0 + -1 * Arg_3) + max(2, 3 + 3 * Arg_0 + max(-3 * Arg_3, min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3))) + nat(3 + 3 * Arg_0 + -3 * Arg_1) + nat(-3 * Arg_3 + max(3 * Arg_1, 3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1))) + nat(2 * Arg_0 + -2 * Arg_3) + nat(-1 * Arg_7 + max(Arg_1 + nat(2 + 2 * Arg_0 + -2 * Arg_1), Arg_1)) + nat(1 + 2 * Arg_0 + max(-2 * Arg_3, min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3))) + nat(max(5 * Arg_1, 5 * Arg_1 + nat(10 + 10 * Arg_0 + -10 * Arg_1)) + max(min(-5 * Arg_3 + min(-10 + -10 * Arg_0 + 10 * Arg_3, 0), -5 * Arg_3), -5 * Arg_3))) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f2 0: f69 -> f71 : [ 0>=1+free ], cost: 1 1: f69 -> f71 : [ free_1>=1 ], cost: 1 12: f69 -> f71 : [], cost: 1 2: f2 -> f5 : [], cost: 1 3: f5 -> f9 : C'=0, [ A>=B ], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 4: f9 -> f9 : D'=1+D, E'=free_2, F'=free_2, [ C>=free_2 && A>=D ], cost: 1 5: f9 -> f9 : C'=free_3, D'=1+D, E'=free_3, F'=free_3, [ free_3>=1+C && A>=D ], cost: 1 27: f9 -> f5 : B'=1+B, [ 0>=1+C && D>=1+A ], cost: 1 28: f9 -> f5 : B'=1+B, [ C>=1 && D>=1+A ], cost: 1 29: f9 -> f5 : B'=1+B, C'=0, [ D>=1+A && C==0 ], cost: 1 6: f23 -> f26 : [ A>=D ], cost: 1 26: f23 -> f1 : [ D>=1+A ], cost: 1 7: f26 -> f30 : G'=free_4, [ D>=1+B ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 8: f30 -> f30 : G'=free_5, H'=1+H, [ B>=1+H ], cost: 1 24: f30 -> f26 : B'=1+B, [ H>=B ], cost: 1 9: f40 -> f44 : G'=free_6, [ A>=B ], cost: 1 21: f40 -> f59 : [ B>=1+A && K>=1+D ], cost: 1 22: f40 -> f59 : [ B>=1+A && D>=1+K ], cost: 1 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 10: f44 -> f44 : G'=free_7, H'=1+H, [ D>=1+H ], cost: 1 19: f44 -> f40 : B'=1+B, Q'=free_11, J'=free_12, [ C>=1+free_11 && H>=D ], cost: 1 20: f44 -> f40 : B'=1+B, C'=free_13, Q'=free_13, J'=free_14, K'=B, [ free_13>=C && H>=D ], cost: 1 11: f59 -> f59 : H'=1+H, Q'=free_8, [ A>=H ], cost: 1 18: f59 -> f69 : [ H>=1+A ], cost: 1 13: f71 -> f74 : Q'=free_9, [ A>=1+D ], cost: 1 14: f71 -> f74 : Q'=free_10, [ D>=1+A ], cost: 1 16: f71 -> f23 : D'=1+A, [ A==D ], cost: 1 15: f74 -> f74 : B'=1+B, [ A>=B ], cost: 1 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Removed unreachable and leaf rules: Start location: f2 0: f69 -> f71 : [ 0>=1+free ], cost: 1 1: f69 -> f71 : [ free_1>=1 ], cost: 1 12: f69 -> f71 : [], cost: 1 2: f2 -> f5 : [], cost: 1 3: f5 -> f9 : C'=0, [ A>=B ], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 4: f9 -> f9 : D'=1+D, E'=free_2, F'=free_2, [ C>=free_2 && A>=D ], cost: 1 5: f9 -> f9 : C'=free_3, D'=1+D, E'=free_3, F'=free_3, [ free_3>=1+C && A>=D ], cost: 1 27: f9 -> f5 : B'=1+B, [ 0>=1+C && D>=1+A ], cost: 1 28: f9 -> f5 : B'=1+B, [ C>=1 && D>=1+A ], cost: 1 29: f9 -> f5 : B'=1+B, C'=0, [ D>=1+A && C==0 ], cost: 1 6: f23 -> f26 : [ A>=D ], cost: 1 7: f26 -> f30 : G'=free_4, [ D>=1+B ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 8: f30 -> f30 : G'=free_5, H'=1+H, [ B>=1+H ], cost: 1 24: f30 -> f26 : B'=1+B, [ H>=B ], cost: 1 9: f40 -> f44 : G'=free_6, [ A>=B ], cost: 1 21: f40 -> f59 : [ B>=1+A && K>=1+D ], cost: 1 22: f40 -> f59 : [ B>=1+A && D>=1+K ], cost: 1 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 10: f44 -> f44 : G'=free_7, H'=1+H, [ D>=1+H ], cost: 1 19: f44 -> f40 : B'=1+B, Q'=free_11, J'=free_12, [ C>=1+free_11 && H>=D ], cost: 1 20: f44 -> f40 : B'=1+B, C'=free_13, Q'=free_13, J'=free_14, K'=B, [ free_13>=C && H>=D ], cost: 1 11: f59 -> f59 : H'=1+H, Q'=free_8, [ A>=H ], cost: 1 18: f59 -> f69 : [ H>=1+A ], cost: 1 13: f71 -> f74 : Q'=free_9, [ A>=1+D ], cost: 1 14: f71 -> f74 : Q'=free_10, [ D>=1+A ], cost: 1 16: f71 -> f23 : D'=1+A, [ A==D ], cost: 1 15: f74 -> f74 : B'=1+B, [ A>=B ], cost: 1 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Simplified all rules, resulting in: Start location: f2 12: f69 -> f71 : [], cost: 1 2: f2 -> f5 : [], cost: 1 3: f5 -> f9 : C'=0, [ A>=B ], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 4: f9 -> f9 : D'=1+D, E'=free_2, F'=free_2, [ C>=free_2 && A>=D ], cost: 1 5: f9 -> f9 : C'=free_3, D'=1+D, E'=free_3, F'=free_3, [ free_3>=1+C && A>=D ], cost: 1 27: f9 -> f5 : B'=1+B, [ 0>=1+C && D>=1+A ], cost: 1 28: f9 -> f5 : B'=1+B, [ C>=1 && D>=1+A ], cost: 1 29: f9 -> f5 : B'=1+B, C'=0, [ D>=1+A && C==0 ], cost: 1 6: f23 -> f26 : [ A>=D ], cost: 1 7: f26 -> f30 : G'=free_4, [ D>=1+B ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 8: f30 -> f30 : G'=free_5, H'=1+H, [ B>=1+H ], cost: 1 24: f30 -> f26 : B'=1+B, [ H>=B ], cost: 1 9: f40 -> f44 : G'=free_6, [ A>=B ], cost: 1 21: f40 -> f59 : [ B>=1+A && K>=1+D ], cost: 1 22: f40 -> f59 : [ B>=1+A && D>=1+K ], cost: 1 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 10: f44 -> f44 : G'=free_7, H'=1+H, [ D>=1+H ], cost: 1 19: f44 -> f40 : B'=1+B, Q'=free_11, J'=free_12, [ C>=1+free_11 && H>=D ], cost: 1 20: f44 -> f40 : B'=1+B, C'=free_13, Q'=free_13, J'=free_14, K'=B, [ free_13>=C && H>=D ], cost: 1 11: f59 -> f59 : H'=1+H, Q'=free_8, [ A>=H ], cost: 1 18: f59 -> f69 : [ H>=1+A ], cost: 1 13: f71 -> f74 : Q'=free_9, [ A>=1+D ], cost: 1 14: f71 -> f74 : Q'=free_10, [ D>=1+A ], cost: 1 16: f71 -> f23 : D'=1+A, [ A==D ], cost: 1 15: f74 -> f74 : B'=1+B, [ A>=B ], cost: 1 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 4: f9 -> f9 : D'=1+D, E'=free_2, F'=free_2, [ C>=free_2 && A>=D ], cost: 1 5: f9 -> f9 : C'=free_3, D'=1+D, E'=free_3, F'=free_3, [ free_3>=1+C && A>=D ], cost: 1 Accelerated rule 4 with metering function 1-D+A, yielding the new rule 31. During metering: Instantiating temporary variables by {free_3==1+C} Accelerated rule 5 with metering function 1-D+A, yielding the new rule 32. Removing the simple loops: 4 5. Accelerating simple loops of location 6. Accelerating the following rules: 8: f30 -> f30 : G'=free_5, H'=1+H, [ B>=1+H ], cost: 1 Accelerated rule 8 with metering function -H+B, yielding the new rule 33. Removing the simple loops: 8. Accelerating simple loops of location 8. Accelerating the following rules: 10: f44 -> f44 : G'=free_7, H'=1+H, [ D>=1+H ], cost: 1 Accelerated rule 10 with metering function D-H, yielding the new rule 34. Removing the simple loops: 10. Accelerating simple loops of location 9. Accelerating the following rules: 11: f59 -> f59 : H'=1+H, Q'=free_8, [ A>=H ], cost: 1 Accelerated rule 11 with metering function 1+A-H, yielding the new rule 35. Removing the simple loops: 11. Accelerating simple loops of location 11. Accelerating the following rules: 15: f74 -> f74 : B'=1+B, [ A>=B ], cost: 1 Accelerated rule 15 with metering function 1+A-B, yielding the new rule 36. Removing the simple loops: 15. Accelerated all simple loops using metering functions (where possible): Start location: f2 12: f69 -> f71 : [], cost: 1 2: f2 -> f5 : [], cost: 1 3: f5 -> f9 : C'=0, [ A>=B ], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 27: f9 -> f5 : B'=1+B, [ 0>=1+C && D>=1+A ], cost: 1 28: f9 -> f5 : B'=1+B, [ C>=1 && D>=1+A ], cost: 1 29: f9 -> f5 : B'=1+B, C'=0, [ D>=1+A && C==0 ], cost: 1 31: f9 -> f9 : D'=1+A, E'=free_2, F'=free_2, [ C>=free_2 && A>=D ], cost: 1-D+A 32: f9 -> f9 : C'=1+C-D+A, D'=1+A, E'=1+C-D+A, F'=1+C-D+A, [ A>=D ], cost: 1-D+A 6: f23 -> f26 : [ A>=D ], cost: 1 7: f26 -> f30 : G'=free_4, [ D>=1+B ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 24: f30 -> f26 : B'=1+B, [ H>=B ], cost: 1 33: f30 -> f30 : G'=free_5, H'=B, [ B>=1+H ], cost: -H+B 9: f40 -> f44 : G'=free_6, [ A>=B ], cost: 1 21: f40 -> f59 : [ B>=1+A && K>=1+D ], cost: 1 22: f40 -> f59 : [ B>=1+A && D>=1+K ], cost: 1 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 19: f44 -> f40 : B'=1+B, Q'=free_11, J'=free_12, [ C>=1+free_11 && H>=D ], cost: 1 20: f44 -> f40 : B'=1+B, C'=free_13, Q'=free_13, J'=free_14, K'=B, [ free_13>=C && H>=D ], cost: 1 34: f44 -> f44 : G'=free_7, H'=D, [ D>=1+H ], cost: D-H 18: f59 -> f69 : [ H>=1+A ], cost: 1 35: f59 -> f59 : H'=1+A, Q'=free_8, [ A>=H ], cost: 1+A-H 13: f71 -> f74 : Q'=free_9, [ A>=1+D ], cost: 1 14: f71 -> f74 : Q'=free_10, [ D>=1+A ], cost: 1 16: f71 -> f23 : D'=1+A, [ A==D ], cost: 1 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 36: f74 -> f74 : B'=1+A, [ A>=B ], cost: 1+A-B Chained accelerated rules (with incoming rules): Start location: f2 12: f69 -> f71 : [], cost: 1 2: f2 -> f5 : [], cost: 1 3: f5 -> f9 : C'=0, [ A>=B ], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 37: f5 -> f9 : C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D ], cost: 2-D+A 38: f5 -> f9 : C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D ], cost: 2-D+A 27: f9 -> f5 : B'=1+B, [ 0>=1+C && D>=1+A ], cost: 1 28: f9 -> f5 : B'=1+B, [ C>=1 && D>=1+A ], cost: 1 29: f9 -> f5 : B'=1+B, C'=0, [ D>=1+A && C==0 ], cost: 1 6: f23 -> f26 : [ A>=D ], cost: 1 7: f26 -> f30 : G'=free_4, [ D>=1+B ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 39: f26 -> f30 : G'=free_5, H'=B, [ D>=1+B && B>=1+H ], cost: 1-H+B 24: f30 -> f26 : B'=1+B, [ H>=B ], cost: 1 9: f40 -> f44 : G'=free_6, [ A>=B ], cost: 1 21: f40 -> f59 : [ B>=1+A && K>=1+D ], cost: 1 22: f40 -> f59 : [ B>=1+A && D>=1+K ], cost: 1 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 40: f40 -> f44 : G'=free_7, H'=D, [ A>=B && D>=1+H ], cost: 1+D-H 41: f40 -> f59 : H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H ], cost: 2+A-H 42: f40 -> f59 : H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H ], cost: 2+A-H 19: f44 -> f40 : B'=1+B, Q'=free_11, J'=free_12, [ C>=1+free_11 && H>=D ], cost: 1 20: f44 -> f40 : B'=1+B, C'=free_13, Q'=free_13, J'=free_14, K'=B, [ free_13>=C && H>=D ], cost: 1 18: f59 -> f69 : [ H>=1+A ], cost: 1 13: f71 -> f74 : Q'=free_9, [ A>=1+D ], cost: 1 14: f71 -> f74 : Q'=free_10, [ D>=1+A ], cost: 1 16: f71 -> f23 : D'=1+A, [ A==D ], cost: 1 43: f71 -> f74 : B'=1+A, Q'=free_9, [ A>=1+D && A>=B ], cost: 2+A-B 44: f71 -> f74 : B'=1+A, Q'=free_10, [ D>=1+A && A>=B ], cost: 2+A-B 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: f2 60: f69 -> f74 : Q'=free_9, [ A>=1+D ], cost: 2 61: f69 -> f74 : Q'=free_10, [ D>=1+A ], cost: 2 62: f69 -> f23 : D'=1+A, [ A==D ], cost: 2 63: f69 -> f74 : B'=1+A, Q'=free_9, [ A>=1+D && A>=B ], cost: 3+A-B 64: f69 -> f74 : B'=1+A, Q'=free_10, [ D>=1+A && A>=B ], cost: 3+A-B 2: f2 -> f5 : [], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 45: f5 -> f5 : B'=1+B, C'=0, [ A>=B && D>=1+A ], cost: 2 46: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 47: f5 -> f5 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D ], cost: 3-D+A 48: f5 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 2-D+A 49: f5 -> [18] : [ A>=B && A>=D ], cost: 2-D+A 6: f23 -> f26 : [ A>=D ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 50: f26 -> f26 : B'=1+B, G'=free_4, [ D>=1+B && H>=B ], cost: 2 51: f26 -> f26 : B'=1+B, G'=free_5, H'=B, [ D>=1+B && B>=1+H ], cost: 2-H+B 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 52: f40 -> f40 : B'=1+B, G'=free_6, Q'=free_11, J'=free_12, [ A>=B && C>=1+free_11 && H>=D ], cost: 2 53: f40 -> f40 : B'=1+B, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=B, [ A>=B && free_13>=C && H>=D ], cost: 2 54: f40 -> f40 : B'=1+B, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=B && D>=1+H && C>=1+free_11 ], cost: 2+D-H 55: f40 -> f40 : B'=1+B, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=B, [ A>=B && D>=1+H && free_13>=C ], cost: 2+D-H 56: f40 -> f69 : [ B>=1+A && K>=1+D && H>=1+A ], cost: 2 57: f40 -> f69 : [ B>=1+A && D>=1+K && H>=1+A ], cost: 2 58: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H ], cost: 3+A-H 59: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H ], cost: 3+A-H 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Accelerating simple loops of location 2. Accelerating the following rules: 45: f5 -> f5 : B'=1+B, C'=0, [ A>=B && D>=1+A ], cost: 2 46: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 47: f5 -> f5 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D ], cost: 3-D+A Accelerated rule 45 with metering function 1+A-B, yielding the new rule 65. Found no metering function for rule 46. Found no metering function for rule 47. Removing the simple loops: 45. Accelerating simple loops of location 5. Accelerating the following rules: 50: f26 -> f26 : B'=1+B, G'=free_4, [ D>=1+B && H>=B ], cost: 2 51: f26 -> f26 : B'=1+B, G'=free_5, H'=B, [ D>=1+B && B>=1+H ], cost: 2-H+B Accelerated rule 50 with backward acceleration, yielding the new rule 66. Accelerated rule 50 with backward acceleration, yielding the new rule 67. Accelerated rule 51 with metering function D-B, yielding the new rule 68. Removing the simple loops: 50 51. Accelerating simple loops of location 7. Accelerating the following rules: 52: f40 -> f40 : B'=1+B, G'=free_6, Q'=free_11, J'=free_12, [ A>=B && C>=1+free_11 && H>=D ], cost: 2 53: f40 -> f40 : B'=1+B, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=B, [ A>=B && free_13>=C && H>=D ], cost: 2 54: f40 -> f40 : B'=1+B, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=B && D>=1+H && C>=1+free_11 ], cost: 2+D-H 55: f40 -> f40 : B'=1+B, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=B, [ A>=B && D>=1+H && free_13>=C ], cost: 2+D-H Accelerated rule 52 with metering function 1+A-B, yielding the new rule 69. Accelerated rule 53 with metering function 1+A-B, yielding the new rule 70. Found no metering function for rule 54. Found no metering function for rule 55. Removing the simple loops: 52 53. Accelerated all simple loops using metering functions (where possible): Start location: f2 60: f69 -> f74 : Q'=free_9, [ A>=1+D ], cost: 2 61: f69 -> f74 : Q'=free_10, [ D>=1+A ], cost: 2 62: f69 -> f23 : D'=1+A, [ A==D ], cost: 2 63: f69 -> f74 : B'=1+A, Q'=free_9, [ A>=1+D && A>=B ], cost: 3+A-B 64: f69 -> f74 : B'=1+A, Q'=free_10, [ D>=1+A && A>=B ], cost: 3+A-B 2: f2 -> f5 : [], cost: 1 30: f5 -> f23 : [ B>=1+A ], cost: 1 46: f5 -> f5 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 47: f5 -> f5 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D ], cost: 3-D+A 48: f5 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 2-D+A 49: f5 -> [18] : [ A>=B && A>=D ], cost: 2-D+A 65: f5 -> f5 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 2+2*A-2*B 6: f23 -> f26 : [ A>=D ], cost: 1 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 66: f26 -> f26 : B'=D, G'=free_4, [ D>=1+B && H>=B && H>=-1+D ], cost: 2*D-2*B 67: f26 -> f26 : B'=1+H, G'=free_4, [ D>=1+B && H>=B && D>=1+H ], cost: 2+2*H-2*B 68: f26 -> f26 : B'=D, G'=free_5, H'=-1+D, [ D>=1+B && B>=1+H ], cost: 3*D-3*B 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 54: f40 -> f40 : B'=1+B, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=B && D>=1+H && C>=1+free_11 ], cost: 2+D-H 55: f40 -> f40 : B'=1+B, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=B, [ A>=B && D>=1+H && free_13>=C ], cost: 2+D-H 56: f40 -> f69 : [ B>=1+A && K>=1+D && H>=1+A ], cost: 2 57: f40 -> f69 : [ B>=1+A && D>=1+K && H>=1+A ], cost: 2 58: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H ], cost: 3+A-H 59: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H ], cost: 3+A-H 69: f40 -> f40 : B'=1+A, G'=free_6, Q'=free_11, J'=free_12, [ A>=B && C>=1+free_11 && H>=D ], cost: 2+2*A-2*B 70: f40 -> f40 : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ A>=B && free_13>=C && H>=D ], cost: 2+2*A-2*B 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f2 60: f69 -> f74 : Q'=free_9, [ A>=1+D ], cost: 2 61: f69 -> f74 : Q'=free_10, [ D>=1+A ], cost: 2 62: f69 -> f23 : D'=1+A, [ A==D ], cost: 2 63: f69 -> f74 : B'=1+A, Q'=free_9, [ A>=1+D && A>=B ], cost: 3+A-B 64: f69 -> f74 : B'=1+A, Q'=free_10, [ D>=1+A && A>=B ], cost: 3+A-B 2: f2 -> f5 : [], cost: 1 71: f2 -> f5 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 72: f2 -> f5 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D ], cost: 4-D+A 73: f2 -> f5 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 3+2*A-2*B 30: f5 -> f23 : [ B>=1+A ], cost: 1 48: f5 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 2-D+A 49: f5 -> [18] : [ A>=B && A>=D ], cost: 2-D+A 6: f23 -> f26 : [ A>=D ], cost: 1 74: f23 -> f26 : B'=D, G'=free_4, [ A>=D && D>=1+B && H>=B && H>=-1+D ], cost: 1+2*D-2*B 75: f23 -> f26 : B'=1+H, G'=free_4, [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 76: f23 -> f26 : B'=D, G'=free_5, H'=-1+D, [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 25: f26 -> f40 : C'=0, [ B>=D ], cost: 1 77: f26 -> f40 : B'=1+B, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ B>=D && A>=B && D>=1+H && 0>=1+free_11 ], cost: 3+D-H 78: f26 -> f40 : B'=1+B, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=B, [ B>=D && A>=B && D>=1+H && free_13>=0 ], cost: 3+D-H 79: f26 -> f40 : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 3+2*A-2*B 80: f26 -> f40 : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ B>=D && A>=B && free_13>=0 && H>=D ], cost: 3+2*A-2*B 23: f40 -> f69 : K'=D, [ B>=1+A && D==K ], cost: 1 56: f40 -> f69 : [ B>=1+A && K>=1+D && H>=1+A ], cost: 2 57: f40 -> f69 : [ B>=1+A && D>=1+K && H>=1+A ], cost: 2 58: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H ], cost: 3+A-H 59: f40 -> f69 : H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H ], cost: 3+A-H 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 90: f23 -> f40 : C'=0, [ A>=D && B>=D ], cost: 2 91: f23 -> f40 : B'=1+B, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && D>=1+H && 0>=1+free_11 ], cost: 4+D-H 92: f23 -> f40 : B'=1+B, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=B, [ A>=D && B>=D && A>=B && D>=1+H && free_13>=0 ], cost: 4+D-H 93: f23 -> f40 : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 94: f23 -> f40 : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ A>=D && B>=D && A>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 95: f23 -> f40 : B'=D, C'=0, G'=free_4, [ A>=D && D>=1+B && H>=B && H>=-1+D ], cost: 2+2*D-2*B 96: f23 -> f40 : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && H>=-1+D && D>=1+H && 0>=1+free_11 ], cost: 4+3*D-H-2*B 97: f23 -> f40 : B'=1+D, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=D, [ A>=D && D>=1+B && H>=B && H>=-1+D && D>=1+H && free_13>=0 ], cost: 4+3*D-H-2*B 98: f23 -> f40 : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 99: f23 -> f40 : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 100: f23 -> f40 : B'=1+H, C'=0, G'=free_4, [ A>=D && D>=1+B && H>=B && D>=1+H && 1+H>=D ], cost: 4+2*H-2*B 101: f23 -> f40 : B'=2+H, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && D>=1+H && 1+H>=D && A>=1+H && 0>=1+free_11 ], cost: 6+D+H-2*B 102: f23 -> f40 : B'=2+H, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=1+H, [ A>=D && D>=1+B && H>=B && D>=1+H && 1+H>=D && A>=1+H && free_13>=0 ], cost: 6+D+H-2*B 103: f23 -> f40 : B'=D, C'=0, G'=free_5, H'=-1+D, [ A>=D && D>=1+B && B>=1+H ], cost: 2+3*D-3*B 104: f23 -> f40 : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 105: f23 -> f40 : B'=1+D, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=D, [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 108: f40 -> f74 : Q'=free_9, K'=D, [ B>=1+A && D==K && A>=1+D ], cost: 3 109: f40 -> f74 : Q'=free_10, K'=D, [ B>=1+A && D==K && D>=1+A ], cost: 3 110: f40 -> f23 : D'=1+A, K'=D, [ B>=1+A && D==K && A==D ], cost: 3 111: f40 -> f74 : Q'=free_9, [ B>=1+A && K>=1+D && H>=1+A && A>=1+D ], cost: 4 112: f40 -> f74 : Q'=free_10, [ B>=1+A && K>=1+D && H>=1+A && D>=1+A ], cost: 4 113: f40 -> f23 : D'=1+A, [ B>=1+A && K>=1+D && H>=1+A && A==D ], cost: 4 114: f40 -> f74 : Q'=free_9, [ B>=1+A && D>=1+K && H>=1+A && A>=1+D ], cost: 4 115: f40 -> f74 : Q'=free_10, [ B>=1+A && D>=1+K && H>=1+A && D>=1+A ], cost: 4 116: f40 -> f23 : D'=1+A, [ B>=1+A && D>=1+K && H>=1+A && A==D ], cost: 4 117: f40 -> f74 : H'=1+A, Q'=free_9, [ B>=1+A && K>=1+D && A>=H && A>=1+D ], cost: 5+A-H 118: f40 -> f74 : H'=1+A, Q'=free_10, [ B>=1+A && K>=1+D && A>=H && D>=1+A ], cost: 5+A-H 119: f40 -> f23 : D'=1+A, H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H && A==D ], cost: 5+A-H 120: f40 -> f74 : H'=1+A, Q'=free_9, [ B>=1+A && D>=1+K && A>=H && A>=1+D ], cost: 5+A-H 121: f40 -> f74 : H'=1+A, Q'=free_10, [ B>=1+A && D>=1+K && A>=H && D>=1+A ], cost: 5+A-H 122: f40 -> f23 : D'=1+A, H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H && A==D ], cost: 5+A-H 123: f40 -> [24] : [ B>=1+A && K>=1+D && A>=H ], cost: 3+A-H 124: f40 -> [24] : [ B>=1+A && D>=1+K && A>=H ], cost: 3+A-H 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Applied pruning (of leafs and parallel rules): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 93: f23 -> f40 : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 98: f23 -> f40 : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 99: f23 -> f40 : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 104: f23 -> f40 : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 105: f23 -> f40 : B'=1+D, C'=free_13, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=D, [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 110: f40 -> f23 : D'=1+A, K'=D, [ B>=1+A && D==K && A==D ], cost: 3 112: f40 -> f74 : Q'=free_10, [ B>=1+A && K>=1+D && H>=1+A && D>=1+A ], cost: 4 113: f40 -> f23 : D'=1+A, [ B>=1+A && K>=1+D && H>=1+A && A==D ], cost: 4 116: f40 -> f23 : D'=1+A, [ B>=1+A && D>=1+K && H>=1+A && A==D ], cost: 4 117: f40 -> f74 : H'=1+A, Q'=free_9, [ B>=1+A && K>=1+D && A>=H && A>=1+D ], cost: 5+A-H 118: f40 -> f74 : H'=1+A, Q'=free_10, [ B>=1+A && K>=1+D && A>=H && D>=1+A ], cost: 5+A-H 119: f40 -> f23 : D'=1+A, H'=1+A, Q'=free_8, [ B>=1+A && K>=1+D && A>=H && A==D ], cost: 5+A-H 120: f40 -> f74 : H'=1+A, Q'=free_9, [ B>=1+A && D>=1+K && A>=H && A>=1+D ], cost: 5+A-H 121: f40 -> f74 : H'=1+A, Q'=free_10, [ B>=1+A && D>=1+K && A>=H && D>=1+A ], cost: 5+A-H 122: f40 -> f23 : D'=1+A, H'=1+A, Q'=free_8, [ B>=1+A && D>=1+K && A>=H && A==D ], cost: 5+A-H 123: f40 -> [24] : [ B>=1+A && K>=1+D && A>=H ], cost: 3+A-H 124: f40 -> [24] : [ B>=1+A && D>=1+K && A>=H ], cost: 3+A-H 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 125: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, K'=D, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D==K && A==D ], cost: 7+2*A-2*B 126: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && H>=1+A && A==D ], cost: 8+2*A-2*B 127: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && H>=1+A && A==D ], cost: 8+2*A-2*B 128: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 129: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A==D ], cost: 9+3*A-H-2*B 130: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 131: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A==D ], cost: 9+3*A-H-2*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 134: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D==K && A==D ], cost: 7+2*A-2*B 135: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && H>=1+A && A==D ], cost: 8+2*A-2*B 136: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && H>=1+A && A==D ], cost: 8+2*A-2*B 137: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 138: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A==D ], cost: 9+3*A-H-2*B 139: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 140: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A==D ], cost: 9+3*A-H-2*B 141: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 143: f23 -> f23 : B'=1+A, C'=free_13, D'=1+A, G'=free_6, Q'=free_13, J'=free_14, K'=D, [ D>=1+B && H>=B && free_13>=0 && H>=D && D==A && A==D ], cost: 7+2*A-2*B 144: f23 -> f74 : B'=1+A, C'=free_13, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 9+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 146: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=D, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && B>=1+H && 0>=1+free_11 && D==K && A==D ], cost: 8+3*D-3*B 147: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && 0>=1+free_11 && K>=1+D && A==D ], cost: 10+2*D+A-3*B 148: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && 0>=1+free_11 && D>=1+K && A==D ], cost: 10+2*D+A-3*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 150: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && D>=1+K ], cost: 8+2*D+A-3*B 151: f23 -> f23 : B'=1+D, C'=free_13, D'=1+A, G'=free_7, H'=D, Q'=free_13, J'=free_14, K'=D, [ D>=1+B && B>=1+H && free_13>=0 && A==D ], cost: 8+3*D-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Applied pruning (of leafs and parallel rules): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 128: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 130: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 134: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D==K && A==D ], cost: 7+2*A-2*B 137: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 138: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A==D ], cost: 9+3*A-H-2*B 139: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 144: f23 -> f74 : B'=1+A, C'=free_13, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 9+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 146: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=D, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && B>=1+H && 0>=1+free_11 && D==K && A==D ], cost: 8+3*D-3*B 147: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && 0>=1+free_11 && K>=1+D && A==D ], cost: 10+2*D+A-3*B 148: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && 0>=1+free_11 && D>=1+K && A==D ], cost: 10+2*D+A-3*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Accelerating simple loops of location 4. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 134: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D==K && A==D ], cost: 7+2*A-2*B 138: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && H>=B && H>=D && K>=1+D && A>=H && A==D ], cost: 9+3*A-H-2*B 146: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=D, Q'=free_11, J'=free_12, K'=D, [ D>=1+B && B>=1+H && 0>=1+free_11 && D==K && A==D ], cost: 8+3*D-3*B 147: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && K>=1+D && A==D ], cost: 10+2*D+A-3*B 148: f23 -> f23 : B'=1+D, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && D>=1+K && A==D ], cost: 10+2*D+A-3*B Accelerated rule 134 with metering function meter (where 2*meter==-2*D+A+K), yielding the new rule 157. Accelerated rule 138 with metering function D+A-2*H, yielding the new rule 158. Accelerated rule 146 with metering function meter_1 (where 2*meter_1==-2*D+A+K), yielding the new rule 159. Accelerated rule 147 with metering function -D+A, yielding the new rule 160. Accelerated rule 148 with metering function -D+A, yielding the new rule 161. Removing the simple loops: 134 138 146 147 148. Accelerated all simple loops using metering functions (where possible): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 128: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 130: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 137: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 139: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 144: f23 -> f74 : B'=1+A, C'=free_13, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 9+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 157: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, Q'=free_11, J'=free_12, K'=1+A, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D==K && A==D && 2*meter==-2*D+A+K && meter>=1 ], cost: 5*meter 158: f23 -> f23 : B'=1+A, C'=0, D'=1+A, G'=free_6, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && H>=B && H>=D && K>=1+D && A>=H && A==D && D+A-2*H>=1 ], cost: 6*D+6*A-12*H 159: f23 -> f23 : B'=2+A, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_11, J'=free_12, K'=1+A, [ D>=1+B && B>=1+H && 0>=1+free_11 && D==K && A==D && 2*meter_1==-2*D+A+K && meter_1>=1 ], cost: 5*meter_1 160: f23 -> f23 : B'=2+A, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && K>=1+D && A==D && -D+A>=1 ], cost: -6*D+6*A 161: f23 -> f23 : B'=2+A, C'=0, D'=1+A, G'=free_7, H'=1+A, Q'=free_8, J'=free_12, [ D>=1+B && B>=1+H && D>=1+K && A==D && -D+A>=1 ], cost: -6*D+6*A 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 128: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 130: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 137: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 139: f23 -> f74 : B'=1+A, C'=0, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 9+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 144: f23 -> f74 : B'=1+A, C'=free_13, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 9+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 17: f74 -> f23 : D'=1+D, [ B>=1+A ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 162: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 163: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 164: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 165: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 166: f23 -> f23 : B'=1+A, C'=free_13, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 10+3*A-H-2*B Accelerating simple loops of location 4. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 162: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 163: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 164: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 165: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 166: f23 -> f23 : B'=1+A, C'=free_13, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 10+3*A-H-2*B Found no metering function for rule 162. Found no metering function for rule 163. Accelerated rule 164 with NONTERM (after strengthening guard), yielding the new rule 167. Accelerated rule 165 with NONTERM (after strengthening guard), yielding the new rule 168. Accelerated rule 166 with NONTERM (after strengthening guard), yielding the new rule 169. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B 162: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 163: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ B>=D && A>=B && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 164: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && H>=D && K>=1+D && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 165: f23 -> f23 : B'=1+A, C'=0, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_12, [ D>=1+B && H>=B && H>=D && D>=1+K && A>=H && A>=1+D ], cost: 10+3*A-H-2*B 166: f23 -> f23 : B'=1+A, C'=free_13, D'=1+D, G'=free_6, H'=1+A, Q'=free_9, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 10+3*A-H-2*B 167: f23 -> [27] : [ D>=1+B && H>=B && H>=D && K>=1+D && A>=H && A>=1+D && 1+D>=2+A && 10+3*A-H-2*B>=1 ], cost: INF 168: f23 -> [27] : [ D>=1+B && H>=B && H>=D && D>=1+K && A>=H && A>=1+D && 1+D>=2+A && 10+3*A-H-2*B>=1 ], cost: INF 169: f23 -> [27] : [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H && 1+D>=2+A && 10+3*A-H-2*B>=1 ], cost: INF Chained accelerated rules (with incoming rules): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B Removed unreachable locations (and leaf rules with constant cost): Start location: f2 81: f2 -> f23 : [ B>=1+A ], cost: 2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 84: f2 -> f23 : B'=1+B, C'=0, D'=1+A, E'=free_2, F'=free_2, [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 85: f2 -> f23 : B'=1+B, C'=1-D+A, D'=1+A, E'=1-D+A, F'=1-D+A, [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 86: f2 -> f23 : B'=1+A, C'=0, [ A>=B && D>=1+A ], cost: 4+2*A-2*B 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 106: f23 -> [23] : [ A>=D && D>=1+B && H>=B && D>=1+H ], cost: 3+2*H-2*B 107: f23 -> [23] : [ A>=D && D>=1+B && B>=1+H ], cost: 1+3*D-3*B 132: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && K>=1+D && A>=H ], cost: 7+3*A-H-2*B 133: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 142: f23 -> [24] : B'=1+A, C'=0, G'=free_6, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D && D>=1+K && A>=H ], cost: 7+3*A-H-2*B 145: f23 -> [24] : B'=1+A, C'=free_13, G'=free_6, Q'=free_13, J'=free_14, K'=A, [ D>=1+B && H>=B && free_13>=0 && H>=D && A>=1+D && A>=H ], cost: 7+3*A-H-2*B 149: f23 -> [24] : B'=1+D, C'=0, G'=free_7, H'=D, Q'=free_11, J'=free_12, [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 && 1+D>=1+A && K>=1+D ], cost: 8+2*D+A-3*B 152: f23 -> [25] : [ A>=D && B>=D && A>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 153: f23 -> [25] : [ A>=D && D>=1+B && H>=B && 0>=1+free_11 && H>=D ], cost: 4+2*A-2*B 154: f23 -> [25] : [ A>=D && D>=1+B && H>=B && free_13>=0 && H>=D ], cost: 4+2*A-2*B 155: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && 0>=1+free_11 ], cost: 5+3*D-3*B 156: f23 -> [25] : [ A>=D && D>=1+B && B>=1+H && free_13>=0 ], cost: 5+3*D-3*B Eliminated locations (on tree-shaped paths): Start location: f2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 170: f2 -> [28] : [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 171: f2 -> [28] : [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 172: f2 -> [28] : [ A>=B && D>=1+A ], cost: 4+2*A-2*B Applied pruning (of leafs and parallel rules): Start location: f2 82: f2 -> [18] : [ A>=B && 0>=free_2 && A>=D ], cost: 3-D+A 83: f2 -> [18] : [ A>=B && A>=D ], cost: 3-D+A 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 89: f2 -> [22] : [ A>=B && D>=1+A ], cost: 3+2*A-2*B 170: f2 -> [28] : [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 171: f2 -> [28] : [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 172: f2 -> [28] : [ A>=B && D>=1+A ], cost: 4+2*A-2*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f2 87: f2 -> [22] : [ A>=B && 0>=free_2 && A>=D ], cost: 4-D+A 88: f2 -> [22] : [ A>=B && A>=D ], cost: 4-D+A 170: f2 -> [28] : [ A>=B && 0>=free_2 && A>=D && 1+B>=1+A ], cost: 5-D+A 171: f2 -> [28] : [ A>=B && A>=D && 1+B>=1+A ], cost: 5-D+A 172: f2 -> [28] : [ A>=B && D>=1+A ], cost: 4+2*A-2*B Computing asymptotic complexity for rule 87 Solved the limit problem by the following transformations: Created initial limit problem: 4-D+A (+), 1-D+A (+/+!), 1+A-B (+/+!), 1-free_2 (+/+!) [not solved] applying transformation rule (C) using substitution {A==B} resulting limit problem: 1 (+/+!), 1-D+B (+/+!), 4-D+B (+), 1-free_2 (+/+!) [not solved] applying transformation rule (C) using substitution {free_2==0} resulting limit problem: 1 (+/+!), 1-D+B (+/+!), 4-D+B (+) [not solved] applying transformation rule (C) using substitution {A==D} resulting limit problem: 1 (+/+!), 1-D+B (+/+!), 4-D+B (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1-D+B (+/+!), 4-D+B (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {D==-n,B==0} resulting limit problem: [solved] Solution: free_2 / 0 D / -n A / 0 B / 0 Resulting cost 4+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: 4+n Rule cost: 4-D+A Rule guard: [ A>=B && 0>=free_2 && A>=D ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)