16.20/7.46 WORST_CASE(Omega(n^1), O(n^1)) 16.20/7.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 16.20/7.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.20/7.48 16.20/7.48 16.20/7.48 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 16.20/7.48 16.20/7.48 (0) CpxIntTrs 16.20/7.48 (1) Koat Proof [FINISHED, 391 ms] 16.20/7.48 (2) BOUNDS(1, n^1) 16.20/7.48 (3) Loat Proof [FINISHED, 5821 ms] 16.20/7.48 (4) BOUNDS(n^1, INF) 16.20/7.48 16.20/7.48 16.20/7.48 ---------------------------------------- 16.20/7.48 16.20/7.48 (0) 16.20/7.48 Obligation: 16.20/7.48 Complexity Int TRS consisting of the following rules: 16.20/7.48 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 2 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= B + 1 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, C, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 + S && A >= D 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, S, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: S >= C && A >= D 16.20/7.48 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: 0 >= S + 1 && A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: S >= 1 && A >= D 16.20/7.48 f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= K 16.20/7.48 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D + 1, E, F, G, H, I, S, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K + 1, L, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D, E, F, G, H, I, J, K, S, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: K >= 1 + A 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, S, T, T, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, -(S), T, S, R)) :|: 0 >= U + 1 && D >= 1 + A 16.20/7.48 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, 0)) :|: D >= 1 + A && C >= 0 && C <= 0 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= C + 1 && D >= 1 + A 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 && D >= 1 + A 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A && 0 >= S + 1 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A 16.20/7.48 16.20/7.48 The start-symbols are:[f0_18] 16.20/7.48 16.20/7.48 16.20/7.48 ---------------------------------------- 16.20/7.48 16.20/7.48 (1) Koat Proof (FINISHED) 16.20/7.48 YES(?, 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 38) 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Initial complexity problem: 16.20/7.48 16.20/7.48 1: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0, 0, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, s, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, s, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, s, t, t, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, -s, t, s, ar_17)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, 0)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_10]. 16.20/7.48 16.20/7.48 We thus obtain the following problem: 16.20/7.48 16.20/7.48 2: T: 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Testing for reachability in the complexity graph removes the following transitions from problem 2: 16.20/7.48 16.20/7.48 f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 We thus obtain the following problem: 16.20/7.48 16.20/7.48 3: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Repeatedly propagating knowledge in problem 3 produces the following problem: 16.20/7.48 16.20/7.48 4: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 A polynomial rank function with 16.20/7.48 16.20/7.48 Pol(f61) = 1 16.20/7.48 16.20/7.48 Pol(f53) = 1 16.20/7.48 16.20/7.48 Pol(f55) = 1 16.20/7.48 16.20/7.48 Pol(f10) = 1 16.20/7.48 16.20/7.48 Pol(f34) = 1 16.20/7.48 16.20/7.48 Pol(f29) = 1 16.20/7.48 16.20/7.48 Pol(f13) = 1 16.20/7.48 16.20/7.48 Pol(f73) = 0 16.20/7.48 16.20/7.48 Pol(f0) = 1 16.20/7.48 16.20/7.48 Pol(koat_start) = 1 16.20/7.48 16.20/7.48 orients all transitions weakly and the transitions 16.20/7.48 16.20/7.48 f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 strictly and produces the following problem: 16.20/7.48 16.20/7.48 5: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 A polynomial rank function with 16.20/7.48 16.20/7.48 Pol(f61) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f53) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f55) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f10) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f34) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f29) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f13) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(f73) = V_1 - V_4 16.20/7.48 16.20/7.48 Pol(f0) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 Pol(koat_start) = V_1 - V_4 + 1 16.20/7.48 16.20/7.48 orients all transitions weakly and the transitions 16.20/7.48 16.20/7.48 f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 strictly and produces the following problem: 16.20/7.48 16.20/7.48 6: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Repeatedly propagating knowledge in problem 6 produces the following problem: 16.20/7.48 16.20/7.48 7: T: 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.20/7.48 16.20/7.48 start location: koat_start 16.20/7.48 16.20/7.48 leaf cost: 0 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 A polynomial rank function with 16.20/7.48 16.20/7.48 Pol(f61) = 1 16.20/7.48 16.20/7.48 Pol(f53) = 1 16.20/7.48 16.20/7.48 Pol(f55) = 1 16.20/7.48 16.20/7.48 Pol(f10) = 0 16.20/7.48 16.20/7.48 Pol(f13) = 0 16.20/7.48 16.20/7.48 and size complexities 16.20/7.48 16.20/7.48 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-0) = ar_0 16.20/7.48 16.20/7.48 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-1) = ar_1 16.20/7.48 16.20/7.48 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-2) = ar_2 16.20/7.48 16.20/7.48 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-3) = ar_3 16.20/7.48 16.20/7.48 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ]", 0-4) = ar_10 16.20/7.48 16.20/7.48 S("f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-0) = ar_0 16.20/7.48 16.20/7.48 S("f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-1) = ar_1 16.20/7.48 16.20/7.48 S("f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-2) = ar_2 16.34/7.48 16.34/7.48 S("f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-3) = ar_3 16.34/7.48 16.34/7.48 S("f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ]", 0-4) = ar_10 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 192 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\\ 0 >= s + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-2) = 0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\\ ar_2 = 0 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\\ ar_0 >= ar_3 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\\ ar_0 >= ar_3 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ]", 0-4) = ? 16.34/7.48 16.34/7.48 S("f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 16.34/7.48 16.34/7.48 S("f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 16.34/7.48 16.34/7.48 S("f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 16.34/7.48 16.34/7.48 S("f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 48 16.34/7.48 16.34/7.48 S("f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ]", 0-4) = ? 16.34/7.48 16.34/7.48 orients the transitions 16.34/7.48 16.34/7.48 f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 weakly and the transition 16.34/7.48 16.34/7.48 f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 strictly and produces the following problem: 16.34/7.48 16.34/7.48 8: T: 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.34/7.48 16.34/7.48 start location: koat_start 16.34/7.48 16.34/7.48 leaf cost: 0 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 A polynomial rank function with 16.34/7.48 16.34/7.48 Pol(f61) = V_1 - V_5 16.34/7.48 16.34/7.48 Pol(f53) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(f55) = V_1 - V_5 16.34/7.48 16.34/7.48 Pol(f10) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(f34) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(f29) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(f13) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(f73) = V_1 - V_5 16.34/7.48 16.34/7.48 Pol(f0) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 Pol(koat_start) = V_1 - V_5 + 1 16.34/7.48 16.34/7.48 orients all transitions weakly and the transition 16.34/7.48 16.34/7.48 f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 strictly and produces the following problem: 16.34/7.48 16.34/7.48 9: T: 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_10 + 1, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.34/7.48 16.34/7.48 start location: koat_start 16.34/7.48 16.34/7.48 leaf cost: 0 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Repeatedly propagating knowledge in problem 9 produces the following problem: 16.34/7.48 16.34/7.48 10: T: 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_10 + 1, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.34/7.48 16.34/7.48 start location: koat_start 16.34/7.48 16.34/7.48 leaf cost: 0 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 A polynomial rank function with 16.34/7.48 16.34/7.48 Pol(f61) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f53) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f55) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f10) = V_1 - V_2 16.34/7.48 16.34/7.48 Pol(f34) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f29) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f13) = V_1 - V_2 - 1 16.34/7.48 16.34/7.48 Pol(f73) = V_1 - V_2 16.34/7.48 16.34/7.48 Pol(f0) = V_1 - V_2 16.34/7.48 16.34/7.48 Pol(koat_start) = V_1 - V_2 16.34/7.48 16.34/7.48 orients all transitions weakly and the transition 16.34/7.48 16.34/7.48 f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 strictly and produces the following problem: 16.34/7.48 16.34/7.48 11: T: 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_10 + 1, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.34/7.48 16.34/7.48 start location: koat_start 16.34/7.48 16.34/7.48 leaf cost: 0 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Repeatedly propagating knowledge in problem 11 produces the following problem: 16.34/7.48 16.34/7.48 12: T: 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10 + 1)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + ar_10 + ar_3 + 2, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_10 + 1, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= ar_10 ] 16.34/7.48 16.34/7.48 (Comp: 9*ar_0 + 9*ar_3 + 9, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_10)) [ ar_10 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 4*ar_0 + 4*ar_3 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_10)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_3 + 1, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_10)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.34/7.48 16.34/7.48 (Comp: 3*ar_0 + ar_1 + 2*ar_3 + 2, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1 + 1, 0, ar_3, ar_10)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.34/7.48 16.34/7.48 (Comp: ar_0 + ar_1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f13(ar_0, ar_1, 0, ar_3, ar_10)) [ ar_0 >= ar_1 + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 /\ 0 >= s + 1 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f73(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_1 >= ar_0 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f10(ar_0, ar_1, ar_2, ar_3, ar_10)) [ ar_0 >= 2 ] 16.34/7.48 16.34/7.48 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_10) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_10)) [ 0 <= 0 ] 16.34/7.48 16.34/7.48 start location: koat_start 16.34/7.48 16.34/7.48 leaf cost: 0 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Complexity upper bound 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 38 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Time: 0.383 sec (SMT: 0.290 sec) 16.34/7.48 16.34/7.48 16.34/7.48 ---------------------------------------- 16.34/7.48 16.34/7.48 (2) 16.34/7.48 BOUNDS(1, n^1) 16.34/7.48 16.34/7.48 ---------------------------------------- 16.34/7.48 16.34/7.48 (3) Loat Proof (FINISHED) 16.34/7.48 16.34/7.48 16.34/7.48 ### Pre-processing the ITS problem ### 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Initial linear ITS problem 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 20: f10 -> f73 : [ B>=A && 0>=1+free_13 ], cost: 1 16.34/7.48 16.34/7.48 21: f10 -> f73 : [ B>=A ], cost: 1 16.34/7.48 16.34/7.48 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.34/7.48 16.34/7.48 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ 0>=1+free_12 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Removed unreachable and leaf rules: 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.34/7.48 16.34/7.48 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ 0>=1+free_12 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Simplified all rules, resulting in: 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.34/7.48 16.34/7.48 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 ### Simplification by acceleration and chaining ### 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 2. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 16.34/7.48 16.34/7.48 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 2 with metering function 1-D+A, yielding the new rule 22. 16.34/7.48 16.34/7.48 Accelerated rule 3 with metering function 1-D+A, yielding the new rule 23. 16.34/7.48 16.34/7.48 Removing the simple loops: 2 3. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 3. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 4 with metering function 1-D+A, yielding the new rule 24. 16.34/7.48 16.34/7.48 Removing the simple loops: 4. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 4. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 5 with metering function 1-D+A, yielding the new rule 25. 16.34/7.48 16.34/7.48 Accelerated rule 6 with metering function 1-D+A, yielding the new rule 26. 16.34/7.48 16.34/7.48 Accelerated rule 7 with metering function 1-D+A, yielding the new rule 27. 16.34/7.48 16.34/7.48 Removing the simple loops: 5 6 7. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 6. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 9 with metering function 1-D+A, yielding the new rule 28. 16.34/7.48 16.34/7.48 Removing the simple loops: 9. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 7. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 10 with metering function 1-D+A, yielding the new rule 29. 16.34/7.48 16.34/7.48 Removing the simple loops: 10. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated all simple loops using metering functions (where possible): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 22: f13 -> f13 : D'=1+A, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 23: f13 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 24: f29 -> f29 : D'=1+A, [ A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 25: f34 -> f34 : D'=1+A, H'=0, Q'=0, [ A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 26: f34 -> f34 : D'=1+A, H'=free_2, Q'=free_3, J'=-free_3*(-1+D-A)+J, [ 0>=1+free_2 && A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 27: f34 -> f34 : D'=1+A, H'=free_4, Q'=free_5, J'=J-(-1+D-A)*free_5, [ free_4>=1 && A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 28: f55 -> f55 : D'=1+A, J'=free_6, [ A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 29: f61 -> f61 : D'=1+A, [ A>=D ], cost: 1-D+A 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Chained accelerated rules (with incoming rules): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 30: f10 -> f13 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 31: f10 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 32: f53 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Eliminated locations (on linear paths): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 16.34/7.48 16.34/7.48 30: f10 -> f13 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 31: f10 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 16.34/7.48 16.34/7.48 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 16: f29 -> f34 : [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 16.34/7.48 16.34/7.48 8: f53 -> f55 : [ A>=K ], cost: 1 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 32: f53 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 33: f55 -> f53 : K'=1+K, L'=free_7, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Eliminated locations (on tree-shaped paths): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 34: f10 -> f10 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, R'=0, [ A>=1+B && A>=D && free_1==0 ], cost: 3-D+A 16.34/7.48 16.34/7.48 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 42: f53 -> f53 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 16.34/7.48 16.34/7.48 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 1. 16.34/7.48 16.34/7.48 Simplified some of the simple loops (and removed duplicate rules). 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 34: f10 -> f10 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 34 with metering function A-B, yielding the new rule 44. 16.34/7.48 16.34/7.48 Found no metering function for rule 35. 16.34/7.48 16.34/7.48 Found no metering function for rule 36. 16.34/7.48 16.34/7.48 Removing the simple loops: 34. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 5. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 42: f53 -> f53 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 16.34/7.48 16.34/7.48 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated rule 42 with metering function 1+A-K, yielding the new rule 45. 16.34/7.48 16.34/7.48 Found no metering function for rule 43. 16.34/7.48 16.34/7.48 Removing the simple loops: 42. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated all simple loops using metering functions (where possible): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 44: f10 -> f10 : B'=A, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2*A-2*B 16.34/7.48 16.34/7.48 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 45: f53 -> f53 : K'=1+A, L'=free_7, [ A>=K && D>=1+A ], cost: 3+3*A-3*K 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Chained accelerated rules (with incoming rules): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 16.34/7.48 16.34/7.48 52: f29 -> f53 : K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 16.34/7.48 16.34/7.48 53: f29 -> f53 : K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 47: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 49: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 51: f53 -> f10 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Eliminated locations (on tree-shaped paths): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 54: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 55: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 56: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 57: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 16.34/7.48 16.34/7.48 47: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 49: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 51: f53 -> f10 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Eliminated locations (on tree-shaped paths): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.34/7.48 16.34/7.48 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 60: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.34/7.48 16.34/7.48 61: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 63: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 64: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 65: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 66: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 68: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Applied pruning (of leafs and parallel rules): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.34/7.48 16.34/7.48 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 61: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 63: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerating simple loops of location 1. 16.34/7.48 16.34/7.48 Accelerating the following rules: 16.34/7.48 16.34/7.48 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.34/7.48 16.34/7.48 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 61: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 63: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Found no metering function for rule 58. 16.34/7.48 16.34/7.48 Found no metering function for rule 59. 16.34/7.48 16.34/7.48 Found no metering function for rule 61. 16.34/7.48 16.34/7.48 Found no metering function for rule 62. 16.34/7.48 16.34/7.48 Found no metering function for rule 63. 16.34/7.48 16.34/7.48 Removing the simple loops:. 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Accelerated all simple loops using metering functions (where possible): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 16.34/7.48 16.34/7.48 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 61: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 16.34/7.48 16.34/7.48 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 63: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Chained accelerated rules (with incoming rules): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 0: f0 -> f10 : [ A>=2 ], cost: 1 16.34/7.48 16.34/7.48 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 70: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 16.34/7.48 16.34/7.48 71: f0 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.34/7.48 16.34/7.48 72: f0 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.34/7.48 16.34/7.48 73: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.34/7.48 16.34/7.48 74: f0 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 16.34/7.48 16.34/7.48 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 16.34/7.48 16.34/7.48 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Eliminated locations (on tree-shaped paths): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 75: f0 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.34/7.48 16.34/7.48 78: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 81: f0 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 82: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 16.34/7.48 16.34/7.48 83: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.34/7.48 16.34/7.48 84: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 16.34/7.48 16.34/7.48 85: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.34/7.48 16.34/7.48 86: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Applied pruning (of leafs and parallel rules): 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 75: f0 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.34/7.48 16.34/7.48 78: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 16.34/7.48 16.34/7.48 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 81: f0 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 85: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.34/7.48 16.34/7.48 86: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 ### Computing asymptotic complexity ### 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Fully simplified ITS problem 16.34/7.48 16.34/7.48 Start location: f0 16.34/7.48 16.34/7.48 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 16.34/7.48 16.34/7.48 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 16.34/7.48 16.34/7.48 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 16.34/7.48 16.34/7.48 81: f0 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 16.34/7.48 16.34/7.48 85: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 16.34/7.48 16.34/7.48 86: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 8-D+6*A-3*K-2*B 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Computing asymptotic complexity for rule 76 16.34/7.48 16.34/7.48 Solved the limit problem by the following transformations: 16.34/7.48 16.34/7.48 Created initial limit problem: 16.34/7.48 16.34/7.48 -1+A (+/+!), 1+free_1 (+/+!), 3-D+A (+), 1-D+A (+/+!), A-B (+/+!) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (C) using substitution {A==2} 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (C) using substitution {A==1+B} 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 3-D (+/+!), 1 (+/+!), 1+free_1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (C) using substitution {free_1==0} 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (C) using substitution {A==D} 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 3-D (+/+!), 1 (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (B), deleting 1 (+/+!) 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 3-D (+/+!), 2-B (+/+!), 5-D (+) [not solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 removing all constraints (solved by SMT) 16.34/7.48 16.34/7.48 resulting limit problem: [solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 applying transformation rule (C) using substitution {D==-n,B==0} 16.34/7.48 16.34/7.48 resulting limit problem: 16.34/7.48 16.34/7.48 [solved] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Solution: 16.34/7.48 16.34/7.48 free_1 / 0 16.34/7.48 16.34/7.48 D / -n 16.34/7.48 16.34/7.48 A / 2 16.34/7.48 16.34/7.48 B / 0 16.34/7.48 16.34/7.48 Resulting cost 5+n has complexity: Poly(n^1) 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Found new complexity Poly(n^1). 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 Obtained the following overall complexity (w.r.t. the length of the input n): 16.34/7.48 16.34/7.48 Complexity: Poly(n^1) 16.34/7.48 16.34/7.48 Cpx degree: 1 16.34/7.48 16.34/7.48 Solved cost: 5+n 16.34/7.48 16.34/7.48 Rule cost: 3-D+A 16.34/7.48 16.34/7.48 Rule guard: [ A>=2 && A>=1+B && free_1>=0 && A>=D ] 16.34/7.48 16.34/7.48 16.34/7.48 16.34/7.48 WORST_CASE(Omega(n^1),?) 16.34/7.48 16.34/7.48 16.34/7.48 ---------------------------------------- 16.34/7.48 16.34/7.48 (4) 16.34/7.48 BOUNDS(n^1, INF) 16.35/7.83 EOF