details

property	value
status	complete
benchmark	create_via_tmps.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n004.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.51271605492 seconds
cpu usage	10.662271737
max memory	4.60771328E8

stage attributes

key	value
output-size	71551
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 705 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 2830 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f1(A, 1 + B, D, B1, Y, Z, A1, C1, D1, E1, D, F1, B, N, O, P, Q, R, S, T, U, V, W, X)) :|: A >= B + 1 && B >= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: B1 >= N + 1 && O >= 0 && A1 >= 2 && Z >= A1 && Y >= B1 + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: B1 >= N + 1 && O >= 0 && A1 >= 2 && Z >= A1 && B1 >= Y + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: N >= B1 + 1 && O >= 0 && A1 >= 2 && Z >= A1 && Y >= B1 + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, U, V, W, X)) :|: N >= B1 + 1 && O >= 0 && A1 >= 2 && Z >= A1 && B1 >= Y + 1 && P >= 0 && P <= 0 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(E1, D1, F1, D, E, F, G, H, G1, J, K, L, M, C1, O, B1, Y, Z, A1, H1, U, V, W, X)) :|: O >= 0 && E1 >= 2 && D1 >= E1 && 0 >= F1 + 1 && P >= N && P <= N f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(E1, D1, F1, D, E, F, G, H, G1, J, K, L, M, C1, O, B1, Y, Z, A1, H1, U, V, W, X)) :|: O >= 0 && E1 >= 2 && D1 >= E1 && F1 >= 1 && P >= N && P <= N f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: C1 >= N + 1 && U >= 0 && A1 >= 2 && Z >= A1 && Y >= C1 + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: C1 >= N + 1 && U >= 0 && A1 >= 2 && Z >= A1 && C1 >= Y + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: N >= C1 + 1 && U >= 0 && A1 >= 2 && Z >= A1 && Y >= C1 + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(A1, Z, Y, D, E, F, G, H, I, J, Y, L, M, N, O, 0, Y, 0, Y, N, -(1) + U, B1, -(1) + U, X)) :|: N >= C1 + 1 && U >= 0 && A1 >= 2 && Z >= A1 && C1 >= Y + 1 && P >= 0 && P <= 0 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(D1, B, C, D, E, F, G, H, E1, J, K, L, M, C1, O, B1, Y, Z, A1, F1, U, V, W, X)) :|: D1 >= 2 && U >= 0 && P >= N && P <= N f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && C >= 1 && 0 >= C + 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && C >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f10(Y, U + 1, C, D, E, F, G, H, I, J, C, L, M, C, U, 0, C, 0, C, C, U, V, W, X)) :|: B >= A && B >= 0 && Z >= Y && Y >= 2 && 0 >= C + 1 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f4(D1, 0, 0, D, E, F, G, H, E1, J, K, L, M, C1, O, B1, Y, Z, A1, F1, U, V, W, X)) :|: 0 >= D1 && 0 >= A f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f1(A, 2, Y, C1, Z, A1, B1, D1, E1, F1, Y, L, M, N, O, P, Q, R, S, T, U, V, W, G1)) :|: A >= 2 The start-symbols are:[f3_24] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, ar_0 + 4*ar_20 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f1(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f1(ar_0, ar_1 + 1, ar_3, y, z, a1, b1, c1, d1, e1, ar_3, f1, ar_1, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20, ar_21, ar_22, ar_23)) [ b1 >= ar_13 + 1 /\ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ a1 >= b1 + 1 /\ ar_15 = 0 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20, ar_21, ar_22, ar_23)) [ b1 >= ar_13 + 1 /\ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ b1 >= a1 + 1 /\ ar_15 = 0 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20, ar_21, ar_22, ar_23)) [ ar_13 >= b1 + 1 /\ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ a1 >= b1 + 1 /\ ar_15 = 0 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20, ar_21, ar_22, ar_23)) [ ar_13 >= b1 + 1 /\ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ b1 >= a1 + 1 /\ ar_15 = 0 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f4(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, b1, ar_9, ar_10, ar_11, ar_12, c1, ar_14, d1, e1, f1, g1, h1, ar_20, ar_21, ar_22, ar_23)) [ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ 0 >= a1 + 1 /\ ar_15 = ar_13 ] (Comp: ?, Cost: 1) f9(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f4(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, b1, ar_9, ar_10, ar_11, ar_12, c1, ar_14, d1, e1, f1, g1, h1, ar_20, ar_21, ar_22, ar_23)) [ ar_14 >= 0 /\ y >= 2 /\ z >= y /\ a1 >= 1 /\ ar_15 = ar_13 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20 - 1, b1, ar_20 - 1, ar_23)) [ c1 >= ar_13 + 1 /\ ar_20 >= 0 /\ y >= 2 /\ z >= y /\ a1 >= c1 + 1 /\ ar_15 = 0 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20 - 1, b1, ar_20 - 1, ar_23)) [ c1 >= ar_13 + 1 /\ ar_20 >= 0 /\ y >= 2 /\ z >= y /\ c1 >= a1 + 1 /\ ar_15 = 0 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20 - 1, b1, ar_20 - 1, ar_23)) [ ar_13 >= c1 + 1 /\ ar_20 >= 0 /\ y >= 2 /\ z >= y /\ a1 >= c1 + 1 /\ ar_15 = 0 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, z, a1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, a1, ar_11, ar_12, ar_13, ar_14, 0, a1, 0, a1, ar_13, ar_20 - 1, b1, ar_20 - 1, ar_23)) [ ar_13 >= c1 + 1 /\ ar_20 >= 0 /\ y >= 2 /\ z >= y /\ c1 >= a1 + 1 /\ ar_15 = 0 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f4(y, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, z, ar_9, ar_10, ar_11, ar_12, a1, ar_14, b1, c1, d1, e1, f1, ar_20, ar_21, ar_22, ar_23)) [ y >= 2 /\ ar_20 >= 0 /\ ar_15 = ar_13 ] (Comp: ?, Cost: 1) f1(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, ar_20 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_2, ar_11, ar_12, ar_2, ar_20, 0, ar_2, 0, ar_2, ar_2, ar_20, ar_21, ar_22, ar_23)) [ ar_1 >= ar_0 /\ ar_1 >= 0 /\ z >= y /\ y >= 2 /\ ar_2 >= 1 /\ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f1(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, ar_20 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_2, ar_11, ar_12, ar_2, ar_20, 0, ar_2, 0, ar_2, ar_2, ar_20, ar_21, ar_22, ar_23)) [ ar_1 >= ar_0 /\ ar_1 >= 0 /\ z >= y /\ y >= 2 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) f1(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f10(y, ar_20 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_2, ar_11, ar_12, ar_2, ar_20, 0, ar_2, 0, ar_2, ar_2, ar_20, ar_21, ar_22, ar_23)) [ ar_1 >= ar_0 /\ ar_1 >= 0 /\ z >= y /\ y >= 2 /\ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f3(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f4(y, 0, 0, ar_3, ar_4, ar_5, ar_6, ar_7, z, ar_9, ar_10, ar_11, ar_12, a1, ar_14, b1, c1, d1, e1, f1, ar_20, ar_21, ar_22, ar_23)) [ 0 >= y /\ 0 >= ar_0 ] (Comp: ?, Cost: 1) f3(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_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f1(ar_0, 2, y, z, a1, b1, c1, d1, e1, f1, y, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, g1)) [ ar_0 >= 2 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f3(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_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_13, ar_14, ar_15, ar_20]. popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Compl Integ Trans Syste 26843