details

property	value
status	complete
benchmark	rlft3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.9200499058 seconds
cpu usage	29.62154855
max memory	4.81386496E8

stage attributes

key	value
output-size	122372
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 832 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 12.2 s] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f16(1, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 1 && A <= 1 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: H >= I f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f18(A, B, C, D, E, F, G, H, I, J, K + 1, L + 2, M, N, O, P, Q, R, S, T, U, V, W)) :|: J >= K f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= A f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, X, Y, Z, A1, B1, C1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 2 f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, I, J, K, L, H - I + 2, 1, 0, P, Q, R, S, T, U, V, W)) :|: 0 >= I && H >= I f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, I, J, K, L, H - I + 2, 1, 0, P, Q, R, S, T, U, V, W)) :|: I >= 2 && H >= I f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, E, F, G, H, 1, J, K, L, 1, 1, 0, P, Q, R, S, T, U, V, W)) :|: H >= 1 && I >= 1 && I <= 1 f35(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: P >= 2 * X && 3 * X >= P + 1 && X + 1 >= Q f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= Q && J >= K f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: Q >= 2 && J >= K f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, X, M, N, O, P, 1, Y, Z, A1, B1, V, W)) :|: 0 >= K && J >= K && Q >= 1 && Q <= 1 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, X, M, N, O, P, 1, Y, Z, A1, B1, V, W)) :|: J >= K && K >= 2 && Q >= 1 && Q <= 1 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, 2, 1, M, N, O, P, 1, X, Y, Z, A1, V, W)) :|: J >= 1 && K >= 1 && K <= 1 && Q >= 1 && Q <= 1 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, J - K + 2, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: 0 >= K f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K + 1, J - K + 2, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: K >= 2 f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, 2, 1, M, N, O, P, Q, X, Y, Z, A1, B1, W)) :|: K >= 1 && K <= 1 f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f35(A, B, C, D, N, F, G, H, I, J, K, L, M, X, Y, P, Q + 1, R, S, T, U, V, W + 2)) :|: K >= 1 + J f35(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: P >= 2 * X && 3 * X >= P + 1 && Q >= 2 + X f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= 2 + A && I >= 1 + H f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 0 && I >= 1 + H f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f76(-(1), B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= 1 + H && A + 1 >= 0 && A + 1 <= 0 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f16(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: K >= 1 + J f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f28(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= 1 + H The start-symbols are:[f0_23] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*ar_7 + 8*ar_8 + 13*ar_9 + 25*ar_10 + 3*ar_15 + 3*ar_16 + 59) Initial complexity problem: 1: T: (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f16(1, x, y, z, a1, b1, c1, 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_0 = 1 ] (Comp: ?, Cost: 1) f16(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) -> Com_1(f18(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_7 >= ar_8 ] (Comp: ?, Cost: 1) f18(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) -> Com_1(f18(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 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_9 >= ar_10 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(ar_0, x, y, z, a1, b1, c1, 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)) [ 0 >= ar_0 ] (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, ar_18, ar_19, ar_20, ar_21, ar_22) -> Com_1(f28(ar_0, x, y, z, a1, b1, c1, 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_0 >= 2 ] (Comp: ?, Cost: 1) f28(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) -> Com_1(f35(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_7 - ar_8 + 2, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ 0 >= ar_8 /\ ar_7 >= ar_8 ] (Comp: ?, Cost: 1) f28(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) -> Com_1(f35(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_7 - ar_8 + 2, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_8 >= 2 /\ ar_7 >= ar_8 ] (Comp: ?, Cost: 1) f28(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) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, 1, ar_9, ar_10, ar_11, 1, 1, 0, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22)) [ ar_7 >= 1 /\ ar_8 = 1 ] (Comp: ?, Cost: 1) f35(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) -> Com_1(f37(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_15 >= 2*x /\ 3*x >= ar_15 + 1 /\ x + 1 >= ar_16 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f52(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)) [ 0 >= ar_16 /\ ar_9 >= ar_10 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f52(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_16 >= 2 /\ ar_9 >= ar_10 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, x, ar_12, ar_13, ar_14, ar_15, 1, y, z, a1, b1, ar_21, ar_22)) [ 0 >= ar_10 /\ ar_9 >= ar_10 /\ ar_16 = 1 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, x, ar_12, ar_13, ar_14, ar_15, 1, y, z, a1, b1, ar_21, ar_22)) [ ar_9 >= ar_10 /\ ar_10 >= 2 /\ ar_16 = 1 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, 2, 1, ar_12, ar_13, ar_14, ar_15, 1, x, y, z, a1, ar_21, ar_22)) [ ar_9 >= 1 /\ ar_10 = 1 /\ ar_16 = 1 ] (Comp: ?, Cost: 1) f52(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_9 - ar_10 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ 0 >= ar_10 ] (Comp: ?, Cost: 1) f52(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_9 - ar_10 + 2, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ ar_10 >= 2 ] (Comp: ?, Cost: 1) f52(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) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, 2, 1, ar_12, ar_13, ar_14, ar_15, ar_16, x, y, z, a1, b1, ar_22)) [ ar_10 = 1 ] (Comp: ?, Cost: 1) f37(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) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_13, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, x, y, ar_15, ar_16 + 1, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22 + 2)) [ ar_10 >= ar_9 + 1 ] popout

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

job log

popout

actions

all output return to Compl Integ Trans Syste 26843