details

property	value
status	complete
benchmark	Loop.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	61.1511 seconds
cpu usage	124.824
user time	122.903
system time	1.92038
max virtual memory	1.8875624E7
max residence set size	326916.0

stage attributes

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

output

124.59/60.70 WORST_CASE(Omega(n^1), O(n^1)) 124.70/60.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 124.70/60.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 124.70/60.71 124.70/60.71 124.70/60.71 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 124.70/60.71 124.70/60.71 (0) CpxIntTrs 124.70/60.71 (1) Koat Proof [FINISHED, 1594 ms] 124.70/60.71 (2) BOUNDS(1, n^1) 124.70/60.71 (3) Loat Proof [FINISHED, 59.1 s] 124.70/60.71 (4) BOUNDS(n^1, INF) 124.70/60.71 124.70/60.71 124.70/60.71 ---------------------------------------- 124.70/60.71 124.70/60.71 (0) 124.70/60.71 Obligation: 124.70/60.71 Complexity Int TRS consisting of the following rules: 124.70/60.71 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && 3 >= P && P >= 1 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && P >= 5 124.70/60.71 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, 3, 4, 1, 0, 3, 4, 2, M, N)) :|: TRUE 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 3, M, N)) :|: 7 >= P && P >= 1 124.70/60.71 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 6, M, N)) :|: 7 >= P && P >= 1 124.70/60.71 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, C, C, E, E, O, 2, 0, P, O, 2, 4, M, N)) :|: 7 >= O && 1 >= P && P >= 0 && O >= 1 124.70/60.71 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, C, C, E, E, O, 7, 1, P, O, 7, 4, M, N)) :|: 7 >= O && 1 >= P && P >= 0 && O >= 1 && H >= 1 && H <= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 0, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H >= 1 && H <= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 0, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H >= 1 && H <= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, P, 4, 0, 0, P, 4, 2, M, N)) :|: M >= E + 2 && N >= C + 2 && M >= 1 && N >= 1 && 7 >= P && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 7, M, N)) :|: E + 1 >= M && C + 1 >= N && 7 >= P && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.70/60.71 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.70/60.71 124.70/60.71 The start-symbols are:[f0_14] 124.70/60.71 124.70/60.71 124.70/60.71 ---------------------------------------- 124.70/60.71 124.70/60.71 (1) Koat Proof (FINISHED) 124.70/60.71 YES(?, 23*ar_4 + 23*ar_12 + 44*ar_2 + 44*ar_13 + 82) 124.70/60.71 124.70/60.71 124.70/60.71 124.70/60.71 Initial complexity problem: 124.70/60.71 124.70/60.71 1: T: 124.70/60.71 124.70/60.71 (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) -> Com_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)) 124.70/60.71 124.70/60.71 (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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, 0, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, 0, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f7(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 7, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, 3, p, 0, 0, 3, p, 2, ar_12, ar_13)) [ 7 >= p /\ 3 >= p /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, 3, p, 0, 0, 3, p, 2, ar_12, ar_13)) [ 7 >= p /\ p >= 5 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f2(0, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, 3, 4, 1, 0, 3, 4, 2, ar_12, ar_13)) 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 7, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 0, p, o, 3, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 0, p, o, 3, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 0, p, 4, 3, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f6(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 6, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f6(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 6, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.70/60.71 124.70/60.71 (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) -> Com_1(f6(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 6, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f6(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) -> Com_1(f4(p, ar_2, ar_2, ar_4, ar_4, o, 2, 0, p, o, 2, 4, ar_12, ar_13)) [ 7 >= o /\ 1 >= p /\ p >= 0 /\ o >= 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f6(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) -> Com_1(f4(p, ar_2, ar_2, ar_4, ar_4, o, 7, 1, p, o, 7, 4, ar_12, ar_13)) [ 7 >= o /\ 1 >= p /\ p >= 0 /\ o >= 1 /\ ar_7 = 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f4(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, p, o, 0, 0, p, o, 2, ar_12, ar_13)) [ ar_12 >= 1 /\ ar_12 >= ar_4 + 1 /\ ar_13 >= 1 /\ ar_13 >= ar_2 + 1 /\ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 /\ ar_7 = 1 ] 124.70/60.71 124.70/60.71 (Comp: ?, Cost: 1) f4(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, p, o, 0, 0, p, o, 2, ar_12, ar_13)) [ ar_12 >= 1 /\ ar_12 >= ar_4 + 1 /\ ar_13 >= 1 /\ ar_13 >= ar_2 + 1 /\ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 /\ ar_7 = 1 ] popout

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actions

all output return to Complexity_ITS 2019-03-21 04.46