details

property	value
status	complete
benchmark	elmhes.c.i.elmhes.pl.t2.nor.t2.rlgfixed.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n165.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	42.5893 seconds
cpu usage	51.468
user time	50.7613
system time	0.706691
max virtual memory	1.8756784E7
max residence set size	248780.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

51.37/42.55 WORST_CASE(Omega(n^1), O(n^2)) 51.37/42.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 51.37/42.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 51.37/42.57 51.37/42.57 51.37/42.57 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 51.37/42.57 51.37/42.57 (0) CpxIntTrs 51.37/42.57 (1) Koat Proof [FINISHED, 795 ms] 51.37/42.57 (2) BOUNDS(1, n^2) 51.37/42.57 (3) Loat Proof [FINISHED, 5511 ms] 51.37/42.57 (4) BOUNDS(n^1, INF) 51.37/42.57 51.37/42.57 51.37/42.57 ---------------------------------------- 51.37/42.57 51.37/42.57 (0) 51.37/42.57 Obligation: 51.37/42.57 Complexity Int TRS consisting of the following rules: 51.37/42.57 f2(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, 0, B, E, F, G, H)) :|: A >= B + 1 51.37/42.57 f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, C, D, E + 1, J, I, H)) :|: A >= E && I >= J 51.37/42.57 f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, J, E, E + 1, I, K, H)) :|: A >= E && I >= 1 + K 51.37/42.57 f19(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E + 1, F, G, J)) :|: A >= E 51.37/42.57 f27(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E + 1, F, G, J)) :|: A >= E 51.37/42.57 f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 51.37/42.57 f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: C >= 1 51.37/42.57 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && 0 >= I + 1 51.37/42.57 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && I >= 1 51.37/42.57 f43(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E + 1, F, G, H)) :|: A >= E 51.37/42.57 f49(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E + 1, F, G, H)) :|: A >= E 51.37/42.57 f36(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0)) :|: A >= D 51.37/42.57 f34(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, 0, D, E, F, G, H)) :|: C >= 0 && C <= 0 51.37/42.57 f49(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A 51.37/42.57 f43(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 51.37/42.57 f36(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A 51.37/42.57 f27(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 51.37/42.57 f19(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 51.37/42.57 f8(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, B, E, F, G, H)) :|: E >= 1 + A && B >= D && B <= D 51.37/42.57 f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: B >= D + 1 && E >= 1 + A 51.37/42.57 f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: D >= 1 + B && E >= 1 + A 51.37/42.57 f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, G, H)) :|: B >= A 51.37/42.57 start(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B, C, D, E, F, G, H)) :|: TRUE 51.37/42.57 51.37/42.57 The start-symbols are:[start_8] 51.37/42.57 51.37/42.57 51.37/42.57 ---------------------------------------- 51.37/42.57 51.37/42.57 (1) Koat Proof (FINISHED) 51.37/42.57 YES(?, 312460831275774*ar_0 + 44637261614347*ar_1 + 267823569665387*ar_4 + 5040*ar_0^2 + 9150*ar_0*ar_4 + 5550*ar_0*ar_1 + 4830*ar_1*ar_4 + 690*ar_1^2 + 4140*ar_4^2 + 267823569661249) 51.37/42.57 51.37/42.57 51.37/42.57 51.37/42.57 Initial complexity problem: 51.37/42.57 51.37/42.57 1: T: 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, j, i, ar_7)) [ ar_0 >= ar_4 /\ i >= j ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1, i, k, ar_7)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_2 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ i >= 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0)) [ ar_0 >= ar_3 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 = 0 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 51.37/42.57 51.37/42.57 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_0 ] popout

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

job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46