details

property	value
status	complete
benchmark	elmhes.c.i.elmhes.pl.t2.fixed.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	46.2775 seconds
cpu usage	55.0673
user time	54.329
system time	0.738368
max virtual memory	1.8738364E7
max residence set size	246216.0

stage attributes

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

output

54.93/46.25 WORST_CASE(Omega(n^1), O(n^2)) 55.02/46.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 55.02/46.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 55.02/46.26 55.02/46.26 55.02/46.26 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 55.02/46.26 55.02/46.26 (0) CpxIntTrs 55.02/46.26 (1) Koat Proof [FINISHED, 812 ms] 55.02/46.26 (2) BOUNDS(1, n^2) 55.02/46.26 (3) Loat Proof [FINISHED, 5656 ms] 55.02/46.26 (4) BOUNDS(n^1, INF) 55.02/46.26 55.02/46.26 55.02/46.26 ---------------------------------------- 55.02/46.26 55.02/46.26 (0) 55.02/46.26 Obligation: 55.02/46.26 Complexity Int TRS consisting of the following rules: 55.02/46.26 f2(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, 0, B, E, F, G, H)) :|: A >= B + 1 55.02/46.26 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 55.02/46.26 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 55.02/46.26 f19(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E + 1, F, G, J)) :|: A >= E 55.02/46.26 f27(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E + 1, F, G, J)) :|: A >= E 55.02/46.26 f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 55.02/46.26 f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: C >= 1 55.02/46.26 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: 0 >= I + 1 && A >= D && I >= C * K && C * K + K >= I + 1 && K >= J && I >= C * L && C * L + L >= I + 1 && J >= L 55.02/46.26 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: I >= 1 && A >= D && I >= C * K && C * K + K >= I + 1 && K >= J && I >= C * L && C * L + L >= I + 1 && J >= L 55.02/46.26 f43(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E + 1, F, G, H)) :|: A >= E 55.02/46.26 f49(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E + 1, F, G, H)) :|: A >= E 55.02/46.26 f36(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0)) :|: A >= D 55.02/46.26 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 55.02/46.26 f49(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A 55.02/46.26 f43(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 55.02/46.26 f36(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A 55.02/46.26 f27(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 55.02/46.26 f19(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 55.02/46.26 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 55.02/46.26 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 55.02/46.26 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 55.02/46.26 f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, G, H)) :|: B >= A 55.02/46.26 start(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B, C, D, E, F, G, H)) :|: TRUE 55.02/46.26 55.02/46.26 The start-symbols are:[start_8] 55.02/46.26 55.02/46.26 55.02/46.26 ---------------------------------------- 55.02/46.26 55.02/46.26 (1) Koat Proof (FINISHED) 55.02/46.26 YES(?, 312460831277084*ar_0 + 44637261614517*ar_1 + 267823569666587*ar_4 + 5180*ar_0^2 + 9480*ar_0*ar_4 + 5570*ar_0*ar_1 + 4860*ar_1*ar_4 + 690*ar_1^2 + 4320*ar_4^2 + 267823569662269) 55.02/46.26 55.02/46.26 55.02/46.26 55.02/46.26 Initial complexity problem: 55.02/46.26 55.02/46.26 1: T: 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ] 55.02/46.26 55.02/46.26 (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)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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 ] 55.02/46.26 55.02/46.26 (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.

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actions

all output return to Complexity_ITS 2019-03-21 04.46