details

property	value
status	complete
benchmark	aaron2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	289.826 seconds
cpu usage	298.3
user time	295.826
system time	2.47406
max virtual memory	1.8789996E7
max residence set size	311904.0

stage attributes

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

output

298.10/289.76 WORST_CASE(Omega(n^1), O(n^1)) 298.10/289.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 298.10/289.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 298.10/289.78 298.10/289.78 298.10/289.78 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(-4 * Arg_2 + max(-4 + 4 * Arg_4, -4 + -4 * Arg_0 + 4 * Arg_4)) + nat(-4 * Arg_2 + 4 * Arg_4) + max(6 + -1 * Arg_2 + Arg_4, 7) + nat(-3 * Arg_2 + 3 * Arg_4) + nat(-2 + -2 * Arg_2 + 2 * Arg_4)). 298.10/289.78 298.10/289.78 (0) CpxIntTrs 298.10/289.78 (1) Koat2 Proof [FINISHED, 4039 ms] 298.10/289.78 (2) BOUNDS(1, nat(-4 * Arg_2 + max(-4 + 4 * Arg_4, -4 + -4 * Arg_0 + 4 * Arg_4)) + nat(-4 * Arg_2 + 4 * Arg_4) + max(6 + -1 * Arg_2 + Arg_4, 7) + nat(-3 * Arg_2 + 3 * Arg_4) + nat(-2 + -2 * Arg_2 + 2 * Arg_4)) 298.10/289.78 (3) Loat Proof [FINISHED, 288.6 s] 298.10/289.78 (4) BOUNDS(n^1, INF) 298.10/289.78 298.10/289.78 298.10/289.78 ---------------------------------------- 298.10/289.78 298.10/289.78 (0) 298.10/289.78 Obligation: 298.10/289.78 Complexity Int TRS consisting of the following rules: 298.10/289.78 start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: 0 >= A + 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 298.10/289.78 start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 0 && C >= E + 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 298.10/289.78 start(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && E >= C && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 298.10/289.78 start(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && E >= C && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 298.10/289.78 lbl91(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: B >= D + 1 && B >= C && A >= 0 && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A 298.10/289.78 lbl91(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: D >= B && 0 >= A + 1 && B >= C && A >= 0 && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A 298.10/289.78 lbl91(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && D >= B && B >= C && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A 298.10/289.78 lbl91(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && D >= B && B >= C && A + D + 1 >= B && E >= A + D + 1 && F >= A && F <= A 298.10/289.78 lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: B >= D + 1 && E >= D && A >= 0 && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A 298.10/289.78 lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: D >= B && 0 >= A + 1 && E >= D && A >= 0 && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A 298.10/289.78 lbl101(A, B, C, D, E, F) -> Com_1(lbl91(A, B, C, D - 1 - F, E, F)) :|: A >= 0 && D >= B && E >= D && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A 298.10/289.78 lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + F + B, C, D, E, F)) :|: A >= 0 && D >= B && E >= D && B >= A + C + 1 && A + D + 1 >= B && F >= A && F <= A 298.10/289.78 start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, E, E, A)) :|: TRUE 298.10/289.78 298.10/289.78 The start-symbols are:[start0_6] 298.10/289.78 298.10/289.78 298.10/289.78 ---------------------------------------- 298.10/289.78 298.10/289.78 (1) Koat2 Proof (FINISHED) 298.10/289.78 YES( ?, 7+max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+4*Arg_4])+max([0, Arg_4-Arg_2]) {O(n)}) 298.10/289.78 298.10/289.78 298.10/289.78 298.10/289.78 Initial Complexity Problem: 298.10/289.78 298.10/289.78 Start: start0 298.10/289.78 298.10/289.78 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 298.10/289.78 298.10/289.78 Temp_Vars: 298.10/289.78 298.10/289.78 Locations: lbl101, lbl91, start, start0, stop 298.10/289.78 298.10/289.78 Transitions: 298.10/289.78 298.10/289.78 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_3 <= Arg_4 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_3 <= Arg_4 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_2 <= Arg_3 && 1+Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_3 <= Arg_4 && 0 <= Arg_0 && Arg_0+Arg_2+1 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && Arg_1 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 lbl91(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_2 <= Arg_1 && 0 <= Arg_0 && Arg_1 <= Arg_0+Arg_3+1 && Arg_0+Arg_3+1 <= Arg_4 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,1+Arg_5+Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_2 <= Arg_4 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl91(Arg_0,Arg_1,Arg_2,Arg_3-1-Arg_5,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_2 <= Arg_4 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0+1 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_4+1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 298.10/289.78 298.10/289.78 start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_0):|: 298.10/289.78 298.10/289.78 298.10/289.78 298.10/289.78 Timebounds: 298.10/289.78 298.10/289.78 Overall timebound: 7+max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])])+max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2])+max([0, -4*Arg_2+4*Arg_4])+max([0, Arg_4-Arg_2]) {O(n)} 298.10/289.78 298.10/289.78 8: lbl101->stop: 1 {O(1)} 298.10/289.78 298.10/289.78 10: lbl101->lbl91: max([0, -4*Arg_2+4*Arg_4])+max([0, -4*Arg_2+max([4*(-1+Arg_4-Arg_0), 4*(-1+Arg_4)])]) {O(n)} 298.10/289.78 298.10/289.78 11: lbl101->lbl101: max([0, Arg_4-Arg_2])+max([0, -1+Arg_4-Arg_2]) {O(n)} 298.10/289.78 298.10/289.78 4: lbl91->stop: 1 {O(1)} 298.10/289.78 298.10/289.78 6: lbl91->lbl91: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 298.10/289.78 298.10/289.78 7: lbl91->lbl101: max([0, -1+Arg_4-Arg_2])+max([0, Arg_4-Arg_2]) {O(n)} 298.10/289.78 298.10/289.78 0: start->stop: 1 {O(1)} 298.10/289.78 298.10/289.78 1: start->stop: 1 {O(1)} 298.10/289.78 298.10/289.78 2: start->lbl91: 1 {O(1)} popout

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all output return to Complexity_ITS 2019-03-21 04.46