details

property	value
status	complete
benchmark	rsd.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.73777 seconds
cpu usage	11.7334
user time	11.2674
system time	0.465963
max virtual memory	1.8774292E7
max residence set size	249972.0

stage attributes

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

output

11.54/7.70 WORST_CASE(Omega(n^1), O(n^2)) 11.54/7.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 11.54/7.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.54/7.71 11.54/7.71 11.54/7.71 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(6, 6 + 16 * Arg_0) + 4 * nat(2 * Arg_0) * max(2, 2 * Arg_0) + nat(1 + 2 * Arg_0)). 11.54/7.71 11.54/7.71 (0) CpxIntTrs 11.54/7.71 (1) Koat2 Proof [FINISHED, 5928 ms] 11.54/7.71 (2) BOUNDS(1, max(6, 6 + 16 * Arg_0) + 4 * nat(2 * Arg_0) * max(2, 2 * Arg_0) + nat(1 + 2 * Arg_0)) 11.54/7.71 (3) Loat Proof [FINISHED, 1016 ms] 11.54/7.71 (4) BOUNDS(n^1, INF) 11.54/7.71 11.54/7.71 11.54/7.71 ---------------------------------------- 11.54/7.71 11.54/7.71 (0) 11.54/7.71 Obligation: 11.54/7.71 Complexity Int TRS consisting of the following rules: 11.54/7.71 start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 11.54/7.71 start(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, 2 * D, F, 2 * D - 1, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 11.54/7.71 start(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, 2 * D, C, D, 2 * D - 1, F, 2 * D - 1, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 11.69/7.71 lbl82(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: E >= A && 2 * A >= E && D >= A && D <= A && G + 1 >= A && G + 1 <= A 11.69/7.71 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, E, F, G - 1, H)) :|: G >= A && E >= G + 1 && 2 * A >= E && G + 1 >= A && D >= A && D <= A 11.69/7.71 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, G, C, D, E - 1, F, E - 1, H)) :|: G >= A && E >= G + 1 && 2 * A >= E && G + 1 >= A && D >= A && D <= A 11.69/7.71 lbl121(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= E + 1 && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A 11.69/7.71 lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, D, E, F, G - 1, H)) :|: E >= A && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A 11.69/7.71 lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, G, C, D, E - 1, F, E - 1, H)) :|: E >= A && 2 * A >= E + 1 && B >= A && E + 1 >= B && G >= E && G <= E && D >= A && D <= A 11.69/7.71 start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE 11.69/7.71 11.69/7.71 The start-symbols are:[start0_8] 11.69/7.71 11.69/7.71 11.69/7.71 ---------------------------------------- 11.69/7.71 11.69/7.71 (1) Koat2 Proof (FINISHED) 11.69/7.71 YES( ?, 6+2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+2*2*max([0, 2*Arg_0])+max([0, 1+2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)}) 11.69/7.71 11.69/7.71 11.69/7.71 11.69/7.71 Initial Complexity Problem: 11.69/7.71 11.69/7.71 Start: start0 11.69/7.71 11.69/7.71 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 11.69/7.71 11.69/7.71 Temp_Vars: 11.69/7.71 11.69/7.71 Locations: lbl121, lbl82, start, start0, stop 11.69/7.71 11.69/7.71 Transitions: 11.69/7.71 11.69/7.71 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,Arg_6,Arg_2,Arg_3,Arg_4-1,Arg_5,Arg_4-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 11.69/7.71 11.69/7.71 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 11.69/7.71 11.69/7.71 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= 1+Arg_6 && 0 <= 2+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= 1+Arg_4 && 0 <= 1+Arg_3+Arg_4 && Arg_3 <= 1+Arg_4 && 0 <= 1+Arg_1+Arg_4 && 0 <= 1+Arg_0+Arg_4 && Arg_0 <= 1+Arg_4 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 0 <= Arg_0 && Arg_4+1 <= Arg_0 && Arg_4+1 <= (2)*Arg_0 && Arg_0 <= Arg_1 && Arg_1 <= Arg_4+1 && Arg_6 <= Arg_4 && Arg_4 <= Arg_6 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 11.69/7.71 11.69/7.71 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,Arg_6,Arg_2,Arg_3,Arg_4-1,Arg_5,Arg_4-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_6 && Arg_6+1 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_0 <= Arg_6+1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 11.69/7.71 11.69/7.71 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_6 && Arg_6+1 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_0 <= Arg_6+1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 11.69/7.71 11.69/7.71 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= 1+Arg_6 && 0 <= 1+Arg_4+Arg_6 && 0 <= 1+Arg_3+Arg_6 && Arg_3 <= 1+Arg_6 && 0 <= 1+Arg_0+Arg_6 && Arg_0 <= 1+Arg_6 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && Arg_3 <= Arg_4 && 0 <= Arg_0+Arg_4 && Arg_0 <= Arg_4 && Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 0 <= Arg_0 && Arg_0 <= Arg_4 && Arg_4 <= (2)*Arg_0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_6+1 <= Arg_0 && Arg_0 <= Arg_6+1 11.69/7.71 11.69/7.71 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl121(Arg_0,(2)*Arg_3,Arg_2,Arg_3,(2)*Arg_3-1,Arg_5,(2)*Arg_3-1,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 11.69/7.71 11.69/7.71 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_3,(2)*Arg_3,Arg_5,(2)*Arg_3-1,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 11.69/7.71 11.69/7.71 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_4 && Arg_4 <= Arg_5 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0+1 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_4 <= Arg_5 && Arg_5 <= Arg_4 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 11.69/7.71 11.69/7.71 start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> start(Arg_0,Arg_2,Arg_2,Arg_0,Arg_5,Arg_5,Arg_7,Arg_7):|: 11.69/7.71 11.69/7.71 11.69/7.71 11.69/7.71 Timebounds: 11.69/7.71 11.69/7.71 Overall timebound: 6+2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+2*2*max([0, 2*Arg_0])+max([0, 1+2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)} 11.69/7.71 11.69/7.71 6: lbl121->stop: 1 {O(1)} 11.69/7.71 11.69/7.71 7: lbl121->lbl82: max([0, 1+2*Arg_0])+max([0, 2*Arg_0]) {O(n)} 11.69/7.71 11.69/7.71 8: lbl121->lbl121: 2*max([0, 2*Arg_0]) {O(n)} 11.69/7.71 11.69/7.71 3: lbl82->stop: 1 {O(1)} 11.69/7.71 11.69/7.71 4: lbl82->lbl82: 2*2*max([0, 2*Arg_0])*max([2, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0])+max([0, 2*Arg_0]) {O(n^2)} 11.69/7.71 11.69/7.71 5: lbl82->lbl121: 2*max([0, 2*Arg_0]) {O(n)} 11.69/7.71 11.69/7.71 0: start->stop: 1 {O(1)} 11.69/7.71 11.69/7.71 1: start->lbl82: 1 {O(1)} 11.69/7.71 11.69/7.71 2: start->lbl121: 1 {O(1)} 11.69/7.71 11.69/7.71 9: start0->start: 1 {O(1)} 11.69/7.71 11.69/7.71 11.69/7.71 popout

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all output return to Complexity_ITS 2019-03-21 04.46