details

property	value
status	complete
benchmark	loops.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n063.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.74888 seconds
cpu usage	14.8123
user time	14.4306
system time	0.381647
max virtual memory	1.872078E7
max residence set size	232736.0

stage attributes

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

output

14.74/8.71 WORST_CASE(?, O(n^2)) 14.74/8.72 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 14.74/8.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.74/8.72 14.74/8.72 14.74/8.72 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, nat(2 * Arg_0 * max(8, -4 + 4 * Arg_0) + min(8 + -8 * Arg_0, -16)) + nat(-1 + Arg_0) + max(8, -8 + 8 * Arg_0) + max(2 * Arg_0, 4) + max(6, 6 + Arg_0)). 14.74/8.72 14.74/8.72 (0) CpxIntTrs 14.74/8.72 (1) Koat2 Proof [FINISHED, 3442 ms] 14.74/8.72 (2) BOUNDS(1, nat(2 * Arg_0 * max(8, -4 + 4 * Arg_0) + min(8 + -8 * Arg_0, -16)) + nat(-1 + Arg_0) + max(8, -8 + 8 * Arg_0) + max(2 * Arg_0, 4) + max(6, 6 + Arg_0)) 14.74/8.72 14.74/8.72 14.74/8.72 ---------------------------------------- 14.74/8.72 14.74/8.72 (0) 14.74/8.72 Obligation: 14.74/8.72 Complexity Int TRS consisting of the following rules: 14.74/8.72 start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, F, E, F)) :|: 0 >= A + 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 14.74/8.72 start(A, B, C, D, E, F) -> Com_1(lbl121(A, 1, C, F - 1, E, F)) :|: A >= 0 && 1 >= A && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 14.74/8.72 start(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, F, E, F)) :|: A >= 2 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A 14.74/8.72 lbl121(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 0 && B >= 0 && B >= 1 && D + 1 >= 0 && D + 1 <= 0 && F >= A && F <= A 14.74/8.72 lbl121(A, B, C, D, E, F) -> Com_1(lbl121(A, 1, C, D - 1, E, F)) :|: D >= 0 && 1 >= D && A >= D + 1 && B >= D + 1 && B >= 1 && D + 1 >= 0 && F >= A && F <= A 14.74/8.72 lbl121(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, D, E, F)) :|: D >= 2 && A >= D + 1 && B >= D + 1 && B >= 1 && D + 1 >= 0 && F >= A && F <= A 14.74/8.72 lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 2 * B, C, D, E, F)) :|: D >= B + 1 && B >= 2 && 2 * D >= B + 2 && A >= D && F >= A && F <= A 14.74/8.72 lbl101(A, B, C, D, E, F) -> Com_1(lbl121(A, B, C, D - 1, E, F)) :|: B >= D && B >= 2 && 2 * D >= B + 2 && A >= D && F >= A && F <= A 14.74/8.72 start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, E, E, A)) :|: TRUE 14.74/8.72 14.74/8.72 The start-symbols are:[start0_6] 14.74/8.72 14.74/8.72 14.74/8.72 ---------------------------------------- 14.74/8.72 14.74/8.72 (1) Koat2 Proof (FINISHED) 14.74/8.72 YES( ?, 5+max([1, 1+Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([0, -1+Arg_0])+max([4, -4+4*Arg_0])+max([4, 2*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([4, -4+4*Arg_0]) {O(n^2)}) 14.74/8.72 14.74/8.72 14.74/8.72 14.74/8.72 Initial Complexity Problem: 14.74/8.72 14.74/8.72 Start: start0 14.74/8.72 14.74/8.72 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 14.74/8.72 14.74/8.72 Temp_Vars: 14.74/8.72 14.74/8.72 Locations: lbl101, lbl121, start, start0, stop 14.74/8.72 14.74/8.72 Transitions: 14.74/8.72 14.74/8.72 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,(2)*Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 4 <= Arg_1+Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_0 && 2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 4 <= Arg_0+Arg_3 && 2 <= Arg_1 && 4 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1+1 <= Arg_3 && 2 <= Arg_1 && Arg_1+2 <= (2)*Arg_3 && Arg_3 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 4 <= Arg_1+Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && Arg_3 <= Arg_0 && 2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 4 <= Arg_0+Arg_3 && 2 <= Arg_1 && 4 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_3 <= Arg_1 && 2 <= Arg_1 && Arg_1+2 <= (2)*Arg_3 && Arg_3 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= 1+Arg_3+Arg_5 && 1+Arg_3 <= Arg_5 && 1 <= Arg_1+Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_1 && 1+Arg_3 <= Arg_0 && 0 <= 1+Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= 1+Arg_0+Arg_3 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 0 <= Arg_0 && 2 <= Arg_3 && Arg_3+1 <= Arg_0 && Arg_3+1 <= Arg_1 && 1 <= Arg_1 && 0 <= 1+Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5 <= Arg_0 && 0 <= Arg_5 && 0 <= 1+Arg_3+Arg_5 && 1+Arg_3 <= Arg_5 && 1 <= Arg_1+Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_1 && 1+Arg_3 <= Arg_0 && 0 <= 1+Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= 1+Arg_0+Arg_3 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 0 <= Arg_0 && 0 <= Arg_3 && Arg_3 <= 1 && Arg_3+1 <= Arg_0 && Arg_3+1 <= Arg_1 && 1 <= Arg_1 && 0 <= 1+Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 lbl121(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 <= 1+Arg_3+Arg_5 && 1+Arg_3 <= Arg_5 && 1 <= Arg_1+Arg_5 && 0 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_1 && 1+Arg_3 <= Arg_0 && 0 <= 1+Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= 1+Arg_0+Arg_3 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && 0 <= Arg_1 && 1 <= Arg_1 && Arg_3+1 <= 0 && 0 <= 1+Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,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 && 2 <= Arg_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 14.74/8.72 14.74/8.72 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_5-1,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_0 <= 1 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 14.74/8.72 14.74/8.72 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,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 && 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 14.74/8.72 14.74/8.72 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):|: 14.74/8.72 14.74/8.72 14.74/8.72 14.74/8.72 Timebounds: 14.74/8.72 14.74/8.72 Overall timebound: 5+max([1, 1+Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([0, -1+Arg_0])+max([4, -4+4*Arg_0])+max([4, 2*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([4, -4+4*Arg_0]) {O(n^2)} 14.74/8.72 14.74/8.72 6: lbl101->lbl101: max([4, -4+4*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([4, -4+4*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])]) {O(n^2)} 14.74/8.72 14.74/8.72 7: lbl101->lbl121: max([4, 2*Arg_0]) {O(n)} 14.74/8.72 14.74/8.72 3: lbl121->stop: 1 {O(1)} 14.74/8.72 14.74/8.72 4: lbl121->lbl121: max([1, 1+Arg_0]) {O(n)} 14.74/8.72 14.74/8.72 5: lbl121->lbl101: max([0, -1+Arg_0]) {O(n)} 14.74/8.72 14.74/8.72 0: start->stop: 1 {O(1)} 14.74/8.72 14.74/8.72 1: start->lbl121: 1 {O(1)} 14.74/8.72 14.74/8.72 2: start->lbl101: 1 {O(1)} 14.74/8.72 14.74/8.72 8: start0->start: 1 {O(1)} 14.74/8.72 14.74/8.72 14.74/8.72 14.74/8.72 Costbounds: 14.74/8.72 14.74/8.72 Overall costbound: 5+max([1, 1+Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([0, -1+Arg_0])+max([4, -4+4*Arg_0])+max([4, 2*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([4, -4+4*Arg_0]) {O(n^2)} 14.74/8.72 14.74/8.72 6: lbl101->lbl101: max([4, -4+4*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])])+max([4, -4+4*Arg_0])+max([0, (-1+Arg_0)*max([8, -4+4*Arg_0])]) {O(n^2)} 14.74/8.72 14.74/8.72 7: lbl101->lbl121: max([4, 2*Arg_0]) {O(n)} 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