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	n108.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.62295818329 seconds
cpu usage	14.512943812
max memory	3.72588544E8

stage attributes

key	value
output-size	12323
starexec-result	WORST_CASE(?, O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, nat(2 * Arg_0 * max(-4 + 4 * Arg_0, 8) + min(8 + -8 * Arg_0, -16)) + nat(-1 + Arg_0) + max(-8 + 8 * Arg_0, 8) + max(4, 2 * Arg_0) + max(6, 6 + Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 3395 ms] (2) BOUNDS(1, nat(2 * Arg_0 * max(-4 + 4 * Arg_0, 8) + min(8 + -8 * Arg_0, -16)) + nat(-1 + Arg_0) + max(-8 + 8 * Arg_0, 8) + max(4, 2 * Arg_0) + max(6, 6 + Arg_0)) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, E, E, A)) :|: TRUE The start-symbols are:[start0_6] ---------------------------------------- (1) Koat2 Proof (FINISHED) 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)}) Initial Complexity Problem: Start: start0 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 Temp_Vars: Locations: lbl101, lbl121, start, start0, stop Transitions: 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 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 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 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 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 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 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 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 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):|: Timebounds: 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)} 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)} 7: lbl101->lbl121: max([4, 2*Arg_0]) {O(n)} 3: lbl121->stop: 1 {O(1)} 4: lbl121->lbl121: max([1, 1+Arg_0]) {O(n)} 5: lbl121->lbl101: max([0, -1+Arg_0]) {O(n)} 0: start->stop: 1 {O(1)} 1: start->lbl121: 1 {O(1)} 2: start->lbl101: 1 {O(1)} 8: start0->start: 1 {O(1)} Costbounds: popout

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

job log

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actions

all output return to Compl Integ Trans Syste 26843