details

property	value
status	complete
benchmark	increase4.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	patrs

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.76449 seconds
cpu usage	3.74206
user time	3.52804
system time	0.214015
max virtual memory	1.8376428E7
max residence set size	214248.0

stage attributes

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

output

3.63/1.73 WORST_CASE(Omega(n^1), O(n^1)) 3.71/1.73 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 3.71/1.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.71/1.73 3.71/1.73 3.71/1.73 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + Arg_0 + -1 * Arg_1)). 3.71/1.73 3.71/1.73 (0) CpxIntTrs 3.71/1.73 (1) Koat2 Proof [FINISHED, 42 ms] 3.71/1.73 (2) BOUNDS(1, max(1, 1 + Arg_0 + -1 * Arg_1)) 3.71/1.73 (3) Loat Proof [FINISHED, 114 ms] 3.71/1.73 (4) BOUNDS(n^1, INF) 3.71/1.73 3.71/1.73 3.71/1.73 ---------------------------------------- 3.71/1.73 3.71/1.73 (0) 3.71/1.73 Obligation: 3.71/1.73 Complexity Int TRS consisting of the following rules: 3.71/1.73 f(A, B) -> Com_1(f(A + 1, B + 2)) :|: A >= B + 1 3.71/1.73 start(A, B) -> Com_1(f(A, B)) :|: TRUE 3.71/1.73 3.71/1.73 The start-symbols are:[start_2] 3.71/1.73 3.71/1.73 3.71/1.73 ---------------------------------------- 3.71/1.73 3.71/1.73 (1) Koat2 Proof (FINISHED) 3.71/1.73 YES( ?, max([1, 1+Arg_0-Arg_1]) {O(n)}) 3.71/1.73 3.71/1.73 3.71/1.73 3.71/1.73 Initial Complexity Problem: 3.71/1.73 3.71/1.73 Start: start 3.71/1.73 3.71/1.73 Program_Vars: Arg_0, Arg_1 3.71/1.73 3.71/1.73 Temp_Vars: 3.71/1.73 3.71/1.73 Locations: f, start 3.71/1.73 3.71/1.73 Transitions: 3.71/1.73 3.71/1.73 f(Arg_0,Arg_1) -> f(Arg_0+1,Arg_1+2):|:Arg_1+1 <= Arg_0 3.71/1.73 3.71/1.73 start(Arg_0,Arg_1) -> f(Arg_0,Arg_1):|: 3.71/1.73 3.71/1.73 3.71/1.73 3.71/1.73 Timebounds: 3.71/1.73 3.71/1.73 Overall timebound: max([1, 1+Arg_0-Arg_1]) {O(n)} 3.71/1.73 3.71/1.73 0: f->f: max([0, Arg_0-Arg_1]) {O(n)} 3.71/1.73 3.71/1.73 1: start->f: 1 {O(1)} 3.71/1.73 3.71/1.73 3.71/1.73 3.71/1.73 Costbounds: 3.71/1.73 3.71/1.73 Overall costbound: max([1, 1+Arg_0-Arg_1]) {O(n)} 3.71/1.73 3.71/1.73 0: f->f: max([0, Arg_0-Arg_1]) {O(n)} 3.71/1.73 3.71/1.73 1: start->f: 1 {O(1)} 3.71/1.73 3.71/1.73 3.71/1.73 3.71/1.73 Sizebounds: 3.71/1.73 3.71/1.73 `Lower: 3.71/1.73 3.71/1.73 0: f->f, Arg_0: Arg_0 {O(n)} 3.71/1.73 3.71/1.73 0: f->f, Arg_1: Arg_1 {O(n)} 3.71/1.73 3.71/1.73 1: start->f, Arg_0: Arg_0 {O(n)} 3.71/1.73 3.71/1.73 1: start->f, Arg_1: Arg_1 {O(n)} 3.71/1.73 3.71/1.73 `Upper: 3.71/1.73 3.71/1.73 0: f->f, Arg_0: Arg_0+max([0, Arg_0-Arg_1]) {O(n)} 3.71/1.73 3.71/1.73 0: f->f, Arg_1: Arg_1+max([0, 2*(Arg_0-Arg_1)]) {O(n)} 3.71/1.73 3.71/1.73 1: start->f, Arg_0: Arg_0 {O(n)} 3.71/1.73 3.71/1.73 1: start->f, Arg_1: Arg_1 {O(n)} 3.71/1.73 3.71/1.73 3.71/1.73 ---------------------------------------- 3.71/1.73 3.71/1.73 (2) 3.71/1.73 BOUNDS(1, max(1, 1 + Arg_0 + -1 * Arg_1)) 3.71/1.73 3.71/1.73 ---------------------------------------- 3.71/1.73 popout

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

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46