details

property	value
status	complete
benchmark	example.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n107.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.08328413963 seconds
cpu usage	4.267632438
max memory	2.36650496E8

stage attributes

key	value
output-size	4885
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(Arg_1) + max(1, 1 + Arg_0)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 160 ms] (2) BOUNDS(1, nat(Arg_1) + max(1, 1 + Arg_0)) (3) Loat Proof [FINISHED, 407 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f1(A, B) -> Com_1(f2(A, B)) :|: A >= 1 && B >= 1 f2(A, B) -> Com_1(f2(A - 1, B)) :|: A >= 2 && B >= 1 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= 1 && B >= 2 The start-symbols are:[f1_2] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, max([0, Arg_1])+max([1, 1+Arg_0]) {O(n)}) Initial Complexity Problem: Start: f1 Program_Vars: Arg_0, Arg_1 Temp_Vars: Locations: f1, f2 Transitions: f1(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1 <= Arg_0 && 1 <= Arg_1 f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && 2 <= Arg_0 && 1 <= Arg_1 f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && 1 <= Arg_0 && 2 <= Arg_1 Timebounds: Overall timebound: max([0, Arg_1])+max([1, 1+Arg_0]) {O(n)} 0: f1->f2: 1 {O(1)} 1: f2->f2: max([0, Arg_0]) {O(n)} 2: f2->f2: max([0, Arg_1]) {O(n)} Costbounds: Overall costbound: max([0, Arg_1])+max([1, 1+Arg_0]) {O(n)} 0: f1->f2: 1 {O(1)} 1: f2->f2: max([0, Arg_0]) {O(n)} 2: f2->f2: max([0, Arg_1]) {O(n)} Sizebounds: `Lower: 0: f1->f2, Arg_0: 1 {O(1)} 0: f1->f2, Arg_1: 1 {O(1)} 1: f2->f2, Arg_0: 1 {O(1)} 1: f2->f2, Arg_1: 1 {O(1)} 2: f2->f2, Arg_0: 1 {O(1)} 2: f2->f2, Arg_1: 1 {O(1)} `Upper: 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