details

property	value
status	complete
benchmark	18.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n112.star.cs.uiowa.edu
space	Beerendonk

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.34025 seconds
cpu usage	4.57345
user time	4.30467
system time	0.268774
max virtual memory	1.8442268E7
max residence set size	222968.0

stage attributes

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

output

4.45/2.30 WORST_CASE(Omega(n^1), O(n^1)) 4.53/2.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.53/2.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.53/2.31 4.53/2.31 4.53/2.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + 2 * Arg_0) + nat(Arg_1)). 4.53/2.31 4.53/2.31 (0) CpxIntTrs 4.53/2.31 (1) Koat2 Proof [FINISHED, 242 ms] 4.53/2.31 (2) BOUNDS(1, max(1, 1 + 2 * Arg_0) + nat(Arg_1)) 4.53/2.31 (3) Loat Proof [FINISHED, 622 ms] 4.53/2.31 (4) BOUNDS(n^1, INF) 4.53/2.31 4.53/2.31 4.53/2.31 ---------------------------------------- 4.53/2.31 4.53/2.31 (0) 4.53/2.31 Obligation: 4.53/2.31 Complexity Int TRS consisting of the following rules: 4.53/2.31 eval(A, B) -> Com_1(eval(A - 1, B)) :|: A >= 1 4.53/2.31 eval(A, B) -> Com_1(eval(A - 1, B)) :|: B >= 1 && A >= 1 4.53/2.31 eval(A, B) -> Com_1(eval(A, B - 1)) :|: A >= 1 && 0 >= A && B >= 1 4.53/2.31 eval(A, B) -> Com_1(eval(A, B - 1)) :|: B >= 1 && 0 >= A 4.53/2.31 eval(A, B) -> Com_1(eval(A, B)) :|: A >= 1 && 0 >= A && 0 >= B 4.53/2.31 eval(A, B) -> Com_1(eval(A, B)) :|: B >= 1 && 0 >= A && 0 >= B 4.53/2.31 start(A, B) -> Com_1(eval(A, B)) :|: TRUE 4.53/2.31 4.53/2.31 The start-symbols are:[start_2] 4.53/2.31 4.53/2.31 4.53/2.31 ---------------------------------------- 4.53/2.31 4.53/2.31 (1) Koat2 Proof (FINISHED) 4.53/2.31 YES( ?, 1+2*max([0, Arg_0])+max([0, Arg_1]) {O(n)}) 4.53/2.31 4.53/2.31 4.53/2.31 4.53/2.31 Initial Complexity Problem: 4.53/2.31 4.53/2.31 Start: start 4.53/2.31 4.53/2.31 Program_Vars: Arg_0, Arg_1 4.53/2.31 4.53/2.31 Temp_Vars: 4.53/2.31 4.53/2.31 Locations: eval, start 4.53/2.31 4.53/2.31 Transitions: 4.53/2.31 4.53/2.31 eval(Arg_0,Arg_1) -> eval(Arg_0-1,Arg_1):|:1 <= Arg_0 4.53/2.31 4.53/2.31 eval(Arg_0,Arg_1) -> eval(Arg_0-1,Arg_1):|:1 <= Arg_1 && 1 <= Arg_0 4.53/2.31 4.53/2.31 eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_1-1):|:1 <= Arg_1 && Arg_0 <= 0 4.53/2.31 4.53/2.31 start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1):|: 4.53/2.31 4.53/2.31 4.53/2.31 4.53/2.31 Timebounds: 4.53/2.31 4.53/2.31 Overall timebound: 1+2*max([0, Arg_0])+max([0, Arg_1]) {O(n)} 4.53/2.31 4.53/2.31 0: eval->eval: max([0, Arg_0]) {O(n)} 4.53/2.31 4.53/2.31 1: eval->eval: max([0, Arg_0]) {O(n)} 4.53/2.31 4.53/2.31 3: eval->eval: max([0, Arg_1]) {O(n)} 4.53/2.31 4.53/2.31 6: start->eval: 1 {O(1)} 4.53/2.31 4.53/2.31 4.53/2.31 4.53/2.31 Costbounds: 4.53/2.31 4.53/2.31 Overall costbound: 1+2*max([0, Arg_0])+max([0, Arg_1]) {O(n)} 4.53/2.31 4.53/2.31 0: eval->eval: max([0, Arg_0]) {O(n)} 4.53/2.31 4.53/2.31 1: eval->eval: max([0, Arg_0]) {O(n)} 4.53/2.31 4.53/2.31 3: eval->eval: max([0, Arg_1]) {O(n)} 4.53/2.31 4.53/2.31 6: start->eval: 1 {O(1)} 4.53/2.31 4.53/2.31 4.53/2.31 4.53/2.31 Sizebounds: 4.53/2.31 4.53/2.31 `Lower: 4.53/2.31 4.53/2.31 0: eval->eval, Arg_0: 0 {O(1)} 4.53/2.31 4.53/2.31 0: eval->eval, Arg_1: min([1, Arg_1]) {O(n)} 4.53/2.31 4.53/2.31 1: eval->eval, Arg_0: 0 {O(1)} 4.53/2.31 4.53/2.31 1: eval->eval, Arg_1: 1 {O(1)} 4.53/2.31 4.53/2.31 3: eval->eval, Arg_0: min([0, Arg_0]) {O(n)} popout

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actions

all output return to Complexity_ITS 2019-03-21 04.46