Complexity_ITS 2019-03-21 04.46 pair #429989790

details

property	value
status	complete
benchmark	div.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	patrs

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.98794 seconds
cpu usage	4.02981
user time	3.78148
system time	0.248324
max virtual memory	1.84784E7
max residence set size	221224.0

stage attributes

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

output

3.71/1.96	WORST_CASE(Omega(n^1), O(n^1))
3.71/1.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.71/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.71/1.96	
3.71/1.96	
3.71/1.96	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(3, 3 + 2 * Arg_1)).
3.71/1.96	
3.71/1.96	(0) CpxIntTrs
3.71/1.96	(1) Koat2 Proof [FINISHED, 173 ms]
3.71/1.96	(2) BOUNDS(1, max(3, 3 + 2 * Arg_1))
3.71/1.96	(3) Loat Proof [FINISHED, 166 ms]
3.71/1.96	(4) BOUNDS(n^1, INF)
3.71/1.96	
3.71/1.96	
3.71/1.96	----------------------------------------
3.71/1.96	
3.71/1.96	(0)
3.71/1.96	Obligation:
3.71/1.96	Complexity Int TRS consisting of the following rules:
3.71/1.96	div(A, B) -> Com_1(end(A, B)) :|: 0 >= A
3.71/1.96	div(A, B) -> Com_1(end(A, B)) :|: A >= B
3.71/1.96	div(A, B) -> Com_1(div(A, B - A)) :|: B >= A + 1 && A >= 1
3.71/1.96	start(A, B) -> Com_1(div(A, B)) :|: TRUE
3.71/1.96	
3.71/1.96	The start-symbols are:[start_2]
3.71/1.96	
3.71/1.96	
3.71/1.96	----------------------------------------
3.71/1.96	
3.71/1.96	(1) Koat2 Proof (FINISHED)
3.71/1.96	YES( ?, max([3, 3+2*Arg_1]) {O(n)})
3.71/1.96	
3.71/1.96	
3.71/1.96	
3.71/1.96	Initial Complexity Problem:
3.71/1.96	
3.71/1.96	  Start:  start  
3.71/1.96	
3.71/1.96	  Program_Vars:  Arg_0, Arg_1  
3.71/1.96	
3.71/1.96	  Temp_Vars:    
3.71/1.96	
3.71/1.96	  Locations:  div, end, start  
3.71/1.96	
3.71/1.96	  Transitions:
3.71/1.96	
3.71/1.96	  div(Arg_0,Arg_1) -> div(Arg_0,Arg_1-Arg_0):|:Arg_0+1 <= Arg_1 && 1 <= Arg_0
3.71/1.97	
3.71/1.97	  div(Arg_0,Arg_1) -> end(Arg_0,Arg_1):|:Arg_0 <= 0
3.71/1.97	
3.71/1.97	  div(Arg_0,Arg_1) -> end(Arg_0,Arg_1):|:Arg_1 <= Arg_0
3.71/1.97	
3.71/1.97	  start(Arg_0,Arg_1) -> div(Arg_0,Arg_1):|:  
3.71/1.97	
3.71/1.97	
3.71/1.97	
3.71/1.97	Timebounds: 
3.71/1.97	
3.71/1.97	  Overall timebound: max([3, 3+2*Arg_1]) {O(n)}
3.71/1.97	
3.71/1.97	  0: div->end: 1 {O(1)}
3.71/1.97	
3.71/1.97	  1: div->end: 1 {O(1)}
3.71/1.97	
3.71/1.97	  2: div->div: max([0, 2*Arg_1]) {O(n)}
3.71/1.97	
3.71/1.97	  3: start->div: 1 {O(1)}
3.71/1.97	
3.71/1.97	
3.71/1.97	
3.71/1.97	Costbounds:
3.71/1.97	
3.71/1.97	  Overall costbound: max([3, 3+2*Arg_1]) {O(n)}
3.71/1.97	
3.71/1.97	  0: div->end: 1 {O(1)}
3.71/1.97	
3.71/1.97	  1: div->end: 1 {O(1)}
3.71/1.97	
3.71/1.97	  2: div->div: max([0, 2*Arg_1]) {O(n)}
3.71/1.97	
3.71/1.97	  3: start->div: 1 {O(1)}
3.71/1.97	
3.71/1.97	
3.71/1.97	
3.71/1.97	Sizebounds:
3.71/1.97	
3.71/1.97	`Lower:
3.71/1.97	
3.71/1.97	  0: div->end, Arg_0: Arg_0 {O(n)}
3.71/1.97	
3.71/1.97	  0: div->end, Arg_1: Arg_1 {O(n)}
3.71/1.97	
3.71/1.97	  1: div->end, Arg_0: min([1, Arg_0]) {O(n)}
3.71/1.97	
3.71/1.97	  1: div->end, Arg_1: min([1, Arg_1]) {O(n)}
3.71/1.97	
3.71/1.97	  2: div->div, Arg_0: 1 {O(1)}
3.71/1.97	
3.71/1.97	  2: div->div, Arg_1: 1 {O(1)}
3.71/1.97

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