Compl Integ Trans Syste 26843 pair #381744500

details

property	value
status	complete
benchmark	p-12.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.75463104248 seconds
cpu usage	3.736658743
max memory	2.5286656E8

stage attributes

key	value
output-size	4255
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, max(2, 3 + Arg_0)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 106 ms]
(2) BOUNDS(1, max(2, 3 + Arg_0))
(3) Loat Proof [FINISHED, 91 ms]
(4) BOUNDS(n^1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f3(A, B) -> Com_1(f1(A, B)) :|: TRUE
f1(A, B) -> Com_1(f1(-(1) + A, B)) :|: A >= 0
f1(A, B) -> Com_1(f300(A, C)) :|: 0 >= A + 1

The start-symbols are:[f3_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([2, 3+Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  f3  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:  C  

  Locations:  f1, f3, f300  

  Transitions:

  f1(Arg_0,Arg_1) -> f1(-1+Arg_0,Arg_1):|:0 <= Arg_0

  f1(Arg_0,Arg_1) -> f300(Arg_0,C):|:Arg_0+1 <= 0

  f3(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:  



Timebounds: 

  Overall timebound: max([2, 3+Arg_0]) {O(n)}

  1: f1->f1: max([0, 1+Arg_0]) {O(n)}

  2: f1->f300: 1 {O(1)}

  0: f3->f1: 1 {O(1)}



Costbounds:

  Overall costbound: max([2, 3+Arg_0]) {O(n)}

  1: f1->f1: max([0, 1+Arg_0]) {O(n)}

  2: f1->f300: 1 {O(1)}

  0: f3->f1: 1 {O(1)}



Sizebounds:

`Lower:

  1: f1->f1, Arg_0: -1 {O(1)}

  1: f1->f1, Arg_1: Arg_1 {O(n)}

  2: f1->f300, Arg_0: min([-1, Arg_0]) {O(n)}

  0: f3->f1, Arg_0: Arg_0 {O(n)}

  0: f3->f1, Arg_1: Arg_1 {O(n)}

`Upper:

  1: f1->f1, Arg_0: Arg_0 {O(n)}

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