Compl Integ Trans Syste 26843 pair #381744077

details

property	value
status	complete
benchmark	terminate.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	TACAS01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.72971606255 seconds
cpu usage	3.750943343
max memory	2.57437696E8

stage attributes

key	value
output-size	2363
starexec-result	WORST_CASE(?, 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(?, 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(1, max(1, 102 + -1 * Arg_0 + Arg_1 + -1 * Arg_2)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 140 ms]
(2) BOUNDS(1, max(1, 102 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval(A, B, C) -> Com_1(eval(C, B - 1, A + 1)) :|: 100 >= A && B >= C
start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE

The start-symbols are:[start_3]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  start  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  eval, start  

  Transitions:

  eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_2,Arg_1-1,Arg_0+1):|:Arg_0 <= 100 && Arg_2 <= Arg_1

  start(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2):|:  



Timebounds: 

  Overall timebound: max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  0: eval->eval: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  1: start->eval: 1 {O(1)}



Costbounds:

  Overall costbound: max([1, 102+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  0: eval->eval: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  1: start->eval: 1 {O(1)}



Sizebounds:

`Lower:

  0: eval->eval, Arg_0: min([Arg_0, Arg_2]) {O(n)}

  0: eval->eval, Arg_1: Arg_1-max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  0: eval->eval, Arg_2: min([Arg_0, Arg_2]) {O(n)}

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

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

  1: start->eval, Arg_2: Arg_2 {O(n)}

`Upper:

  0: eval->eval, Arg_0: max([101, Arg_2]) {O(n)}

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

  0: eval->eval, Arg_2: 101 {O(1)}

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

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