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


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WORST_CASE(?, 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(1, max(1, 1 + Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 80 ms]
(2) BOUNDS(1, max(1, 1 + Arg_1))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B) -> Com_1(f1(A, B)) :|: A >= 1
f1(A, B) -> Com_1(f1(1 + A, -(A) + B)) :|: B >= 1

The start-symbols are:[f0_2]


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



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:    

  Locations:  f0, f1  

  Transitions:

  f0(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1 <= Arg_0

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



Timebounds: 

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

  0: f0->f1: 1 {O(1)}

  1: f1->f1: max([0, Arg_1]) {O(n)}



Costbounds:

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

  0: f0->f1: 1 {O(1)}

  1: f1->f1: max([0, Arg_1]) {O(n)}



Sizebounds:

`Lower:

  0: f0->f1, Arg_0: 1 {O(1)}

  0: f0->f1, Arg_1: Arg_1 {O(n)}

  1: f1->f1, Arg_0: 2 {O(1)}

`Upper:

  0: f0->f1, Arg_0: Arg_0 {O(n)}

  0: f0->f1, Arg_1: Arg_1 {O(n)}

  1: f1->f1, Arg_0: Arg_0+max([0, Arg_1]) {O(n)}

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


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(2)
BOUNDS(1, max(1, 1 + Arg_1))