/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(1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 0 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f2(A, B) -> Com_1(f3(-(1) + A, C)) :|: A >= 0
f2(A, B) -> Com_1(f3(A, C)) :|: 0 >= A + 1

The start-symbols are:[f2_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, 2 {O(1)})



Initial Complexity Problem:

  Start:  f2  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:  C  

  Locations:  f2, f3  

  Transitions:

  0: f2->f3

  1: f2->f3  



Timebounds: 

  Overall timebound: 2 {O(1)}

  0: f2->f3: 1 {O(1)}

  1: f2->f3: 1 {O(1)}



Costbounds:

  Overall costbound: 2 {O(1)}

  0: f2->f3: 1 {O(1)}

  1: f2->f3: 1 {O(1)}



Sizebounds:

`Lower:

  

`Upper:

  


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(2)
BOUNDS(1, 1)