/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(1))
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 25 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f8(A, B, C) -> Com_1(f12(2, 1, C)) :|: A >= 2 && A <= 2
f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: 1 >= A
f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: A >= 3
f0(A, B, C) -> Com_1(f12(1, 1, 1)) :|: TRUE

The start-symbols are:[f0_3]


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(1) Koat2 Proof (FINISHED)
YES( ?, 4 {O(1)})



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  f0, f12, f8  

  Transitions:

  3: f0->f12

  0: f8->f12

  1: f8->f12

  2: f8->f12  



Timebounds: 

  Overall timebound: 4 {O(1)}

  3: f0->f12: 1 {O(1)}

  0: f8->f12: 1 {O(1)}

  1: f8->f12: 1 {O(1)}

  2: f8->f12: 1 {O(1)}



Costbounds:

  Overall costbound: 4 {O(1)}

  3: f0->f12: 1 {O(1)}

  0: f8->f12: 1 {O(1)}

  1: f8->f12: 1 {O(1)}

  2: f8->f12: 1 {O(1)}



Sizebounds:

`Lower:

  

`Upper:

  


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(2)
BOUNDS(1, 1)