/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 27 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B) -> Com_1(f1(3000, B)) :|: TRUE
f1(A, B) -> Com_1(f1(A, B + 1000)) :|: B + 889 >= 0 && 1999 >= A

The start-symbols are:[f0_2]


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



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:    

  Locations:  f0, f1  

  Transitions:

  f0(Arg_0,Arg_1) -> f1(3000,Arg_1):|:  



Timebounds: 

  Overall timebound: 1 {O(1)}

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



Costbounds:

  Overall costbound: 1 {O(1)}

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



Sizebounds:

`Lower:

  0: f0->f1, Arg_0: 1024 {O(1)}

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

`Upper:

  0: f0->f1, Arg_0: 3000 {O(1)}

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


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(2)
BOUNDS(1, 1)