/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(10 + -8 * Arg_1, 10, 2 + 8 * Arg_0)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 136 ms]
(2) BOUNDS(1, max(10 + -8 * Arg_1, 10, 2 + 8 * Arg_0))


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

The start-symbols are:[f0_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, 2+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)})



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:    

  Locations:  f0, f1  

  Transitions:

  0: f0->f1

  1: f1->f1  



Timebounds: 

  Overall timebound: 2+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)}

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

  1: f1->f1: 1+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)}



Costbounds:

  Overall costbound: 2+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)}

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

  1: f1->f1: 1+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)}



Sizebounds:

`Lower:

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

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

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

`Upper:

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

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

  1: f1->f1, Arg_0: (1+8*max([1, max([Arg_0, 1-Arg_1])]))*max([0, -(Arg_1)])+max([Arg_0, max([Arg_1, 1+Arg_1+8*max([1, max([Arg_0, 1-Arg_1])])])]) {O(n^2)}

  1: f1->f1, Arg_1: 1+Arg_1+8*max([1, max([Arg_0, 1-Arg_1])]) {O(n)}


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(2)
BOUNDS(1, max(10 + -8 * Arg_1, 10, 2 + 8 * Arg_0))