/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(3, 4 + Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 239 ms]
(2) BOUNDS(1, max(3, 4 + Arg_1))


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

The start-symbols are:[start_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([3, 4+Arg_1]) {O(n)})



Initial Complexity Problem:

  Start:  start  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:    

  Locations:  div, end, start  

  Transitions:

  2: div->div

  0: div->end

  1: div->end

  3: start->div  



Timebounds: 

  Overall timebound: max([3, 4+Arg_1]) {O(n)}

  0: div->end: 1 {O(1)}

  1: div->end: 1 {O(1)}

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

  3: start->div: 1 {O(1)}



Costbounds:

  Overall costbound: max([3, 4+Arg_1]) {O(n)}

  0: div->end: 1 {O(1)}

  1: div->end: 1 {O(1)}

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

  3: start->div: 1 {O(1)}



Sizebounds:

`Lower:

  0: div->end, Arg_0: Arg_0 {O(n)}

  0: div->end, Arg_1: Arg_1 {O(n)}

  1: div->end, Arg_0: min([1, Arg_0]) {O(n)}

  1: div->end, Arg_1: min([1, Arg_1]) {O(n)}

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

  2: div->div, Arg_1: 1 {O(1)}

  3: start->div, Arg_0: Arg_0 {O(n)}

  3: start->div, Arg_1: Arg_1 {O(n)}

`Upper:

  0: div->end, Arg_0: 0 {O(1)}

  0: div->end, Arg_1: Arg_1 {O(n)}

  1: div->end, Arg_0: Arg_0 {O(n)}

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

  2: div->div, Arg_0: Arg_0 {O(n)}

  2: div->div, Arg_1: Arg_1 {O(n)}

  3: start->div, Arg_0: Arg_0 {O(n)}

  3: start->div, Arg_1: Arg_1 {O(n)}


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(2)
BOUNDS(1, max(3, 4 + Arg_1))