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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(3 + Arg_0 + -1 * Arg_1, 3)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 430 ms]
(2) BOUNDS(1, max(3 + Arg_0 + -1 * Arg_1, 3))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f4(A, B, C, D, E, F, G) -> Com_1(f4(A + B, B, C, D, E, F, G)) :|: A >= 0
f4(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: 0 >= A + 1
f5(A, B, C, D, E, F, G) -> Com_1(f4(A, B, C, D, E, F, G)) :|: 0 >= B + 1
f5(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: B >= 0

The start-symbols are:[f5_7]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([3, 3+Arg_0-Arg_1]) {O(n)})



Initial Complexity Problem:

  Start:  f5  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6  

  Temp_Vars:    

  Locations:  f4, f5, f6  

  Transitions:

  f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:1+Arg_1 <= 0 && 0 <= Arg_0

  f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:1+Arg_1 <= 0 && Arg_0+1 <= 0

  f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1+1 <= 0

  f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:0 <= Arg_1  



Timebounds: 

  Overall timebound: max([3, 3+Arg_0-Arg_1]) {O(n)}

  0: f4->f4: max([0, Arg_0-Arg_1]) {O(n)}

  1: f4->f6: 1 {O(1)}

  2: f5->f4: 1 {O(1)}

  3: f5->f6: 1 {O(1)}



Costbounds:

  Overall costbound: max([3, 3+Arg_0-Arg_1]) {O(n)}

  0: f4->f4: max([0, Arg_0-Arg_1]) {O(n)}

  1: f4->f6: 1 {O(1)}

  2: f5->f4: 1 {O(1)}

  3: f5->f6: 1 {O(1)}



Sizebounds:

`Lower:

  0: f4->f4, Arg_0: Arg_1 {O(n)}

  0: f4->f4, Arg_1: Arg_1 {O(n)}

  0: f4->f4, Arg_2: Arg_2 {O(n)}

  0: f4->f4, Arg_3: Arg_3 {O(n)}

  0: f4->f4, Arg_4: Arg_4 {O(n)}

  0: f4->f4, Arg_5: Arg_5 {O(n)}

  0: f4->f4, Arg_6: Arg_6 {O(n)}

  1: f4->f6, Arg_0: min([Arg_0, Arg_1]) {O(n)}

  1: f4->f6, Arg_1: Arg_1 {O(n)}

  1: f4->f6, Arg_2: 0 {O(1)}

  1: f4->f6, Arg_3: 0 {O(1)}

  1: f4->f6, Arg_4: 0 {O(1)}

  1: f4->f6, Arg_5: 0 {O(1)}

  1: f4->f6, Arg_6: 0 {O(1)}

  2: f5->f4, Arg_0: Arg_0 {O(n)}

  2: f5->f4, Arg_1: Arg_1 {O(n)}

  2: f5->f4, Arg_2: Arg_2 {O(n)}

  2: f5->f4, Arg_3: Arg_3 {O(n)}

  2: f5->f4, Arg_4: Arg_4 {O(n)}

  2: f5->f4, Arg_5: Arg_5 {O(n)}

  2: f5->f4, Arg_6: Arg_6 {O(n)}

  3: f5->f6, Arg_0: Arg_0 {O(n)}

  3: f5->f6, Arg_1: 0 {O(1)}

  3: f5->f6, Arg_2: 0 {O(1)}

  3: f5->f6, Arg_3: 0 {O(1)}

  3: f5->f6, Arg_4: 0 {O(1)}

  3: f5->f6, Arg_5: 0 {O(1)}

  3: f5->f6, Arg_6: 0 {O(1)}

`Upper:

  0: f4->f4, Arg_0: Arg_0 {O(n)}

  0: f4->f4, Arg_1: -1 {O(1)}

  0: f4->f4, Arg_2: Arg_2 {O(n)}

  0: f4->f4, Arg_3: Arg_3 {O(n)}

  0: f4->f4, Arg_4: Arg_4 {O(n)}

  0: f4->f4, Arg_5: Arg_5 {O(n)}

  0: f4->f4, Arg_6: Arg_6 {O(n)}

  1: f4->f6, Arg_0: -1 {O(1)}

  1: f4->f6, Arg_1: -1 {O(1)}

  1: f4->f6, Arg_2: 0 {O(1)}

  1: f4->f6, Arg_3: 0 {O(1)}

  1: f4->f6, Arg_4: 0 {O(1)}

  1: f4->f6, Arg_5: 0 {O(1)}

  1: f4->f6, Arg_6: 0 {O(1)}

  2: f5->f4, Arg_0: Arg_0 {O(n)}

  2: f5->f4, Arg_1: -1 {O(1)}

  2: f5->f4, Arg_2: Arg_2 {O(n)}

  2: f5->f4, Arg_3: Arg_3 {O(n)}

  2: f5->f4, Arg_4: Arg_4 {O(n)}

  2: f5->f4, Arg_5: Arg_5 {O(n)}

  2: f5->f4, Arg_6: Arg_6 {O(n)}

  3: f5->f6, Arg_0: Arg_0 {O(n)}

  3: f5->f6, Arg_1: Arg_1 {O(n)}

  3: f5->f6, Arg_2: 0 {O(1)}

  3: f5->f6, Arg_3: 0 {O(1)}

  3: f5->f6, Arg_4: 0 {O(1)}

  3: f5->f6, Arg_5: 0 {O(1)}

  3: f5->f6, Arg_6: 0 {O(1)}


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(2)
BOUNDS(1, max(3 + Arg_0 + -1 * Arg_1, 3))