/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(n^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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, max(4, 5 + Arg_0)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 331 ms]
(2) BOUNDS(1, max(4, 5 + Arg_0))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f300(A, B, C) -> Com_1(f300(-(1) + A, -(2) + A, C)) :|: A >= 1 && B + A >= 1 && B >= 1
f300(A, B, C) -> Com_1(f1(A, B, D)) :|: A >= 1 && 0 >= B + A && B >= 1
f300(A, B, C) -> Com_1(f1(A, B, D)) :|: B >= 1 && 0 >= A
f300(A, B, C) -> Com_1(f1(A, B, D)) :|: 0 >= B
f2(A, B, C) -> Com_1(f300(A, B, C)) :|: TRUE

The start-symbols are:[f2_3]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([4, 5+Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  f2  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:  D  

  Locations:  f1, f2, f300  

  Transitions:

  4: f2->f300

  1: f300->f1

  2: f300->f1

  3: f300->f1

  0: f300->f300  



Timebounds: 

  Overall timebound: max([4, 5+Arg_0]) {O(n)}

  4: f2->f300: 1 {O(1)}

  0: f300->f300: max([0, 1+Arg_0]) {O(n)}

  1: f300->f1: 1 {O(1)}

  2: f300->f1: 1 {O(1)}

  3: f300->f1: 1 {O(1)}



Costbounds:

  Overall costbound: max([4, 5+Arg_0]) {O(n)}

  4: f2->f300: 1 {O(1)}

  0: f300->f300: max([0, 1+Arg_0]) {O(n)}

  1: f300->f1: 1 {O(1)}

  2: f300->f1: 1 {O(1)}

  3: f300->f1: 1 {O(1)}



Sizebounds:

`Lower:

  4: f2->f300, Arg_0: Arg_0 {O(n)}

  4: f2->f300, Arg_1: Arg_1 {O(n)}

  4: f2->f300, Arg_2: Arg_2 {O(n)}

  0: f300->f300, Arg_0: 0 {O(1)}

  0: f300->f300, Arg_1: -1 {O(1)}

  0: f300->f300, Arg_2: Arg_2 {O(n)}

  1: f300->f1, Arg_0: inf {Infinity}

  1: f300->f1, Arg_1: inf {Infinity}

  1: f300->f1, Arg_2: inf {Infinity}

  2: f300->f1, Arg_0: Arg_0 {O(n)}

  2: f300->f1, Arg_1: 1 {O(1)}

  3: f300->f1, Arg_0: min([0, Arg_0]) {O(n)}

  3: f300->f1, Arg_1: min([-1, Arg_1]) {O(n)}

`Upper:

  4: f2->f300, Arg_0: Arg_0 {O(n)}

  4: f2->f300, Arg_1: Arg_1 {O(n)}

  4: f2->f300, Arg_2: Arg_2 {O(n)}

  0: f300->f300, Arg_0: Arg_0 {O(n)}

  0: f300->f300, Arg_1: -2+Arg_0 {O(n)}

  0: f300->f300, Arg_2: Arg_2 {O(n)}

  1: f300->f1, Arg_0: -(inf) {Infinity}

  1: f300->f1, Arg_1: -(inf) {Infinity}

  1: f300->f1, Arg_2: -(inf) {Infinity}

  2: f300->f1, Arg_0: 0 {O(1)}

  2: f300->f1, Arg_1: Arg_1 {O(n)}

  3: f300->f1, Arg_0: Arg_0 {O(n)}

  3: f300->f1, Arg_1: 0 {O(1)}


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(2)
BOUNDS(1, max(4, 5 + Arg_0))