/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(2 + 27 * Arg_0, 29 + -27 * Arg_2, 29, 29 + 27 * Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 159 ms]
(2) BOUNDS(1, max(2 + 27 * Arg_0, 29 + -27 * Arg_2, 29, 29 + 27 * Arg_1))


----------------------------------------

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

The start-symbols are:[f0_3]


----------------------------------------

(1) Koat2 Proof (FINISHED)
YES( ?, 2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]) {O(n)})



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  f0, f1  

  Transitions:

  0: f0->f1

  1: f1->f1  



Timebounds: 

  Overall timebound: 2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]) {O(n)}

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

  1: f1->f1: 1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]) {O(n)}



Costbounds:

  Overall costbound: 2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]) {O(n)}

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

  1: f1->f1: 1+27*max([1, max([Arg_0, max([1-Arg_2, 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)}

  0: f0->f1, Arg_2: Arg_2 {O(n)}

  1: f1->f1, Arg_0: min([-(-1+inf*(1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]))+max([-(Arg_2), max([-(Arg_1), -(Arg_2)])])), -(-1-Arg_1)]) {Infinity}

  1: f1->f1, Arg_1: min([Arg_2, min([Arg_1, Arg_2])])+-(inf)*(1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])])) {Infinity}

  1: f1->f1, Arg_2: Arg_2 {O(n)}

`Upper:

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

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

  0: f0->f1, Arg_2: Arg_2 {O(n)}

  1: f1->f1, Arg_0: (1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]))*max([0, max([Arg_1, (1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]))*max([0, -(Arg_2)])+max([Arg_1, max([Arg_2, 1+Arg_2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])])])])])])+max([Arg_0, max([Arg_1, (1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]))*max([0, -(Arg_2)])+max([Arg_1, max([Arg_2, 1+Arg_2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])])])])])]) {O(n^3)}

  1: f1->f1, Arg_1: (1+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]))*max([0, -(Arg_2)])+max([Arg_1, max([Arg_2, 1+Arg_2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])])])]) {O(n^2)}

  1: f1->f1, Arg_2: 1+Arg_2+27*max([1, max([Arg_0, max([1-Arg_2, 1+Arg_1])])]) {O(n)}


----------------------------------------

(2)
BOUNDS(1, max(2 + 27 * Arg_0, 29 + -27 * Arg_2, 29, 29 + 27 * Arg_1))