/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, 2 + Arg_0 + Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 143 ms]
(2) BOUNDS(1, max(1, 2 + Arg_0 + Arg_1))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
l0(A, B, C) -> Com_1(l1(A, B, C)) :|: TRUE
l1(A, B, C) -> Com_1(l1(A + B + C, -(C) - 1, C)) :|: A >= 0 && A + B >= 0

The start-symbols are:[l0_3]


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



Initial Complexity Problem:

  Start:  l0  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  l0, l1  

  Transitions:

  0: l0->l1

  1: l1->l1  



Timebounds: 

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

  0: l0->l1: 1 {O(1)}

  1: l1->l1: max([0, 1+Arg_0+Arg_1]) {O(n)}



Costbounds:

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

  0: l0->l1: 1 {O(1)}

  1: l1->l1: max([0, 1+Arg_0+Arg_1]) {O(n)}



Sizebounds:

`Lower:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  1: l1->l1, Arg_0: Arg_2 {O(n)}

  1: l1->l1, Arg_1: -1-Arg_2 {O(n)}

  1: l1->l1, Arg_2: Arg_2 {O(n)}

`Upper:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  1: l1->l1, Arg_0: max([Arg_2, max([Arg_1, max([Arg_0, max([Arg_2, -1-Arg_2])])])])+max([0, (1+Arg_0+Arg_1)*(max([0, max([Arg_1, -1-Arg_2])])+max([0, Arg_2]))]) {O(n^2)}

  1: l1->l1, Arg_1: -1-Arg_2 {O(n)}

  1: l1->l1, Arg_2: Arg_2 {O(n)}


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(2)
BOUNDS(1, max(1, 2 + Arg_0 + Arg_1))