On the solutions of a max-type system of difference equations with period-two parameters

In this paper, we study the following max-type system of difference equations: casesxₙ = max ₙ,yₙ₋₁xₙ₋₂ \,\\ yₙ = max ₙ ,xₙ₋₁yₙ₋₂ \, cases n∈ \0,1,2,…\, where Aₙ,Bₙ∈(0, +∞) are periodic sequences with period 2 and the initial values x₋₁,y₋₁,x₋₂,y₋₂∈ (0,+∞) . We show that every solution of the above system is eventually periodic.