On the solutions of a system of difference equations with maximum

In this paper, we study the following max-type system of difference equations {xn=max{1xn−m,min{1,Ayn−r}},yn=max{1yn−m,min{1,Bxn−t}},n∈N0where A,B∈(0,+∞),A,B∈(0,+∞),m,r,t∈{1,2,…}m,r,t∈{1,2,…} with r ≠ m and t ≠ m  . We show that every solution of this system with the initial values x−d,y−d,x−d+1,y−d+1,…,x−1,y−1∈(0,+∞)x−d,y−d,x−d+1,y−d+1,…,x−1,y−1∈(0,+∞) is eventually periodic with period 2m  , where d=max{m,r,t}d=max{m,r,t}.