Solutions of a max-type system of difference equations

We show, in an elegant way, that the general solution to the following max-type system of difference equations x(n+1) = max {A/x(n),y(n)/x(n)}, y(n+1) = max {A/y(n),x(n)/y(n)}, n is an element of N-0, for the case y(0), x(0) >= A > 0, y(0)/x(0) >= max{A, 1/A}, is given by: x(n) = (A(fk(n) 1 alpha(n)) x(0)(fk(n))/y(0)(fk(n)))((-1)n), n is an element of N, y(1) = x(0)/y(0), and y(n) = (y(0)(fk(n) (1)+1)/A(fk(n) (1)+alpha(n)-1)x(0)(fk(n) (1)+1))((-1)n), n >= 2, where k(n) = n, for n even, k(n) = n + 1, for n odd, n is an element of N-o, alpha(n) n(mod 2), for n is an element of N-o, and where the sequence (f(n))(n is an element of N) is the Fibonacci sequence, correcting and giving a proof of a wrong result in the paper [ D. Simsek, B. Demir, C. Cinar, On the solutions of the system of difference equations x(n+1) = max{A/xn, yn/xn}, y(n+1) max{A/y(n), x(n)/y(n)}, Discrete Dyn. Nat. Soc. 2009 (2009), 11 pp. (Article ID 325296)]. (C) 2012 Elsevier Inc. All rights reserved.