On some solvable systems of difference equations (Q426520)

The author studies the following system of difference equations NEWLINE\[NEWLINE x_{n+1}=\frac{u_n}{1+v_n}, \qquad y_{n+1}=\frac {w_n}{1+s_n}, \qquad n\in \mathbb{N}_0, NEWLINE\]NEWLINE where \(u_n\), \(v_n\), \(w_n\), \(s_n\) are some of the sequences \(x_n\) or \(y_n\), with real initial values \(x_0\) and \(y_0\). For fourteen of the sixteen possible cases, the author obtains the general solutions. The unsolved cases are NEWLINE\[NEWLINE x_{n+1}=\frac{y_n}{1+y_n}, \qquad y_{n+1}=\frac{y_n}{1+x_n}, \qquad n\in \mathbb{N}_0 NEWLINE\]NEWLINE and the symmetric counterpart NEWLINE\[NEWLINE x_{n+1}=\frac {x_n}{1+y_n}, \qquad y_{n+1}=\frac{x_n}{1+x_n}, \qquad n\in \mathbb{N}_0. NEWLINE\]