For the following phrase structure grammar I want to construct the type of string that satisfy it, but I am not sure the way to go.
$$\begin{align*} S &\to xTy \\ T &\to xTT \\ xTx &\to xx \end{align*}$$
The thing I am struggling with is that I can't seem to be able to reduce it fully to the alphabet ($x$ or $y$) and the recursive nature seems to keep repeating the same irreducible pattern. For instance, here is what I tried
$xTy$
$x(xTT)y$
$xx(xTT)Ty$ (expanding left first)
$xxxTT(xTT)y$ (then expand right)
$xxxT(xTT)xTTy$ (expand middle)
$xxxxTTxTTy$ (simplify)
And then when I try to simply things again it tends to start it self again kind of repeating the process at step 2 again for the T's.