This language is regular since we have flexibility in choosing x and y we can convert it to set of strings containing 00 or 11 as substring.
suppose x=110001, y=100011, w=0110, w^r=0110, w=011, w^r=110
then XWW^rY = 11000101100110100011 or 1100010111100100011.
so REGULAR EXPRESSION is = (1+0)*(00)(1+0)* + (1+0)*(11)(1+0)*
i have confirmed through application form that...