xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy
Well...no. Every relation is of the form $\displaystyle u=v$ where $\displaystyle |u| = 6$ and $\displaystyle |v|=4$. As you are in a semigroup there is no way of getting a relation of the form $\displaystyle u=v$ where $\displaystyle |u|=1=|v|$ as you cannot cancel anything.
What do you mean by the element $\displaystyle a$?