irreducible words in a semigroup

Question

Let $S$ be a monoid generated by $\{x_1,x_2,x_3,x_4,x_5\}$ with the following relations: $x_i^2=0$ for all $i$, $x_ix_j=x_jx_i$ for all $|i-j| \geq 2$ and $x_ix_{i+1}x_i=x_{i+1}x_ix_{i+1}$ for all $i$. I want to apply the Bergman's Diamond lemma to find out a set of irreducible words. How do I do this ? What are all possible ambiguities and what is a possible set of irreducible words ?