  Let $I$ be a monomial ideal in two variables generated by three monomials and
let $\mathcal{R}(I)$ be its Rees ideal. We describe an algorithm to compute the
minimal generating set of $\mathcal{R}(I)$. Based on the data obtained by this
algorithm, we build a graph that encodes the minimal free resolution of
$\mathcal{R}(I)$. We explicitly describe the modules and differentials on the
minimal free resolution of $\mathcal{R}(I)$.
