Regularity conjecture for even associated lattices

Let $a>2$ be even and let $b$ be sufficiently large. Consider an Ulam set with generators $v_1$ and $v_2$ whose associated lattice is generated by $(-a,b)$. Regularity conjecture. The Ulam set contains finitely many elements of the form $2xv_1+yv_2$ and is therefore regular. The claim is based on computations and is presented as unresolved in the source.