  Let $A$ be a unital simple separable C*-algebra satisfying the UCT. Assume
that $\mathrm{dr}(A)<+\infty$, $A$ is Jiang-Su stable, and
$\mathrm{K}_0(A)\otimes \mathbb{Q}\cong \mathbb{Q}$. Then $A$ is an ASH algebra
(indeed, $A$ is a rationally AH algebra).
