$(10$ points$)$ Consider the language:

$U_{\text{D}\text{F}\text{A}}=\{\begin{array}{ccc}(\text{:}{D}_1,& D_2,& w\text{:})|D_1\end{array}$ and $D_2$ are DFAs and $w$ is a string such that

$\{$:winL$(D_1)L(D_2)\}.$ Is $U_{\text{D}\text{F}\text{A}}$ decidable? Prove your assertion.