Property of two ANEAs is in NP
Hint: Suppose that $\mathcal{A}_1$ has $n$ states. Since it is acyclic, all the words it accepts have length at most $n-1$ (why?). Therefore if $L(\mathcal{A}_1) \nsubseteq L(\mathcal{A}_2)$ there must exist a word $w$ of length at most $n-1$ that $\mathcal{A}_1$ accepts but $\mathcal{A}_2$ rejects.