The Word Problem below Order Three

For a proper combinator $A=\lambda x_1\ldots x_n.M$, define its order to be the order assigned to $A$ by the source's simple-type hierarchy. Consider applicative terms formed from all proper combinators of order strictly less than $3$. Is there an algorithm that, given two such terms $P$ and $Q$, decides whether

$$P =_{\beta\eta} Q?$$