Reduce the word reachability problem restricted to the alphabet $\{a,b\}$ to the set of tuples $\langle u,v,R\rangle$ where $u,v$ are words, $R$ is a word rewrite system, the used alphabet has at most $2$ symbols, $u$ reaches $v$ using $R$, and the number of rules of $R$ is even (by considering $R$ as a list, i.e., each different rule is counted as many times as it occurs in $R$), in order to prove that such set is undecidable (not recursive). The use of morphism is not allowed in the description of this reduction.