Reduce the word reachability problem restricted to the alphabet $\{a,b\}$ to the set of tuples $\langle u,v,w,R\rangle$ where $u,v,w$ are words, $R$ is a word rewrite system, the used alphabet has at most $2$ symbols, $u$ reaches $v$ using $R$, $v$ reaches $w$ using $R$, $u$ is different from $v$, and $v$ is different from $w$, in order to prove that such set is undecidable (not recursive).