We transform the method of Glasson into a sufficient condition under which a monoid is non-finitely related, add a new member to the collection of interlocking word-patterns, and use it to show that the monoid \(M(ab^2a, a^2b^2)\) is non-finitely related. We also give a sufficient condition under which a monoid is finitely related and use it to show that \(M(a^2b^2)\) is finitely related. Together with the results of Glasson, this completes the description of all finitely related monoids among the monoids of the form M(W) where every word \(\textbf{u} \in W\) depends on two variables and every variable occurs twice in \(\textbf{u}\) .
