  A limit variety is a variety that is minimal with respect to being
non-finitely based. Since the turn of the millennium, much attention has been
given to the classification of limit varieties of aperiodic monoids. Seven
explicit examples have so far been found, and the task of locating other
examples has recently been reduced to two subproblems, one of which is
concerned with monoids that satisfy the identity $xsxt \approx xsxtx$. In the
present article, we provide a complete solution to this subproblem by showing
that there are precisely two limit varieties that satisfy this identity. One of
them turns out to be the first example having infinitely many subvarieties.
  It is also deduced that the variety generated by any monoid of order five or
less contains at most countably many subvarieties.
