On a special monoid with a single defining relation

We show that no finite union of congruence classes [w], w being an arbitrary element of the free monoid {a, b}¹ with unit 1, is a context-free language if the congruence is defined by the single pair (abbaab, 1). This congruence is neither confluent nor even preperfect. The monoid formed by its congruence classes is a group which has infinitely many isomorphic proper subgroups.