Uniqueness of the smallest chameleon in the class of monoids

A semigroup is a chameleon if it is the reduct of both a finitely based involution semigroup and a non-finitely based involution semigroup. Recently, a certain monoid K of order six was shown to be a smallest chameleon in the class of monoids. The main objective of the present article is to show that although there exist 2237 monoids of order six up to isomorphism, examples of chameleons different from K do not exist. Consequently, up to isomorphism, K is the unique smallest example of chameleon in the class of monoids.