Term equivalence of semigroups

A term operation of a semigroup is an operation that is induced from a term (a semigroup word). Two semigroups are term equivalent if they have the same elements and the same term operations. For example, every semigroup $(S,\cdot)$ is term equivalent to its opposite $(S,*)$ where $x*y := yx$. We will discuss some non trivial instances of term equivalence and open problems in this area. This is joint work with Oleg Kosik (Tartu, Estonia).