Examples of varieties of semigroups

An example of a variety $\mathfrak M$ of semigroups is formulated, where $\mathfrak M$ is defined by a finite number of identity relations for which the set of all identities (here strictly in two variables $x$, $y$) that hold on all semigroups of $\mathfrak M$ is nonrecursive. It is shown how to formulate similar varieties of semigroups with 1.