Abstract of S. markovski, L. Goracinova Ilieva, A. Sokolova
Free groupoids with the identity $(xy)y = yx$

A construction of free groupoids in the variety $\mathcal{V}$ defined by
Stein identity $(xy)y=yx$ is given. The construction is
canonical i.e. the free groupoid is constructed with universe a subset of
the absolutely free groupoid and suitably defined operation. In fact a
countable closed set of identities that are consequences of the defining one
is obtained.