An inherently nonfinitely based commutative directoid (Q1272236)

A finite algebra is said to be inherently nonfinitely based if every locally finite variety containing it is nonfinitely based. \textit{J. Ježek} and \textit{R. Quackenbush} investigated directoids [Algebra Univers. 27, No. 1, 46-69 (1990; Zbl 0699.08002)], i.e. groupoids satisfying the identities \(x^2=x\), \((xy)x=xy\), \(y(xy)=xy\) and \(x((xy)z)=(xy)z\). They asked whether every finite directoid is finitely based or not. The author answers this question in the negative giving an example of an inherently nonfinitely based commutative 6-element directoid.