Example CS-GL-6. Nearly (4) associative cancellative (gL)-groupoids are not necessarily commutative.

\{ \begin{matrix}cancellation \\ x(y(zu)) = (x(yz))u \end{matrix} \} =(gL)≠⇒ \{xy = yx\}.

Proof. The hypotheses have the noncommutative (gL)-model x · y = x + 2y (mod 3).