Problem ABGT-9. A simple basis for A2. The type is ⟨2, 0⟩ with constant e. Find the smallest possible equational basis for A2.

A2 = \{ \begin{matrix}(xe)e = x \\ e(ex) = x \\ ee = e \\ e(xe) = (ex)e \\ ((xx)e)(xx) = e \end{matrix} \} .