Well formed words of the language $\mathcal L$ over the alphabet $A,B,C,\dots a,b,c,\dots,x,y,z$ are given in the following way: each letter $x,y,z$, is a word in $\mathcal L$ and if $w_1,w_2$, tea are words in $\mathcal L$, then $Aw_1\ w_2$ is also the word in $\mathcal L$. Nothing else is in $\mathcal L$. If the conditions $A_1$. --- $AAxzAyz=Axy$, $A_2$. --- $AAxxAAyyy=y\quad AAxxx$ are valid in $\mathcal L$, and if, by definition, $Bx=AAxx$, $Cx=AxBy$, then $\mathcal L$ with respect to $Cxy$ defines a group, $Bx$ being the inverse of $x$ and $Cxy$ the group operation. The independence of $A_1,A_2$ can be proved by applying the two models: $A_3$. --- $Axy=x$, $A_4$. --- $Axy=y$, over any alphabet with no less than two letters.