Left Recursion

We should eliminate the left recursion without changing the language.

$$A\to A\alpha \beta$$

The language the above generates is $\beta {\alpha }^{\ast }$ The above representation is not in the grammar form.

We can convert the above language to left recursive form like this.

$$\begin{array}{r}\begin{array}{c}A\to \beta A^{\prime }\\ A^{\prime }\to ϵ|\alpha A^{\prime }\end{array}\end{array}$$