\begin{frame}{Mixing Right and Left Linear Rules} \begin{alertblock}{} Mixing right \emph{and} left linear rules, the generated language is \emph{not} always regular. \end{alertblock} \bigskip \begin{example} Let $G$ be the grammar \begin{talign} S &\to aA \\ A &\to Sb \\ S &\to \lambda \end{talign} Every rule of $G$ is either right or left linear. \medskip However, the language $L(G)=\{a^nb^n\mid n\geq 0\}$ is \emph{not} regular. \end{example} \end{frame}