\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}