\begin{frame}{Example}
  \begin{exampleblock}{}
    We construct a TM $M$ with $L(M) = \{\, a^n b^n c^n \mid n \geq 1 \,\}$.
    \pause\medskip
    
    \emph{Idea:}
    stepwise replace one $a$ by $0$, one $b$ by $1$ and one $c$ by $2$.
    \pause
    
    \begin{itemize}\setlength{\itemsep}{0mm}
    \item $\Sigma = \{\,a,b,c\,\}$ and $\Gamma = \{\,a,b,c,0,1,2,\Box\,\}$
    \item \alert{$q_0$}: Read $a$, replace by $0$, move right and switch to $q_1$.
    \item \alert{$q_1$}: Keep moving right until we read $b$.\\
      \quad\;\;Replace $b$ by $1$, move right and switch to $q_2$.
    \item \alert{$q_2$}: Keep moving right until we read $c$.\\
      \quad\;\;Replace $c$ by $2$, move left and switch to $q_3$.
    \item \alert{$q_3$}: Keep moving left until we read $0$.\\
      \quad\;\;Move right and switch back to $q_0$.
    \item If we read $1$ in \alert{$q_0$}, switch to $q_4$.
    \item \alert{$q_4$}: Keep moving right to check whether there are $a$'s, $b$'s\\
      \quad\;\;or $c$'s left. If not, then go to \alert{final state} \alert{$q_5$}.
    \end{itemize}
  \end{exampleblock}
\end{frame}