\begin{frame}{Example}
\begin{exampleblock}{}
The language
\begin{talign}
\{\, a^n b^n c^n \mid n \geq 1 \,\}
\end{talign}
is generated by the context-sensitive grammar:
\begin{talign}
S &\to aAbc\mid abc \\
A &\to aAB \mid aB \\
Bb &\to bB \\
Bc &\to bcc
\end{talign}
Example derivation:
\begin{talign}
\begin{array}{ccccccc}
\alert{S} &\Rightarrow& a\alert{A}bc &\Rightarrow& aa\alert{AB}bc &\Rightarrow& aa\alert{A}b\alert{B}c \\
&\Rightarrow& aa\alert{A}bbcc &\Rightarrow& aaa\alert{B}bbcc &\Rightarrow& aaab\alert{B}bcc \\
&\Rightarrow& aaabb\alert{B}cc &\Rightarrow& aaabbbccc
\end{array}
\end{talign}
\end{exampleblock}
\end{frame}