\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}