\begin{frame}
\small

\begin{definition}[Normal Forms]
\begin{itemize}
\item
\alert<1,2>{normal form} is element $x$ such that $x \not\to y$
for all $y$ 
\item<3->
$\alert<3,4>{\NF(}\AA\alert<3,4>{)}$ denotes set of normal forms of ARS
$\AA$
\item<5->
$x \to^{\alert<5,6>{!}} y$ if $x \to^* y$ for normal form $y$
($x$ \alert<5>{has} normal form $y$)
\smallskip
\end{itemize}
\end{definition}

\bigskip

\begin{example}<2->
\begin{center}
\begin{tabular}{@{}l@{\quad}l@{}}
\begin{minipage}[t]{4cm}
\GREEN{\begin{tikzpicture}[on grid]
\node (1)              {$\e{\m{a}}$};
\node (2) [right=of 1] {\alert<6>{$\e{\m{b}}$}};
\node (3) [right=of 2] {\alert<6>{$\e{\m{c}}$}};
\node (4) [right=of 3] {\alert<2,4>{$\e{\m{d}}$}};
\node (5) [below=of 2] {$\e{\m{e}}$};
\node (6) [below=of 3] {\alert<6>{$\e{\m{f}}$}};
\node (7) [below=of 6] {\alert<4,6>{$\e{\m{g}}$}};
\draw[->] (1) -- (5);
\draw[->] (2) -- (1);
\alert<6>{
\draw[->] (2) -- (3);
}
\draw[->] (3) -- (4);
\alert<6>{
\draw[->] (3) -- (6);
}
\draw[->] (5) -- (2);
\draw[->] (5) -- (7);
\draw[->] (6) -- (5);
\alert<6>{
\draw[->] (6) -- (7);
}
\end{tikzpicture}}
\end{minipage}
&\quad
\begin{minipage}[t]{4cm}
\bigskip
ARS $\AA = \ARS$
\begin{itemize}
\item<2->~
$\mG{d}$ is \alert<2>{normal form}
\item<4->~
$\alert<4>{\NF(}\AA\alert<4>{)} = \{ \mG{d}, \mG{g} \}$
\item<6->~
\alert<6>{$\mG{b} \to^! \mG{g}$}
\end{itemize}
\end{minipage}
\end{tabular}
\end{center}
\end{example}

\end{frame}