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\begin{frame}
\small

\begin{block}{Terminology}
\begin{itemize}[<+->]
\item
if $x \to^* y$ then $x$ \alert<1,2>{rewrites} to $y$ and
$y$ is \alert<1,2>{reduct} of $x$
\item<3->
if $x \to^* z \FromP{*} y$ then $z$ is \alert<3-6>{common reduct}
of $x$ and $y$
\item<7->
if $x \conv y$ then $x$ and $y$ are \alert<7,8>{convertible}
\smallskip
\end{itemize}
\end{block}

\bigskip

\begin{example}<2->
\begin{center}
\begin{tabular}{@{}l@{\quad}l@{}}
\begin{minipage}[t]{4cm}
\GREEN{\begin{tikzpicture}[on grid]
\node (1)              {\alert<2>{$\e{\m{a}}$}};
\node (2) [right=of 1] {\alert<2,5>{$\e{\m{b}}$}};
\node (3) [right=of 2] {\alert<2,5,8>{$\e{\m{c}}$}};
\node (4) [right=of 3] {\alert<5,8>{$\e{\m{d}}$}};
\node (5) [below=of 2] {\alert<2,4,5>{$\e{\m{e}}$}};
\node (6) [below=of 3] {\alert<2,4,5,8>{$\e{\m{f}}$}};
\node (7) [below=of 6] {\alert<6,8>{$\e{\m{g}}$}};
\node (8) [below=of 4] {\alert<5,6,8>{$\e{\m{h}}$}};
\alert<2>{
\draw[->] (1) -- (5);
}
\draw[->] (2) -- (1);
\alert<2,5>{
\draw[->] (2) -- (3);
}
\alert<5,8>{
\draw[->] (3) -- (4);
}
\alert<2,8>{
\draw[->] (3) -- (6);
}
\alert<2,5>{
\draw[->] (5) -- (2);
}
\draw[->] (5) -- (7);
\alert<4,5>{
\draw[->] (6) -- (5);
}
\alert<8>{
\draw[->] (6) -- (7);
}
\alert<5,8>{
\draw[->] (8) -- (4);
}
\end{tikzpicture}}
\end{minipage}
&
\begin{minipage}[t]{5cm}
\bigskip
\bigskip
\begin{itemize}
\item<2->~
\alert<2>{$\mG{a} \to^* \mG{f}$}
\item<4->~
\alert<4>{$\mG{e} \join \mG{f}$} \quad
\onslide<5->{\alert<5>{$\mG{f} \join \mG{h}$}} \quad
\onslide<6->{\alert<6>{not $\mG{g} \join \mG{h}$}}
\item<8->~
\alert<8>{$\mG{g} \conv \mG{h}$}
\end{itemize}
\end{minipage}
\end{tabular}
\end{center}
\end{example}

\end{frame}