\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}