\begin{frame}
  \small
  \frametitle{ARSs with Multiple Relations}
  
  \begin{definitions}
  \begin{itemize}
  \item
    \alert<1-5>{abstract rewrite system} (\alert<1-5>{ARS}) is
    set $A$ with binary relations $\to_{i}$ for $i \in \II$
    \onslide<2->
    \begin{tabular}{@{}l@{\qquad}l@{}}
    \begin{minipage}[t]{3.5cm}
    \GREEN{
    \begin{tikzpicture}[on grid,baseline=3mm]
    \node (a)              {$\e{\m{a}}$};
    \node (b) [right=of a] {$\e{\m{b}}$};
    \node (c) [right=of b] {$\e{\m{c}}$};
    \node (d) [right=of c] {$\e{\m{d}}$};
    \node (e) [below=of b] {$\e{\m{e}}$};
    \node (f) [below=of c] {$\e{\m{f}}$};
    \node (g) [below=of f] {$\e{\m{g}}$};
    \draw[->] (a) -- (e) node [midway,above] {$_1$};
    \draw[->] (b) -- (a) node [midway,above] {$_2$};
    \draw[->] (b) -- (c) node [midway,above] {$_1$};
    \draw[->] (c) -- (d) node [midway,above] {$_1$};
    \draw[->] (c) -- (f) node [midway,right] {$_2$};
    \draw[->] (e) -- (b) node [midway,right] {$_1$};
    \draw[->] (e) -- (g) node [midway,above] {$_1$};
    \draw[->] (f) -- (e) node [midway,above] {$_3$};
    \draw[->] (f) -- (g) node [midway,right] {$_1$};
    \end{tikzpicture}}
    \end{minipage} &
    \onslide<3->
    \begin{minipage}[t]{7cm}
    \bigskip
    \bigskip
    ARS $\AA = \langle A, \to_1,\to_2,\to_3 \rangle$
    \begin{itemize}
    \item
      $A = \{ \mG{a}, \mG{b}, \mG{c}, \mG{d}, \mG{e}, \mG{f}, \mG{g} \}$
      \smallskip
    \item
      ${\to_1} = \left\{\begin{array}{@{}l@{}}
      (\mG{a},\mG{e}),
      (\mG{b},\mG{c}), (\mG{c},\mG{d}),
      \\[.5ex]
      (\mG{e},\mG{b}), (\mG{e},\mG{g}),
      (\mG{f},\mG{g}) 
      \end{array}\right\}$
    \item
      ${\to_2} = \left\{\begin{array}{@{}l@{}}
      (\mG{b},\mG{a}), (\mG{c},\mG{f})
      \end{array}\right\}$
    \item
      ${\to_3} = \left\{\begin{array}{@{}l@{}}
      (\mG{f},\mG{e})
      \end{array}\right\}$
    \end{itemize}
    \end{minipage}
    \end{tabular}
  \item<3->
    ${\to} = {\to_1} \cup {\to_2} \cup {\to_3}$
  \item<4->
    ${\to_{12}} = {\to_1} \cup {\to_2}$, \quad \onslide<5->${\to_{13}} = {\to_1} \cup {\to_3}$, \quad \ldots
  \end{itemize}
  \smallskip
  \end{definitions}

\end{frame}