\begin{frame}
  \small
  
  \begin{example}
  \[
  \GREEN{\begin{array}{r@{~}c@{~}l@{\qquad\qquad}r@{~}c@{~}l}
  \m{f}(\m{a},\m{g}(x)) & \to & \m{f}(x,x) & \m{g(b)} & \to & \m{c}
  \end{array}}
  \]
  \onslide<2->
  three peaks \\ \smallskip
  \begin{tikzpicture}[on grid,baseline=(1).baseline,node distance=17mm]
  \alt<5>{
  \node (1)
  {\alert{$\strut \m{f}(\underline{\m{g(b)}},\overline{\m{g(b)}})$}};
  }{
  \node (1) {\GREEN{$\strut \m{f}(\ul{\m{g(b)}},\ol{\m{g(b)}})$}};
  }
  \node (2) [below left=of 1]  {\GREEN{$\m{f(c,g(b))}$}};
  \node (3) [below right=of 1] {\GREEN{$\m{f(g(b),c)}$}};
  \draw[->] (1) -- (2) node[midway,left]  {\scriptsize $1~$};
  \draw[->] (1) -- (3) node[midway,right] {\scriptsize $~2$};
  \onslide<3->{
  \alt<6>{
  \node (4) [node distance=43mm,right=of 1]
  {\alert{$\overline{\strut \m{f}(\m{a},\m{g(\underline{g(b)})})}$}};
  }{
  \node (4) [node distance=43mm,right=of 1]
  {\GREEN{$\ol{\strut \m{f}(\m{a},\m{g(\ul{g(b)})})}$}};
  }
  \node (5) [below left=of 4]  {\GREEN{$\m{f(a,g(c))}$}};
  \node (6) [below right=of 4] {\GREEN{$\m{f(g(b),g(b))}$}};
  \draw[->] (4) -- (5) node[midway,left]  {\scriptsize $21~$};
  \draw[->] (4) -- (6) node[midway,right] {\scriptsize $~\epsilon$};
  }
  \onslide<4->{
  \alt<7>{
  \node (7) [node distance=43mm,right=of 4]
  {\alert{$\strut \overline{\m{f}(\m{a},\m{\underline{g(b)}})}$}};
  }{
  \node (7) [node distance=43mm,right=of 4]
  {\GREEN{$\strut \ol{\m{f}(\m{a},\m{\ul{g(b)}})}$}};
  }
  \node (8) [below left=of 7]  {\GREEN{$\m{f(a,c)}$}};
  \node (9) [below right=of 7] {\GREEN{$\m{f(b,b)}$}};
  \draw[->] (7) -- (8) node[midway,left]  {\scriptsize $2~$};
  \draw[->] (7) -- (9) node[midway,right] {\scriptsize $~\epsilon$};
  }
  \onslide<5->{
  \node (a) [node distance=20mm,below=of 1] {\alert<5>{parallel redexes}};
  }
  \onslide<6->{
  \node (b) [node distance=20mm,below=of 4] {\alert<6>{nested redexes / variable overlap}};
  }
  \onslide<7->{
  \node (c) [node distance=20mm,below=of 7] {\alert<7>{overlapping redexes}};
  }
  \onslide<8->{
  \node [node distance=5mm,below=of a] {non-critical};
  \node [node distance=5mm,below=of b] {non-critical};
  \node [node distance=5mm,below=of c] {\alert{critical}};
  }
  \end{tikzpicture}
  \end{example}
\end{frame}