\begin{frame}
\small

\begin{definition}[Operations on Terms]
\begin{itemize}
\item
$\alert<1>{\depth(\:\cdot\:)}$, the \alert<1>{height (or depth) of a term} \\[1ex]
\(
\depth(t) =
\begin{cases}
0 & \text{if $t \in \VV$ or $t$ is a constant} \\[.5ex]
\displaystyle 1 +
\underset{1 \leqslant i \leqslant n}{\text{max}}\:\depth(t_i) &
\text{if $t = f(\seq{t})$ with $n \geqslant 1$}
\end{cases}
\)
\end{itemize}
\end{definition}

\vfill

\begin{example}<2->
$\depth(\GREEN{(2:x)+((1:x):y)}) = \alert<2>{3}$ \qquad
\GREEN{\begin{tikzpicture}[on grid,baseline=(1).baseline]
\matrix[ampersand replacement=\&,row sep=5mm]{
\& \& \& \node (1) {$+$}; \& \& \& \\
\& \node (2) {$:$}; \& \& \& \& \node (3) {$:$}; \& \\
\node (4) {$2$}; \& \& \node (5) {$x$}; \& \& \node (6) {$:$}; \& \&
\node (7) {$y$}; \\
\& \& \& \node (8) {$1$}; \& \& \node (9) {$x$}; \& \\};
\draw (1) -- (2);
\alert<2>{\draw (1) -- (3);}
\draw (2) -- (4) (2) -- (5);
\alert<2>{\draw (3) -- (6);}
\draw (3) -- (7);
\alert<2>{\draw (6) -- (8);}
\draw (6) -- (9);
\end{tikzpicture}}
\end{example}

\end{frame}