\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}