\begin{frame} \frametitle{Termination, Example 1} \begin{example} \vspace{-1em} \begin{align*} {\rm A}(x,{\rm s}(y)) &\to {\rm s}({\rm A}(x,y))\\ {\rm A}(x,{\rm 0}) &\to x \end{align*} \vspace{-1.5em} \begin{center} \includegraphics{../graphics/pstricks/reduction} \end{center} \vspace{-.5em} \pause \smallskip Looks terminating: \begin{itemize} \item second rule makes terms smaller \item first rule makes `${\rm s}$' move upwards \end{itemize} \smallskip \end{example} \end{frame}