\begin{frame} \small \begin{example}[From Turing Machine Configurations to Terms] \bigskip \turing{\Box,a_{-2},a_{-1},a_0,a_1,a_2,\Box}{q}{0} becomes $q(a_{-1}(a_{-2}(\tmiblank)), a_0(a_1(a_2(\tmiblank))))$: \begin{center} \begin{tikzpicture}[node distance=8mm] \node (q) {$q$}; \node (a0) [below right of=q] {$a_0$}; \draw (q) -- (a0); \node (a1) [below of=a0] {$a_1$}; \draw (a0) -- (a1); \node (a2) [below of=a1] {$a_2$}; \draw (a1) -- (a2); \node (a3) [below of=a2] {$\tmiblank$}; \draw (a2) -- (a3); \node (a-1) [below left of=q] {$a_{-1}$}; \draw (q) -- (a-1); \node (a-2) [below of=a-1] {$a_{-2}$}; \draw (a-1) -- (a-2); \node (a-3) [below of=a-2] {$\tmiblank$}; \draw (a-2) -- (a-3); \end{tikzpicture} \end{center} \end{example} \vspace{-3ex} \pause \begin{align*} \bfunap{\astate}{x}{\funap{f}{y}} &\to \bfunap{\astate'}{\funap{f'}{x}}{y} &&\text{ for every }\tmtrans{\astate}{f} = \triple{\astate'}{f'}{\tmR}\\ \bfunap{\astate}{\funap{g}{x}}{\funap{f}{y}} &\to \bfunap{\astate'}{x}{\funap{g}{\funap{f'}{y}}} &&\text{ for every }\tmtrans{\astate}{f} = \triple{\astate'}{f'}{\tmL} \end{align*} \end{frame}