\begin{frame} \small \begin{definition} \smallskip A TRS is \alert{left-normal} if variables do not precede function symbols in left-hand sides (where the left-hand sides are written in prefix notation). \end{definition} \smallskip \begin{example}<2-> \begin{itemize} \item \makebox[4cm][l]{$\GREEN{\m{f}(\alert<3->{x},\; \m{g}(y,z)) \to \m{g}(y,\; \m{f}(x,z))}$} \qquad \onslide<3->{$\huil$} \item<4-> \makebox[4cm][l]{$\GREEN{\m{f}(\m{g}(x,y),\; z) \to \m{g}(x,\; \m{g}(y,z))}$} \qquad \onslide<5->{$\lach$} \smallskip \end{itemize} \end{example} \smallskip \begin{theorem}<6-> \smallskip \structure{Leftmost outermost} strategy is normalizing for orthogonal left-normal TRSs. \end{theorem} \smallskip \begin{block}<7->{Remark} \smallskip %easy but \alert<7>{important} result: \alert{Combinatory Logic} is left-normal \GREEN{\begin{xalignat*}{3} \m{I}\,x &\to x & \m{K}\,x\,y &\to x & \m{S}\,x\,y\,z &\to x\,z\,(y\,z) \end{xalignat*}} \vspace{-4ex} \end{block} \end{frame}