\begin{frame} \small \vspace{-1ex} \begin{definition} \smallskip For orthogonal TRSs the \alert{full substitution} strategy performs \alert{complete development} of all redexes. \smallskip \end{definition} \smallskip \begin{example}<2-> \smallskip \begin{itemize} \item rewrite rules \vspace{-1ex} \GREEN{\begin{xalignat*}{2} \m{0} + y & \to y & \m{0} \times y &\to \m{0} \\ \m{s}(x) + y &\to \m{s}(x + y) & \m{s}(x) \times y &\to (x \times y) + y \end{xalignat*}} \vspace{-5ex} \item full substitution strategy \GREEN{\begin{align*} \m{s}(\m{s}(\m{0}))& {} \alert{\times} (\m{s}(\m{0}) \alert{+} \m{s}(\m{s}(\m{0}))) \\ &\onslide<3->{\dev (\m{s}(\m{0}) \alert{\times} \m{s}(\m{0} \alert{+} \m{s}(\m{s}(\m{0})))) + \m{s}(\m{0} \alert{+} \m{s}(\m{s}(\m{0})))} \\ &\onslide<4->{\dev ((\m{0} \alert{\times} \m{s}(\m{s}(\m{s}(\m{0})))) + \m{s}(\m{s}(\m{s}(\m{0})))) + \m{s}(\m{s}(\m{s}(\m{0})))} \\ &\onslide<5->{\to (\m{0} \alert{+} \m{s}(\m{s}(\m{s}(\m{0})))) + \m{s}(\m{s}(\m{s}(\m{0})))} \\ &\onslide<6->{\to \m{s}(\m{s}(\m{s}(\m{0}))) \alert{+} \m{s}(\m{s}(\m{s}(\m{0})))} \\ &\onslide<7->{\to \ldots \to \m{s}(\m{s}(\m{s}(\m{s}(\m{s}(\m{s}(\m{0}))))))} \end{align*}} \vspace{-4ex} \end{itemize} \end{example} \end{frame}