\begin{frame} \small \begin{examples} \smallskip \begin{itemize} \item $\GREEN{x+\m{s}(y+z)}$ matches $\GREEN{\m{s}(y)+\m{s}((x+\ms{s}(0))+z)}$% \onslide<2->: \begin{align*} & \hspace{-2cm} \{ \GREEN{x \alert<3>{+} \m{s}(y+z)} \mapsto \GREEN{\m{s}(y) \alert<3>{+} \m{s}((x+\ms{s}(0))+z)} \} \\ \onslide<3->{\Longrightarrow} \quad & \makebox[6cm][l]{$\onslide<3->{\{ \GREEN{x} \mapsto \GREEN{\m{s}(y)},\: \GREEN{\alert<4>{\m{s}}(y+z)} \mapsto \GREEN{\alert<4>{\m{s}}((x+\ms{s}(0))+z)} \}}$} \\ \onslide<4->{\Longrightarrow} \quad & \onslide<4->{\{ \GREEN{x} \mapsto \GREEN{\m{s}(y)},\: \GREEN{y \alert<5>{+} z} \mapsto \GREEN{(x \alert<5>{+} \ms{s}(0))+z} \}} \\ \onslide<5->{\Longrightarrow} \quad & \onslide<5->{\{ \GREEN{x} \mapsto \GREEN{\m{s}(y)},\: \GREEN{y} \mapsto \GREEN{x+\ms{s}(0)},\: \GREEN{z} \mapsto \GREEN{z} \}} \end{align*} \item<6-> $\GREEN{x^{-} \cdot (x \cdot y)}$ does not match $\GREEN{(\m{e} \cdot x)^{-} \cdot ((\m{e} \cdot \m{e}) \cdot x)}$: \begin{align*} & \hspace{-2cm} \{ \GREEN{x^{-} \alert<7>{\cdot} (x \cdot y)} \mapsto \GREEN{(\m{e} \cdot x)^{-} \alert<7>{\cdot} ((\m{e} \cdot \m{e}) \cdot x)} \} \\ \onslide<7->{\Longrightarrow} \quad & \makebox[6cm][l]{$\onslide<7->{\{ \GREEN{x^{\alert<8>{-}}} \mapsto \GREEN{(\m{e} \cdot x)^{\alert<8>{-}}},\: \GREEN{x \cdot y} \mapsto \GREEN{(\m{e} \cdot \m{e}) \cdot x} \}}$} \\ \onslide<8->{\Longrightarrow} \quad & \onslide<8->{\{ \GREEN{x} \mapsto \GREEN{\m{e} \cdot x},\: \GREEN{x \alert<9>{\cdot} y} \mapsto \GREEN{(\m{e} \cdot \m{e}) \alert<9>{\cdot} x} \}} \\ \onslide<9->{\Longrightarrow} \quad & \onslide<9->{\{ \GREEN{x} \mapsto \GREEN{\alert<10>{\m{e} \cdot x}},\: \GREEN{x} \mapsto \GREEN{\alert<10>{\m{e} \cdot \m{e}}},\: \GREEN{y} \mapsto \GREEN{x} \}} \\ \onslide<10->{\Longrightarrow} \quad & \onslide<10->{\bot} \end{align*} \vspace{-3ex} \end{itemize} \end{examples} \end{frame}