\begin{frame} \small \vspace{-1ex} \begin{example}[cont'd] \[ \begin{array}{lr@{~}c@{~}l@{\qquad}lr@{~}c@{~}l} \structure{\text{\ding{192}}} & \GREEN{x+\m{0}} & \GREEN{\to} & \GREEN{x} & \structure{\text{\ding{193}}} & \GREEN{x+\m{s}(y)} & \GREEN{\to} & \GREEN{\m{s}(x+y)} \\ \structure{\text{\ding{194}}} & \GREEN{x-\m{0}} & \GREEN{\to} & \GREEN{x} & \structure{\text{\ding{195}}} & \GREEN{x-\m{s}(y)} & \GREEN{\to} & \GREEN{\m{p}(x-y)} \\ \structure{\text{\ding{196}}} & \GREEN{\m{p}(\m{s}(x))} & \GREEN{\to} & \GREEN{x} & \structure{\text{\ding{197}}} & \GREEN{\m{s}(\m{p}(x))} & \GREEN{\to} & \GREEN{x} \\ \onslide<0->{\alert{\text{\ding{198}}}} & \onslide<0->{\GREEN{\m{s}(x+\m{p}(y))}} & \onslide<0->{\GREEN{\to}} & \onslide<0->{\GREEN{x+y}} & \onslide<0->{\alert{\text{\ding{199}}}} & \onslide<0->{\GREEN{\m{p}(x-\m{p}(y))}} & \onslide<0->{\GREEN{\to}} & \onslide<0->{\GREEN{x-y}} \\ \onslide<5->{\alert{\text{\ding{200}}}} & \onslide<5->{\GREEN{x+\m{p}(y)}} & \onslide<5->{\GREEN{\to}} & \onslide<5->{\GREEN{\m{p}(x+y)}} & \onslide<6->{\alert{\text{\ding{201}}}} & \onslide<6->{\GREEN{x-\m{p}(y)}} & \onslide<6->{\GREEN{\to}} & \onslide<6->{\GREEN{\m{s}(x-y)}} \end{array} \]\vspace{-2ex} \begin{itemize} \item added rewrite rules $\structure{\text{\ding{198}}}$ and $\structure{\text{\ding{199}}}$ preserve termination \onslide<2-> and do not change $\xleftrightarrow{*}$ \item<3-> new critical pairs \\ \begin{tabbing} \begin{tikzpicture}[on grid,baseline=(1).baseline,node distance=17mm] \node (1) {\MG{\ol{\m{p}(\ul{\m{s}(x+\m{p}(y))})}}}; \node (2) [below left=of 1] {\MGr{\m{p}(x+y)}}; \node (3) [below right=of 1] {\MGl{x+\m{p}(y)}}; \draw[->] (1) -- (2) node[midway,left] {\ssd{198}}; \draw[->] (1) -- (3) node[midway,right] {\ssd{196}}; \onslide<5->{\alert{ \draw[->] (3) -- (2) node[midway,below] {\scriptsize \ding{200}}; }} \end{tikzpicture} \qquad\qquad\qquad \= \begin{tikzpicture}[on grid,baseline=(1).baseline,node distance=17mm] \node (1) {\MG{\ol{\m{s}(x+\ul{\m{p}(\m{s}(y))})}}}; \node (2) [below left=of 1] {\MGr{\m{s}(x+y)}}; \node (3) [below right=of 1] {\MGl{x+\m{s}(y)}}; \draw[->] (1) -- (2) node[midway,left] {\ssd{196}}; \draw[->] (1) -- (3) node[midway,right] {\ssd{198}}; \onslide<4->{ \draw[->] (3) -- (2) node[midway,below] {\ssd{193}}; } \end{tikzpicture} \\[2ex] \begin{tikzpicture}[on grid,baseline=(1).baseline,node distance=17mm] \node (1) {\MG{\ol{\m{s}(\ul{\m{p}(x-\m{p}(y))})}}}; \node (2) [below left=of 1] {\MGr{\m{s}(x-y)}}; \node (3) [below right=of 1] {\MGl{x-\m{p}(y)}}; \draw[->] (1) -- (2) node[midway,left] {\ssd{199}}; \draw[->] (1) -- (3) node[midway,right] {\ssd{197}}; \onslide<6->{\alert{ \draw[->] (3) -- (2) node[midway,below] {\scriptsize \ding{201}}; }} \end{tikzpicture} \> \begin{tikzpicture}[on grid,baseline=(1).baseline,node distance=17mm] \node (1) {\MG{\ol{\m{p}(x-\ul{\m{p}(\m{s}(y))})}}}; \node (2) [below left=of 1] {\MGr{\m{p}(x-y)}}; \node (3) [below right=of 1] {\MGl{x-\m{s}(y)}}; \draw[->] (1) -- (2) node[midway,left] {\ssd{196}}; \draw[->] (1) -- (3) node[midway,right] {\ssd{199}}; \onslide<4->{ \draw[->] (3) -- (2) node[midway,below] {\ssd{195}}; } \end{tikzpicture} \end{tabbing} \end{itemize} \end{example} \end{frame}