\begin{frame}[t] \begin{block}{} \begin{center} $\begin{array}{llcl} (1)&e\cdot x&\to&x\\ (2)&I(x)\cdot x&\to&e\\ (3)&(x\cdot y)\cdot z &\to& x\cdot (y\cdot z)\\ (4)&I(x)\cdot (x\cdot z)&\to& z\\ (5)&I(e)\cdot z&\to& z\\ (6)& I(I(y))\cdot e &\to& y\\ (7)& I(I(y))\cdot x &\to& y\cdot x\\ (8)&y\cdot e&\to& y \end{array}$ \end{center} \end{block} \bigskip Overlap between rules (8) and (6) with critical pair: \pause \begin{center} \begin{tikzpicture}[very thick,->] \node (t) {$I(I(y))\cdot e$}; \node (l) [below left=of t] {$I(I(y))$}; \node (r) [below right=of t] {$y$}; \draw (t) -- (l) node [midway,above left] {$8$}; \draw (t) -- (r) node [midway,above right] {$6$}; \onslide<3->{\draw [dashed] (l) -- (r) node [midway,above] {$9$};} \end{tikzpicture} \end{center} \pause Add a rule: \begin{block}{} (9)\hspace{2em} $I(I(y))\to y$ \end{block} \end{frame}