\begin{frame}[t] \begin{block}{} \begin{center} $\begin{array}{llcl} (1)&e\cdot x&\to&x\\ (2)&I(x)\cdot x&\to&e\\ (3)&(x\cdot y)\cdot z &\to& x\cdot (y\cdot z)\\ (4)&I(x)\cdot (x\cdot z)&\to& z\\ (5)&I(e)\cdot z&\to& z\\ (6)& I(I(y))\cdot e &\to& y \end{array}$ \end{center} \end{block} \bigskip Overlap between rules (3) and (6) with critical pair: \smallskip\pause \begin{center} \begin{tikzpicture}[very thick,->,node distance=7mm] \node (t) {$(I(I(y))\cdot e)\cdot x$}; \node (l) [below left=of t] {$y\cdot x$}; \node (r) [below right=of t] {$I(I(y))\cdot (e\cdot x)$}; \onslide<3->{\node (r') [below right=of r] {$I(I(y))\cdot x$};} \draw (t) -- (l) node [midway,above left] {$6$}; \draw (t) -- (r) node [midway,above right] {$3$}; \onslide<3->{\draw (r) -- (r') node [midway,above] {$1$};} \onslide<4->{\draw [dashed] (r') -- (l) node [midway,above] {$7$};} \end{tikzpicture} \end{center} \vspace{-2ex} \pause\pause Add a rule: \begin{block}{} (7)\hspace{2em} $I(I(y))\cdot x\to y\cdot x$ \end{block} \end{frame}