\begin{frame}[t] \begin{block}{} \begin{center} $\begin{array}{llcl} (1)&e\cdot x&\to&x\\ (2)&I(x)\cdot x&\to&e\\ (3)&(x\cdot y)\cdot z &\to& x\cdot (y\cdot z)\\ (4)&I(x)\cdot (x\cdot z)&\to& z\\ (8)&y\cdot e&\to& y\\ (9)& I(I(y)) &\to& y\\ (10)&I(e)&\to& e\\ (11)&y\cdot I(y)&\to& e \end{array}$ \end{center} \end{block} \bigskip Overlap between rules (11) and (3) with critical pair: \pause \begin{center} \begin{tikzpicture}[very thick,->,node distance=7mm] \node (t) {$(y\cdot I(y))\cdot x$}; \node (l) [below left=of t] {$e\cdot x$}; \onslide<3->{\node (l') [below left=of l] {$x$};} \node (r) [below right=of t] {$y\cdot (I(y)\cdot x)$}; \draw (t) -- (l) node [midway,above left] {$11$}; \draw (t) -- (r) node [midway,above right] {$3$}; \onslide<3->{\draw (l) -- (l') node [midway,above] {$1$};} \onslide<4->{\draw [dashed] (r) -- (l') node [midway,above] {$12$};} \end{tikzpicture} \end{center} \vspace{-2ex} \pause\pause Add a rule: \begin{block}{} (12)\hspace{2em} $y\cdot (I(y)\cdot x)\to x$ \end{block} \end{frame}