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