\begin{frame}[t] \begin{block}{} \begin{center} $\begin{array}{llcl} (1)&e\cdot x&\to&x\\ (2)&I(x)\cdot x&\to&e\\ (3)&(x\cdot y)\cdot z &\to& x\cdot (y\cdot z)\\ (4)&I(x)\cdot (x\cdot z)&\to& z\\ (8)&y\cdot e&\to& y\\ (9)& I(I(y)) &\to& y\\ (10)&I(e)&\to& e\\ (11)&y\cdot I(y)&\to& e\\ (12)&y\cdot (I(y) \cdot x) &\to& x\\ (13)&x\cdot (y\cdot I(x\cdot y)) &\to& e \end{array}$ \end{center} \end{block} \bigskip Overlap between rules (4) and (13) with critical pair: \pause \begin{center} \begin{tikzpicture}[very thick,->,node distance=7mm] \node (t) {$I(x)\cdot (x\cdot (y\cdot I(x\cdot y)))$}; \node (l) [below left=of t] {$I(x)\cdot e$}; \onslide<3->{\node (l') [node distance=12mm,right=of l] {$I(x)$};} \node (r) [below right=of t] {$y\cdot I(x\cdot y)$}; \draw (t) -- (l) node [midway,above left] {$13$}; \draw (t) -- (r) node [midway,above right] {$4$}; \onslide<3->{\draw (l) -- (l') node [midway,above] {$8$};} \onslide<4->{\draw [dashed] (r) -- (l') node [midway,above] {$14$};} \end{tikzpicture} \end{center} \vspace{-1ex} \pause\pause \begin{block}{} (14)\hspace{2em} $y\cdot I(x\cdot y)\to I(x)$ \end{block} \end{frame}