\begin{frame}[t]
  \frametitle{Removing Another Redundant Reduction Rule}

  \begin{block}{}  
  \begin{center}
  $\begin{array}{llcl}
  (1)&e\cdot x&\to&x\\
  (2)&I(x)\cdot x&\to&e\\
  (3)&(x\cdot y)\cdot z &\to& x\cdot (y\cdot z)\\
  (4)&I(x)\cdot (x\cdot z)&\to& z\\
  (5)&I(e)\cdot z&\to& z\\
  (8)&y\cdot e&\to& y\\
  (9)& I(I(y)) &\to& y\\
  (10)&I(e)&\to& e
  \end{array}$
  \end{center}
  \end{block}
    
  \bigskip\bigskip\pause
  
  Rule (5) can now be dropped:\pause
  $$I(e)\cdot z \; \to_{10} \; e \cdot z \; \to_1 \; z$$
\end{frame}