\begin{frame}
  \small
  
  \begin{definition}
    A \alert{one-step} strategy maps every reducible term to a set of one-step reductions.
  \end{definition}
  
  \begin{example}
  There exists no fair one-step strategy for $\atrs = \{I(x) \to I(x)\}$.
  \medskip\pause

  For the term:  
  \begin{align*}
    t = I(I(x))
  \end{align*}
  there are only 3 possible mappings:
  \begin{itemize}
  \pause
    \item $\SS(t) = \{\alert{I}(I(x)) \to_{\varepsilon} I(I(x))\}$,
  \pause
    \item $\SS(t) = \{I(\alert{I}(x)) \to_{1} I(I(x))\}$, or
  \pause
    \item $\SS(t) = \{\alert{I}(I(x)) \to_{\varepsilon} I(I(x)), \; I(\alert{I}(x)) \to_1 I(I(x))\}$.
  \end{itemize}
  \pause
  None of these is fair as we can always continue to reduce the same occurrence of $I$.
  \end{example}
\end{frame}