\begin{frame}
  \begin{remark}[The failure of Newmann's Lemma for infinitary rewriting]
  $$\text{WCR} \wedge \SNi \not\Rightarrow \CRi$$
  \bigskip\pause
  For example: 
  \vspace{-2ex}
  \begin{align*}
    R = \{\; &a \to b(a),\\
             &a \to c(a),\\
             &c(b(x)) \to b(b(x)) \;\}
  \end{align*}
  \vspace{-2ex}

  is WCR and $\SNi$, but not $\CRi$.
  \end{remark}
\end{frame}