\begin{frame}[t]
  \frametitle{Case (c): overlapping redexes}
 
  \begin{minipage}{.5\textwidth}
  \includegraphics[width=.90\textwidth]{../graphics/critpairlemma}\\[1ex]
  \end{minipage}
  \begin{minipage}{.49\textwidth}
  Trivial overlaps are uninteresting.
  \pause\bigskip
  
  Let $s_1$ be \alert{overlapping} $s_0$\\
  (with $s_1$ at lower or equal position).
  \pause\bigskip
  
  Let $C[\;]$ be the prefix of $s_0$.
  \pause\bigskip

  
  Then $t_0,t_1$ are instances $C[{c_0}^\rho],C[{c_1}^\rho]$, 
  for some critical pair  $\langle c_1,c_0 \rangle$.
  \pause\bigskip
  
  The critical pair is convergent,\\
  say with common reduct $s_2$.
  \pause\bigskip
  
  Take $t_2 = C[{s_2}^\rho]$.
  \end{minipage}
\end{frame}