\begin{frame}
  \frametitle{Swapping Actions}
    
  \begin{block}{}
    We can \emph{swap actions} (of different transactions) 
    without changing the outcome,
    if the actions are \emph{non-conflicting}. 
  \end{block}
  \pause

  \begin{exampleblock}{}
    {\def\scheduleWidth{1cm}
    \begin{tcenter}
      \begin{tikzpicture}
        \schedule{}{2}{2rV|1rY|2rY|2wY}
        \begin{scope}[xshift=5.5cm,yshift=1cm]
        \schedule{}{2}{2rV|2rY|1rY|2wY}
        \end{scope}
        \begin{scope}[xshift=5.5cm,yshift=-1cm]
        \schedule{}{2}{1rY|2rV|2rY|2wY}
        \end{scope}
        \draw [->,very thick] (4.5cm,.1cm) -- (5.3cm,.5cm);
        \draw [->,very thick] (4.5cm,-1.3cm) -- (5.3cm,-1.6cm);
      \end{tikzpicture}
    \end{tcenter}
    }
  \end{exampleblock}
  \pause
  \medskip
  
  \begin{goal}{Conflict Equivalent Schedules}
    Two schedules are \emph{conflict equivalent}
    if they can be transformed into each other by a sequence of 
    \emph{swaps of non-conflicting, adjacent actions} (of different transactions).
  \end{goal}
\end{frame}