\begin{frame}{Example}
  \begin{exampleblock}{}
    Consider the following instance of the MPCP:
    \begin{talign}
      w_1 &= 11 & w_2 &= 1  \\
      v_1 &= 1  & v_2 &= 11
    \end{talign}
    It reduces to the following PCP problem:
    \begin{talign}
      y_0 &= @ \$1\$1\$ & y_1 &= 1\$1\$ & y_2 &= 1\$    & y_3 &= \#   \\
      z_0 &= @ \$1      & z_1 &= \$1    & z_2 &= \$1\$1 & z_3 &= \$\#
    \end{talign}
    \pause
    Example solution MPCP:
    \begin{talign}
      w_1 w_2 = 111 = v_1 v_2
    \end{talign}
    Corresponding solution PCP:
    \begin{talign}
      y_0 y_2 y_3 = @ \$1\$1\$ 1\$ \# = z_0 z_2 z_3
    \end{talign}
  \end{exampleblock}
  \pause\medskip
  
  In general: the original MPCP instance has a solution\\
  \hfill $\iff$ the resulting PCP instance has a solution
\end{frame}