\begin{frame}{Bounded Tiling Problem is NP-complete}
  \begin{block}{Proof continued\ldots (the types of tiles)}
    Tiles for building the first row (for every $a \in \Sigma$):
    \begin{center}\vspace{-.5ex}
      \begin{tikzpicture}[default,nodes={rectangle}]
        \tilew{0}{0}{$\vphantom{W}\Box$}{}{}{}
        \tilew{2}{0}{$q_0,\!a$}{}{}{}
        \tilew{4}{0}{$a$}{}{}{}
      \end{tikzpicture}
    \end{center}
    \pause
    Tiles simulating the computation of $M$ (for every $c \in \Gamma$):
    \begin{center}\vspace{-.5ex}
      \begin{tikzpicture}[default,nodes={rectangle}]
        \tilew{0}{0}{$b$}{\rotatebox{90}{$r,\!R$}}{$q,\!a$}{}
        \tilew{1.5}{0}{$r,\!c$}{}{$c$}{\rotatebox{90}{$r,\!R$}}
        \node [scale=.8,anchor=north] at (1.25,-.1) {for $(r,b,R) \in \delta(q,a)$};

        \tilew{4}{0}{$r,\!c$}{\rotatebox{90}{$r,\!L$}}{$c$}{}
        \tilew{5.5}{0}{$b$}{}{$q,\!a$}{\rotatebox{90}{$r,\!L$}}
        \node [scale=.8,anchor=north] at (5.25,-.1) {for $(r,b,L) \in \delta(q,a)$};
      \end{tikzpicture}
    \end{center}
    \pause
    Tiles for leaving the tape unchanged (for every \alert{$q \in F$}, $c \in \Gamma$):
    \begin{center}\vspace{-.5ex}
      \begin{tikzpicture}[default,nodes={rectangle}]
        \tilew{7}{0}{$q,\!c$}{}{$q,\!c$}{}
        \tilew{8.5}{0}{$c$}{}{$c$}{}
      \end{tikzpicture}
    \end{center}
    \hfill\pause
    \textcolor{gray}{continued on the next slide\ldots}
  \end{block}
  \vspace{10cm}
\end{frame}