\begin{frame}{Example} \begin{exampleblock}{} \begin{center} \input{tikz/tiles_example.tex} \end{center} \end{exampleblock} \vspace{-1ex} \begin{exampleblock}{} Consider the input word \alert{$aaa \not\in L(M)$}. Then $n = 2p(3) + 1 = 7$. \begin{center}\vspace{-1ex} \begin{tikzpicture}[default,nodes={rectangle}] \mpause[1]{ \tilew{0}{0}{$\vphantom{W}\Box$}{}{}{} \tilew{1}{0}{$\vphantom{W}\Box$}{}{}{} \tilew{2}{0}{$\vphantom{W}\Box$}{}{}{} \tilew{3}{0}{$q_0,\!a$}{}{}{} \tilew{4}{0}{$a$}{}{}{} \tilew{5}{0}{$a$}{}{}{} \tilew{6}{0}{$\vphantom{W}\Box$}{}{}{} } \mpause{ \tilew{0}{1}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{1}{1}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{2}{1}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{3}{1}{$b$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}}{$q_0,\!a$}{} \tilew{4}{1}{$q_0,\!a$}{}{$a$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}} \tilew{5}{1}{$a$}{}{$a$}{} \tilew{6}{1}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} } \mpause{ \tilew{0}{2}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{1}{2}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{2}{2}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{3}{2}{$b$}{}{$b$}{} \tilew{4}{2}{$b$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}}{$q_0,\!a$}{} \tilew{5}{2}{$q_0,\!a$}{}{$a$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}} \tilew{6}{2}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} } \mpause{ \tilew{0}{3}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{1}{3}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{2}{3}{$\vphantom{W}\Box$}{}{$\vphantom{W}\Box$}{} \tilew{3}{3}{$b$}{}{$b$}{} \tilew{4}{3}{$b$}{}{$b$}{} \tilew{5}{3}{$b$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}}{$q_0,\!a$}{} \tilew{6}{3}{$q_0,\!\Box$}{}{$\Box$}{\rotatebox{90}{$q_0,\!\raisebox{-2pt}{R}$}} } \end{tikzpicture}\vspace{-2ex} \end{center} \pause\pause\pause\pause\pause The \alert{tiling cannot be completed}. \end{exampleblock} \bigskip \end{frame}