121 

   121 \section{ $(a^*\cdot a^*)^*$ against $\protect\underbrace{aa\ldots a}_\text{n \textit{a}s}$ After Simplification}

   122 

   122 We 

   123 Unlike in \ref{fig:BetterWaterloo}, the size with simplification now stay nicely constant with current

   124 simplification rules (we put the graphs together to show the contrast)

   125 \begin{tabular}{ll}

   126 \begin{tikzpicture}

   127 \begin{axis}[

   128     xlabel={$n$},

   129     ylabel={derivative size},

   130         width=7cm,

   131     height=4cm, 

   132     legend entries={Lexer with $\bsimp$},  

   133     legend pos=  south east,

   134     legend cell align=left]

   135 \addplot[red,mark=*, mark options={fill=white}] table {BitcodedLexer.data};

   136 \end{axis}

   137 \end{tikzpicture} %\label{fig:BitcodedLexer}

   138 &

   139 \begin{tikzpicture}

   140 \begin{axis}[

   141     xlabel={$n$},

   142     ylabel={derivative size},

   143     width = 7cm,

   144     height = 4cm,

   145     legend entries={Lexer without $\bsimp$},  

   146     legend pos=  north west,

   147     legend cell align=left]

   148 \addplot[red,mark=*, mark options={fill=white}] table {BetterWaterloo.data};

   149 \end{axis}

   150 \end{tikzpicture} 

   151 \end{tabular}