--- a/ChengsongTanPhdThesis/Chapters/Bitcoded2.tex	Thu Jun 09 12:57:53 2022 +0100
+++ b/ChengsongTanPhdThesis/Chapters/Bitcoded2.tex	Thu Jun 09 22:07:44 2022 +0100
@@ -118,8 +118,37 @@
 
 
 
-
-
+\section{ $(a^*\cdot a^*)^*$ against $\protect\underbrace{aa\ldots a}_\text{n \textit{a}s}$ After Simplification}
+We 
+Unlike in \ref{fig:BetterWaterloo}, the size with simplification now stay nicely constant with current
+simplification rules (we put the graphs together to show the contrast)
+\begin{tabular}{ll}
+\begin{tikzpicture}
+\begin{axis}[
+    xlabel={$n$},
+    ylabel={derivative size},
+        width=7cm,
+    height=4cm, 
+    legend entries={Lexer with $\bsimp$},  
+    legend pos=  south east,
+    legend cell align=left]
+\addplot[red,mark=*, mark options={fill=white}] table {BitcodedLexer.data};
+\end{axis}
+\end{tikzpicture} %\label{fig:BitcodedLexer}
+&
+\begin{tikzpicture}
+\begin{axis}[
+    xlabel={$n$},
+    ylabel={derivative size},
+    width = 7cm,
+    height = 4cm,
+    legend entries={Lexer without $\bsimp$},  
+    legend pos=  north west,
+    legend cell align=left]
+\addplot[red,mark=*, mark options={fill=white}] table {BetterWaterloo.data};
+\end{axis}
+\end{tikzpicture} 
+\end{tabular}