\begin{figure}[!h]
\begin{center}
\begin{tabular}{|c|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|}\hline
\multicolumn{17}{|c|}{Brooks' Law Query on Test Set}\\\hline
row&
\emph{\begin{sideways}apex\end{sideways}}&
\emph{\begin{sideways}plex\end{sideways}}&
\emph{\begin{sideways}ltex\end{sideways}}&
\begin{sideways}pmat\end{sideways}&
\begin{sideways}rely\end{sideways}&
\begin{sideways}data\end{sideways}&
\begin{sideways}cplx\end{sideways}&
\begin{sideways}time\end{sideways}&
\begin{sideways}stor\end{sideways}&
\begin{sideways}pvol\end{sideways}&
\begin{sideways}acap\end{sideways}&
\begin{sideways}pcap\end{sideways}&
\begin{sideways}tool\end{sideways}&
\begin{sideways}sced\end{sideways}&
effort&
overlap\\\hline
\cellcolor[rgb]{0.8,0.8,0.8}11 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 24 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}15 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}19 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}18 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 60 & 10\\
21 & \lightergray3 & \lightergray3 & \lightergray4 & \lightergray4 & 4 & 2 & 4 & \lightergray3 & 3 & 2 & 3 & 3 & 3 & 2 & 60 & 9\\
\cellcolor[rgb]{0.8,0.8,0.8}10 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 5 & 3 & 3 & 72 & 10\\
71 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 3 & 2 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 72 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}24 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & \lightergray3 & 4 & 3 & 3 & 3 & 4 & 3 & 3 & 90 & 11\\
\cellcolor[rgb]{0.8,0.8,0.8}63 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 3 & \lightergray3 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 162 & 9\\
31 & \lightergray4 & 2 & \lightergray4 & \lightergray4 & 3 & \lightergray5 & 4 & 5 & 5 & 2 & 5 & 3 & 3 & 2 & 170 & 10\\
73 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 3 & 3 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 300 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}45 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 4 & \lightergray4 & \lightergray3 & \lightergray3 & 3 & 2 & 3 & 4 & 3 & 3 & 400 & 8\\
79 & \lightergray3 & \lightergray4 & \lightergray4 & \lightergray4 & 4 & 3 & 5 & 4 & 4 & 2 & 4 & 3 & 3 & 3 & 409 & 10\\
84 & \lightergray5 & 1 & 1 & \lightergray4 & 4 & 2 & 5 & 5 & \lightergray6 & 2 & 5 & 5 & 4 & 3 & 430 & 11\\
\cellcolor[rgb]{0.8,0.8,0.8}67 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 5 & 3 & 4 & 4 & 3 & 2 & 4 & 4 & 3 & 3 & 444 & 11\\
80 & \lightergray3 & \lightergray4 & \lightergray4 & \lightergray4 & 4 & 3 & 5 & 4 & 4 & 2 & 4 & 3 & 3 & 3 & 703 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}60 & \lightergray3 & \lightergray4 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 5 & 5 & 3 & 3 & 720 & 10\\
76 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 4 & \lightergray5 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 756 & 9\\
%87 & \lightergray4 & \lightergray4 & \lightergray4 & \lightergray4 & 5 & \lightergray4 & 5 & \lightergray6 & \lightergray6 & 3 & 4 & 4 & 3 & 3 & 1645.9 & 7\\
%88 & \lightergray4 & \lightergray4 & \lightergray4 & \lightergray4 & 5 & \lightergray4 & \lightergray6 & \lightergray6 & \lightergray6 & 3 & 4 & 4 & 3 & 3 & 1924.5 & 6\\\hline
46 & \lightergray4 & \lightergray3 & \lightergray4 & 2 & \lightergray2 & 3 & \lightergray3 & \lightergray3 & 3 & 2 & 4 & 5 & 3 & 3 & 2400 & 8\\
%85 & \lightergray4 & \lightergray4 & \lightergray4 & \lightergray4 & 5 & \lightergray4 & 5 & \lightergray6 & \lightergray6 & 3 & 4 & 4 & 3 & 3 & 4178.2 & 7\\
59 & \lightergray5 & 1 & \lightergray4 & 2 & 5 & 2 & \lightergray6 & \lightergray6 & 5 & 2 & 4 & 4 & 3 & 3 & 4560 & 10\\\hline

\end{tabular}
\end{center}
\caption{Applying $q \cup S_1$ to the 20 most relevant cases from the testing set. Here, cases highlighted represent those that include $pmat = 3$, learned during training.}\label{fig:testing}
\end{figure}


\begin{figure}[!h]
\begin{center}
\begin{tabular}{|c|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|@{\hspace{0.5mm}}c@{\hspace{0.5mm}}|}\hline
\multicolumn{17}{|c|}{Brooks' Law Query $\cup$ {\em pmat=3}}\\\hline
row&
\emph{\begin{sideways}apex\end{sideways}}&
\emph{\begin{sideways}plex\end{sideways}}&
\emph{\begin{sideways}ltex\end{sideways}}&
\begin{sideways}pmat\end{sideways}&
\begin{sideways}rely\end{sideways}&
\begin{sideways}data\end{sideways}&
\begin{sideways}cplx\end{sideways}&
\begin{sideways}time\end{sideways}&
\begin{sideways}stor\end{sideways}&
\begin{sideways}pvol\end{sideways}&
\begin{sideways}acap\end{sideways}&
\begin{sideways}pcap\end{sideways}&
\begin{sideways}tool\end{sideways}&
\begin{sideways}sced\end{sideways}&
effort&
overlap\\\hline
\cellcolor[rgb]{0.8,0.8,0.8}11 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 24 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}15 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}19 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}18 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 60 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}10 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 5 & 3 & 3 & 72 & 10\\
\cellcolor[rgb]{0.8,0.8,0.8}24 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & \lightergray3 & 4 & 3 & 3 & 3 & 4 & 3 & 3 & 90 & 11\\
\cellcolor[rgb]{0.8,0.8,0.8}63 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 3 & \lightergray3 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 162 & 9\\
\cellcolor[rgb]{0.8,0.8,0.8}45 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 4 & \lightergray4 & \lightergray3 & \lightergray3 & 3 & 2 & 3 & 4 & 3 & 3 & 400 & 8\\
\cellcolor[rgb]{0.8,0.8,0.8}67 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 5 & 3 & 4 & 4 & 3 & 2 & 4 & 4 & 3 & 3 & 444 & 11\\
\cellcolor[rgb]{0.8,0.8,0.8}60 & \lightergray3 & \lightergray4 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 5 & 5 & 3 & 3 & 720 & 10\\\hline
\end{tabular}
\end{center}
\caption{The testing set with all cases not containing $pmat = 3$ removed. The impact of applying $pmat = 3$ is reported as the median effort value of the cases. In this case, 81.}\label{fig:testing-constrained}
\end{figure}


\begin{figure}[!h]
\begin{center}
{\scriptsize
\begin{tabular}{| r         | @{}c@{}         | @{}c@{}          |        @{}c         |}\hline
                             & Effort    & Effort     & Effort Distrubtion \\
                   Query     & Median    & Spread     &        366 \\\hline

$q$ (Initial)           &  235 &  508 &  \boxplot{5.737704918}{23.08743169}{28.82513661}{46.2431694}{75.06830601}\\ 
$q \cup pmat=3$ (Final) &   81 &  352 &  \boxplot{3.278688525}{4.508196721}{7.786885246}{43.57923497}{51.36612022}\\\hline 
\end{tabular}}
\end{center}
\caption{Result of applying the learned constraint $pmat = 3$ to the Brooks' Law query $q$ during testing. The median estimate reduction from 235 to 81 represents a 66\% reduction is software effort by applying $pmat = 3$.}
\label{fig:testing-result}
\end{figure}