\begin{figure}[!t]
\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
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
57 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 &  3 & 3 & 38 & 13\\
56 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 & 3 & 3 & 12 & 13\\ 
55 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 & 3 & 3 & 480 & 13\\ 
53 & 2 & 1 & 2 & 2 & 5 & 2 & 5 & 5 & \lightergray6 & 2 & 4 & 3 & 4 & 3 & 648 & 13\\
35 & \lightergray4 & \lightergray3 & 3 & 2 & 4 & 3 & 4 & 4 & 4 & 2 & 3 & 3 & 3 & 3 & 370 & 12\\ 
26 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 114 & 12\\
09 & \lightergray4 & 2 & 1 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 4 & 4 & 4 & 3 & 3 & 215 & 12\\
40 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 4 & 3 & 4 & 4 & 3 & 2 & 4 & 4 & 3 & 3 & 636 & 11\\ 
25 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 42 & 11\\ 
23 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 60 & 11\\ 
22 & \lightergray3 & \lightergray3 & 3 & 3 & 4 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 42 & 11\\ 
17 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 4 & 3 & 3 & 210 & 11\\ 
16 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & \lightergray3 & 4 & 3 & 3 & 3 & 4 & 3 & 3 & 90 & 11\\ 
47 & \lightergray3 & \lightergray4 & \lightergray4 & \lightergray4 & 4 & 3 & 5 & 4 & 4 & 2 & 4 & 3 & 3 & 3 & 703 & 10\\ 
44 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 3 & 3 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 300 & 10\\ 
43 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 3 & 3 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 300 & 10\\ 
41 & \lightergray4 & \lightergray4 & \lightergray4 & 2 & 4 & 3 & 4 & \lightergray3 & 5 & 2 & 4 & 4 & 3 & 2 & 576 & 10\\ 
36 & \lightergray3 & 2 & 3 & \lightergray4 & 3 & \lightergray4 & 5 & \lightergray3 & 3 & 2 & 4 & 5 & 3 & 2 & 278 & 10\\ 
34 & \lightergray4 & \lightergray3 & \lightergray4 & 2 & 3 & \lightergray4 & 4 & 5 & 3 & 3 & 4 & 4 & 3 & 3 & 155 & 10\\ 
33 & \lightergray4 & \lightergray3 & \lightergray4 & 2 & 3 & \lightergray4 & 4 & 5 & 3 & 3 & 4 & 4 & 3 & 3 & 98.8 & 10\\\hline
\end{tabular}
\caption{A $K_1=20$ neighborhood of $context_1$ (NASA93ii train set).}\label{fig:testing}
\end{center}
\end{figure}


%
%$q_0 \wedge test$  24,48,48,60,60,72,72,90,162,170, 300,400,409,430,444,703,720,756,2400,4560 
%
%235
%
%$q_1 \wedge test$ 24,48,48,60,72,90,162,400,444,720
%
%81
%%
\begin{figure}[!t]
\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
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
56 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 & 3 & 3 & 12 & 13\\ 
57 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 &  3 & 3 & 38 & 13\\
25 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 42 & 11\\ 
22 & \lightergray3 & \lightergray3 & 3 & 3 & 4 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 42 & 11\\ 
23 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 3 & 3 & 3 & 60 & 11\\ 
16 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & \lightergray3 & 4 & 3 & 3 & 3 & 4 & 3 & 3 & 90 & 11\\
26 & \lightergray3 & \lightergray3 & 3 & 3 & 3 & 3 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 114 & 12\\
17 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & 4 & \lightergray3 & 3 & 3 & 3 & 4 & 3 & 3 & 210 & 11\\ 
09 & \lightergray4 & 2 & 1 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 4 & 4 & 4 & 3 & 3 & 215 & 12\\
55 & \lightergray3 & 2 & 2 & 3 & 4 & 3 & 5 & 5 & 5 & 4 & 3 & 3 & 3 & 3 & 480 & 13\\ 
40 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 4 & 3 & 4 & 4 & 3 & 2 & 4 & 4 & 3 & 3 & 636 & 11\\ \hline
\end{tabular}
\end{center}
\caption{All rows of \fig{testing} satisfying $R_1 : pmat=3$.
}\label{fig:testing-constrained}
\end{figure}
\begin{figure}[!t]
\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
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
11 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 24 & 10\\
15 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
19 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 48 & 10\\
18 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 60 & 10\\
10 & \lightergray5 & \lightergray3 & \lightergray4 & 3 & 3 & 2 & 4 & \lightergray3 & 3 & 2 & 4 & 5 & 3 & 3 & 72 & 10\\
24 & \lightergray4 & \lightergray3 & 3 & 3 & 4 & 3 & \lightergray3 & 4 & 3 & 3 & 3 & 4 & 3 & 3 & 90 & 11\\
63 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 3 & 3 & \lightergray3 & \lightergray3 & 3 & 2 & 4 & 4 & 3 & 3 & 162 & 9\\
45 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 4 & \lightergray4 & \lightergray3 & \lightergray3 & 3 & 2 & 3 & 4 & 3 & 3 & 400 & 8\\
67 & \lightergray4 & \lightergray3 & \lightergray4 & 3 & 5 & 3 & 4 & 4 & 3 & 2 & 4 & 4 & 3 & 3 & 444 & 11\\
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. 
}\label{fig:testing-applied}
\end{figure}

\begin{figure}[!h]
\begin{center}
\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}
