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\section{General approach}
Implementing all the problems by hand in SMT-Lib format would be too much work
and therefore all problems have an accompanying bash script contains a function
\lstinline{generate} that generates the SMT-Lib format. The script feeds the
SMT-Lib format to yices after which the output is feeded to a Python script
that visualizes the solution. This means that for all problems $p$ for $p\in
\{1,\ldots, 4\}$ there exist $2$ files. \texttt{ap.bash} that generates the
solution and \texttt{ap.py} that visualizes the solution. All solving is done
on the benchmark system listed in Listing~\ref{listing:benchmark}.

\begin{lstlisting}[caption={Benchmark system},label={listing:benchmark}]
CPU: 3600MHz AMD FX(tm)-4100 Quad-Core Processor
RAM: 8GB

Yices: 2.4.1
SMT-Lib: 1.2
Bash: 4.3.30(1)
\end{lstlisting}

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