\item \lect 
Consider the example of an elevator.
Initially, the elevator is in the ground floor. 
From the ground floor, it can either go basement, stay there for a while,
and then go back to the ground floor, or it can go from the ground floor 
to the second floor, stay there for a while, and go back to the ground floor.
While traveling between ground floor to second floor, the elevator passes the first floor, but it cannot stop there.

Model this elevator as \emph{transition system}.




\iffalse
\item \lect 
  Given the following graph representation of a \textit{transition system}, state the contents of the sets $S, S_0 and R$

\begin{center}
\vspace{-2em}
\begin{tikzpicture}[auto, node distance=3cm,shorten >=1pt,
thick,node/.style={circle,draw,minimum size=20pt}]
    \node[node] (s0) {$s0$};
    \node (s0s2) [below= 1cm of s0] {};
    \node[node] (s1) [right of=s0s2] {$s1$};
    \node[node] (s2) [below of=s0]   {$s2$};
    \node (start1) [left=1cm of s0] {};
    
    \path[->] (start1) edge (s0);
    \path[->] (s1) edge (s0);
    \path[->] (s0) edge [bend left] (s2);
    \path[->] (s2) edge (s1);
    \path[->] (s2) edge [bend left] (s0);
    \path[->] (s0.30) edge[bend right=90, looseness=15, out=240, in=300] (s0.60);
    \path[->] (s1.30) edge[bend right=90, looseness=15, out=240, in=300] (s1.60);
\end{tikzpicture}
\end{center}
\fi