\item \self Convert the following BDD into a \emph{reduced  ordered} BDD.

\begin{center}
\begin{forest}
for tree={circle, draw, no edge,
            minimum size=2em,
            inner sep=0pt,
            s sep=6mm,
            l sep=6mm}
[$f$, rectangle, draw,  tikz={\draw [line] () to (p.north);}
    [$q$, name=q, tikz={\draw [line] () to (s1.north); \draw [dot=.5] () to (s2.north);}
        [$s$, name=s1, tikz={\draw [line] () to (240:4.1); \draw [fulldot=.5] () to (r1.north);}
            [,phantom]
            [$r$, name=r1, tikz={\draw [line] () to (p1.north); \draw[dot=.5] () to (p2.north);}
                [$p$, name=p1, tikz={\draw [line] () to (254:6.57); \draw[fulldot=.5] () to (263:6.37);}]
                [$p$, name=p2, tikz={\draw [line] () to (266:6.33); \draw[dot=.5] () to (275:6.35);}]
            ]
        ]
        [$s$, name=s2, tikz={\draw [line] () to (281:3.6); \draw [fulldot=.5] () to (r2.north);}
            [,phantom]
            [$r$, name=r2, tikz={\draw [line] () to (p3.north); \draw[dot=.5] () to (p4.north);}
                [$p$, name=p3, tikz={\draw [line] () to (277:6.38); \draw[fulldot=.5] () to (286:6.6);}]
                [$p$, name=p4, tikz={\draw [line] () to (288:6.65); \draw[dot=.5] () to (297:7.1);}]
            ]
        ]
    ]
]
\end{forest}
\end{center}
