\begin{cofactors} $f$ \= $= (((p \lor q) \land \lnot (p \land q)) \land r)$\\ \>$f_{q}$ \= $= (\lnot (p \land q) \land r)$\\ \>\>$f_{qp}$ \= $= \false$\\ \>\>$f_{q\lnot p}$ \= $= r$\\ \>\>\>$f_{q\lnot pr}$ \= $= \true$\\ \>\>\>$f_{q\lnot p\lnot r}$ \= $= \false$\\ \>$f_{\lnot q}$ \= $= (p \land r)$\\ \>\>$f_{\lnot qp}$ \= $= f_{q\lnot p}$\\ \>\>$f_{\lnot q\lnot p}$ \= $= \false$\\ \end{cofactors} The final ROBDD: \begin{center} \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: f_E -> q0 \draw [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp) .. (72.5bp,175.3bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.5bp,195.3bp) node {\Large$\bullet$}; % Edge: f_q -> p1 \draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp) .. (123.5bp,117.3bp); \draw (123.5bp,137.3bp) node {\Large$\bullet$}; % Edge: f_q!p -> r2 \draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp) .. (72.5bp,59.304bp); % Edge: f_!q -> p3 \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp) .. (21.5bp,117.3bp); % Edge: q0 -> p3 \draw [] (65.409bp,155.21bp) .. controls (55.665bp,144.51bp) and (38.243bp,125.38bp) .. (28.531bp,114.72bp); \draw (41.998bp,129.51bp) node {\Large$\bullet$}; % Edge: q0 -> p1 \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp) .. (116.47bp,114.72bp); % Edge: p3 -> r2 \draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp) .. (65.469bp,56.72bp); % Edge: p3 -> 3 \draw [] (21.5bp,94.988bp) .. controls (21.5bp,79.384bp) and (21.5bp,50.854bp) .. (21.5bp,49.086bp); \draw (21.5bp,69.086bp) node {\Large$\bullet$}; % Edge: p1 -> r2 \draw [] (116.41bp,97.213bp) .. controls (106.66bp,86.514bp) and (89.243bp,67.385bp) .. (79.531bp,56.72bp); \draw (92.998bp,71.507bp) node {\Large$\bullet$}; % Edge: p1 -> 0 \draw [] (123.5bp,94.988bp) .. controls (123.5bp,79.384bp) and (123.5bp,50.854bp) .. (123.5bp,49.086bp); % Edge: r2 -> 1 \draw [] (70.503bp,36.791bp) .. controls (67.934bp,23.663bp) and (63.77bp,2.3815bp) .. (63.513bp,1.0642bp); % Edge: r2 -> 2 \draw [] (74.719bp,36.791bp) .. controls (77.573bp,23.663bp) and (82.2bp,2.3815bp) .. (82.486bp,1.0642bp); \draw (78.237bp,20.608bp) node {\Large$\bullet$}; % Node: f_E \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (94.0bp,233.0bp) -- (51.0bp,233.0bp) -- (51.0bp,211.0bp) -- (94.0bp,211.0bp) -- cycle; \draw (72.5bp,222.0bp) node {$f$}; \end{scope} % Node: q0 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.5bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (72.5bp,164.0bp) node {$q$}; \end{scope} % Node: f_q \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (145.0bp,175.0bp) -- (102.0bp,175.0bp) -- (102.0bp,153.0bp) -- (145.0bp,153.0bp) -- cycle; \draw (123.5bp,164.0bp) node {$f_{q}$}; \end{scope} % Node: p1 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (123.5bp,106.0bp) ellipse (11.0bp and 11.0bp); \draw (123.5bp,106.0bp) node {$p$}; \end{scope} % Node: f_q!p \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (94.0bp,117.0bp) -- (51.0bp,117.0bp) -- (51.0bp,95.0bp) -- (94.0bp,95.0bp) -- cycle; \draw (72.5bp,106.0bp) node {$f_{q\lnot p}$}; \end{scope} % Node: r2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.5bp,48.0bp) ellipse (11.0bp and 11.0bp); \draw (72.5bp,48.0bp) node {$r$}; \end{scope} % Node: f_!q \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (43.0bp,175.0bp) -- (0.0bp,175.0bp) -- (0.0bp,153.0bp) -- (43.0bp,153.0bp) -- cycle; \draw (21.5bp,164.0bp) node {$f_{\lnot q}$}; \end{scope} % Node: p3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (21.5bp,106.0bp) ellipse (11.0bp and 11.0bp); \draw (21.5bp,106.0bp) node {$p$}; \end{scope} % \end{tikzpicture} } \end{center}