\begin{cofactors} $f$ \= $= (((a \lor \lnot b) \land \lnot (c \lor d)) \lor (a \land b))$\\ \>$f_{a}$ \= $= (\lnot (c \lor d) \lor b)$\\ \>\>$f_{ab}$ \= $= \true$\\ \>\>$f_{a\lnot b}$ \= $= \lnot (c \lor d)$\\ \>\>\>$f_{a\lnot bc}$ \= $= \false$\\ \>\>\>$f_{a\lnot b\lnot c}$ \= $= \lnot d$\\ \>\>\>\>$f_{a\lnot b\lnot cd}$ \= $= \false$\\ \>\>\>\>$f_{a\lnot b\lnot c\lnot d}$ \= $= \true$\\ %\>\>\>$f_{a\lnot b\lnot c}$ \= $= f_{a\lnot b}$\\ \>$f_{\lnot a}$ \= $= (\lnot b \land \lnot (c \lor d))$\\ \>\>$f_{\lnot ab}$ \= $= \false$\\ \>\>$f_{\lnot a\lnot b}$ \= $= f_{a\lnot b}$\\ \end{cofactors} The final ROBDD: \begin{center} \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: f_E -> a0 \draw [] (72.5bp,268.99bp) .. controls (72.5bp,258.92bp) and (72.5bp,243.47bp) .. (72.5bp,233.3bp); % Edge: f_a -> b1 \draw [] (123.5bp,210.99bp) .. controls (123.5bp,200.92bp) and (123.5bp,185.47bp) .. (123.5bp,175.3bp); % Edge: f_a!b -> c2 \draw [] (72.679bp,152.99bp) .. controls (72.859bp,142.92bp) and (73.134bp,127.47bp) .. (73.316bp,117.3bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.959bp,137.3bp) node {\Large$\bullet$}; % Edge: f_a!b!c -> d3 \draw [] (157.14bp,94.988bp) .. controls (151.54bp,84.544bp) and (142.84bp,68.308bp) .. (137.42bp,58.183bp); \draw (146.86bp,75.812bp) node {\Large$\bullet$}; % Edge: f_!a -> b4 \draw [] (21.5bp,210.99bp) .. controls (21.5bp,200.92bp) and (21.5bp,185.47bp) .. (21.5bp,175.3bp); \draw (21.5bp,195.3bp) node {\Large$\bullet$}; % Edge: a0 -> b4 \draw [] (65.409bp,213.21bp) .. controls (55.665bp,202.51bp) and (38.243bp,183.38bp) .. (28.531bp,172.72bp); \draw (41.998bp,187.51bp) node {\Large$\bullet$}; % Edge: a0 -> b1 \draw [] (79.591bp,213.21bp) .. controls (89.335bp,202.51bp) and (106.76bp,183.38bp) .. (116.47bp,172.72bp); % Edge: b4 -> c2 \draw [] (28.73bp,155.21bp) .. controls (38.665bp,144.51bp) and (56.429bp,125.38bp) .. (66.331bp,114.72bp); \draw (52.722bp,129.38bp) node {\Large$\circ$}; % Edge: b4 -> 4 \draw [] (21.5bp,152.99bp) .. controls (21.5bp,137.38bp) and (21.5bp,108.85bp) .. (21.5bp,107.09bp); % Edge: b1 -> c2 \draw [] (116.55bp,155.21bp) .. controls (107.0bp,144.51bp) and (89.915bp,125.38bp) .. (80.393bp,114.72bp); \draw (93.714bp,129.64bp) node {\Large$\bullet$}; % Edge: b1 -> 0 \draw [] (123.32bp,152.99bp) .. controls (123.04bp,137.38bp) and (122.53bp,108.85bp) .. (122.5bp,107.09bp); % Edge: c2 -> c2 %\draw [] (81.517bp,113.81bp) .. controls (91.167bp,119.7bp) and (102.5bp,117.1bp) .. (102.5bp,106.0bp) .. controls (102.5bp,94.898bp) and (91.167bp,92.297bp) .. (81.517bp,98.194bp); %\draw (99.287bp,89.018bp) node {\Large$\bullet$}; % Edge: c2 -> d3 \draw [] (81.213bp,97.679bp) .. controls (92.583bp,86.887bp) and (113.71bp,66.836bp) .. (124.97bp,56.146bp); \draw (110.47bp,69.914bp) node {\Large$\circ$}; % Edge: c2 -> 1 \draw [] (73.5bp,94.988bp) .. controls (73.5bp,79.384bp) and (73.5bp,50.854bp) .. (73.5bp,49.086bp); % Edge: d3 -> 2 \draw [] (130.28bp,36.791bp) .. controls (127.43bp,23.663bp) and (122.8bp,2.3815bp) .. (122.51bp,1.0642bp); % Edge: d3 -> 3 \draw [] (134.5bp,36.791bp) .. controls (137.07bp,23.663bp) and (141.23bp,2.3815bp) .. (141.49bp,1.0642bp); \draw (137.65bp,20.692bp) node {\Large$\bullet$}; % Node: f_E \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (94.0bp,291.0bp) -- (51.0bp,291.0bp) -- (51.0bp,269.0bp) -- (94.0bp,269.0bp) -- cycle; \draw (72.5bp,280.0bp) node {$f$}; \end{scope} % Node: a0 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.5bp,222.0bp) ellipse (11.0bp and 11.0bp); \draw (72.5bp,222.0bp) node {$a$}; \end{scope} % Node: f_a \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (145.0bp,233.0bp) -- (102.0bp,233.0bp) -- (102.0bp,211.0bp) -- (145.0bp,211.0bp) -- cycle; \draw (123.5bp,222.0bp) node {$f_{a}$}; \end{scope} % Node: b1 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (123.5bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (123.5bp,164.0bp) node {$b$}; \end{scope} % Node: f_a!b \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (94.0bp,175.0bp) -- (51.0bp,175.0bp) -- (51.0bp,153.0bp) -- (94.0bp,153.0bp) -- cycle; \draw (72.5bp,164.0bp) node {$f_{a\lnot b}$}; \end{scope} % Node: c2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (73.5bp,106.0bp) ellipse (11.0bp and 11.0bp); \draw (73.5bp,106.0bp) node {$c$}; \end{scope} % Node: f_a!b!c \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (184.0bp,117.0bp) -- (141.0bp,117.0bp) -- (141.0bp,95.0bp) -- (184.0bp,95.0bp) -- cycle; \draw (162.5bp,106.0bp) node {$f_{a\lnot b\lnot c}$}; \end{scope} % Node: d3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (132.5bp,48.0bp) ellipse (11.0bp and 11.0bp); \draw (132.5bp,48.0bp) node {$d$}; \end{scope} % Node: f_!a \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (43.0bp,233.0bp) -- (0.0bp,233.0bp) -- (0.0bp,211.0bp) -- (43.0bp,211.0bp) -- cycle; \draw (21.5bp,222.0bp) node {$f_{\lnot a}$}; \end{scope} % Node: b4 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (21.5bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (21.5bp,164.0bp) node {$b$}; \end{scope} % \end{tikzpicture} } \end{center}