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\begin{cofactors} $f$ \= $= (((a \land b) \lor (\lnot c \land d)) \lor (e \land \lnot a))$\\ \>$f_{a}$ \= $= (b \lor (\lnot c \land d))$\\ \>\>$f_{ab}$ \= $= \true$\\ \>\>$f_{a\lnot b}$ \= $= (\lnot c \land d)$\\ \>\>\>$f_{a\lnot bc}$ \= $= \false$\\ \>\>\>$f_{a\lnot b\lnot c}$ \= $= d$\\ \>\>\>\>$f_{a\lnot b\lnot cd}$ \= $= \true$\\ \>\>\>\>$f_{a\lnot b\lnot c\lnot d}$ \= $= \false$\\ \>$f_{\lnot a}$ \= $= ((\lnot c \land d) \lor e)$\\ \>\>$f_{\lnot ac}$ \= $= e$\\ \>\>\>$f_{\lnot ace}$ \= $= \true$\\ \>\>\>$f_{\lnot ac\lnot e}$ \= $= \false$\\ \>\>$f_{\lnot a\lnot c}$ \= $= (d \lor e)$\\ \>\>\>$f_{\lnot a\lnot cd}$ \= $= \true$\\ \>\>\>$f_{\lnot a\lnot c\lnot d}$ \= $= f_{\lnot ac}$\\ \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 [] (84.143bp,268.99bp) .. controls (84.143bp,258.92bp) and (84.143bp,243.47bp) .. (84.143bp,233.3bp); % Edge: f_a -> b1
\draw [] (135.14bp,210.99bp) .. controls (135.14bp,200.92bp) and (135.14bp,185.47bp) .. (135.14bp,175.3bp); % Edge: f_a!b -> c2
\draw [] (184.35bp,152.99bp) .. controls (182.53bp,142.8bp) and (179.73bp,127.09bp) .. (177.91bp,116.93bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (181.43bp,136.61bp) node {\Large$\bullet$}; % Edge: f_a!b!c -> d3
\draw [] (225.18bp,94.988bp) .. controls (223.17bp,84.795bp) and (220.09bp,69.087bp) .. (218.09bp,58.925bp); % Edge: f_!a -> c4
\draw [] (33.143bp,210.99bp) .. controls (33.143bp,200.92bp) and (33.143bp,185.47bp) .. (33.143bp,175.3bp); % Edge: f_!ac -> e5
\draw [] (33.143bp,94.988bp) .. controls (33.143bp,84.921bp) and (33.143bp,69.474bp) .. (33.143bp,59.304bp); % Edge: f_!a!c -> d6
\draw [] (84.143bp,152.99bp) .. controls (84.143bp,142.92bp) and (84.143bp,127.47bp) .. (84.143bp,117.3bp); % Edge: a0 -> c4
\draw [] (77.051bp,213.21bp) .. controls (67.308bp,202.51bp) and (49.886bp,183.38bp) .. (40.174bp,172.72bp); \draw (53.64bp,187.51bp) node {\Large$\circ$}; % Edge: a0 -> b1
\draw [] (91.234bp,213.21bp) .. controls (100.98bp,202.51bp) and (118.4bp,183.38bp) .. (128.11bp,172.72bp); % Edge: c4 -> d6
\draw [] (40.234bp,155.21bp) .. controls (49.978bp,144.51bp) and (67.4bp,125.38bp) .. (77.112bp,114.72bp); \draw (63.645bp,129.51bp) node {\Large$\circ$}; % Edge: c4 -> e5
\draw [] (25.797bp,155.3bp) .. controls (18.182bp,146.73bp) and (6.7572bp,132.1bp) .. (2.1426bp,117.0bp) .. controls (-0.71421bp,107.65bp) and (-0.71421bp,104.35bp) .. (2.1426bp,95.0bp) .. controls (6.7572bp,79.895bp) and (18.182bp,65.265bp) .. (25.797bp,56.7bp); % Edge: d6 -> e5
\draw [] (77.051bp,97.213bp) .. controls (67.308bp,86.514bp) and (49.886bp,67.385bp) .. (40.174bp,56.72bp); \draw (53.64bp,71.507bp) node {\Large$\circ$}; % Edge: d6 -> 6
\draw [] (84.143bp,94.988bp) .. controls (84.143bp,79.384bp) and (84.143bp,50.854bp) .. (84.143bp,49.086bp); % Edge: e5 -> 4
\draw [] (31.145bp,36.791bp) .. controls (28.577bp,23.663bp) and (24.413bp,2.3815bp) .. (24.155bp,1.0642bp); % Edge: e5 -> 5
\draw [] (35.362bp,36.791bp) .. controls (38.216bp,23.663bp) and (42.842bp,2.3815bp) .. (43.129bp,1.0642bp); \draw (38.88bp,20.608bp) node {\Large$\bullet$}; % Edge: b1 -> c2
\draw [] (141.19bp,154.74bp) .. controls (148.94bp,144.15bp) and (162.3bp,125.9bp) .. (170.07bp,115.3bp); \draw (158.25bp,131.43bp) node {\Large$\bullet$}; % Edge: b1 -> 0
\draw [] (135.14bp,152.99bp) .. controls (135.14bp,137.38bp) and (135.14bp,108.85bp) .. (135.14bp,107.09bp); % Edge: c2 -> d3
\draw [] (182.39bp,96.25bp) .. controls (189.95bp,85.668bp) and (202.59bp,67.976bp) .. (210.07bp,57.505bp); \draw (198.44bp,73.78bp) node {\Large$\bullet$}; % Edge: c2 -> 1
\draw [] (176.14bp,94.988bp) .. controls (176.14bp,79.384bp) and (176.14bp,50.854bp) .. (176.14bp,49.086bp); % Edge: d3 -> 2
\draw [] (213.92bp,36.791bp) .. controls (211.07bp,23.663bp) and (206.44bp,2.3815bp) .. (206.16bp,1.0642bp); % Edge: d3 -> 3
\draw [] (218.14bp,36.791bp) .. controls (220.71bp,23.663bp) and (224.87bp,2.3815bp) .. (225.13bp,1.0642bp); \draw (221.29bp,20.692bp) node {\Large$\bullet$}; % Node: f_E
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (105.64bp,291.0bp) -- (62.64bp,291.0bp) -- (62.64bp,269.0bp) -- (105.64bp,269.0bp) -- cycle; \draw (84.143bp,280.0bp) node {$f$}; \end{scope} % Node: a0
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (84.14bp,222.0bp) ellipse (11.0bp and 11.0bp); \draw (84.143bp,222.0bp) node {$a$}; \end{scope} % Node: f_a
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (156.64bp,233.0bp) -- (113.64bp,233.0bp) -- (113.64bp,211.0bp) -- (156.64bp,211.0bp) -- cycle; \draw (135.14bp,222.0bp) node {$f_{a}$}; \end{scope} % Node: b1
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (135.14bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (135.14bp,164.0bp) node {$b$}; \end{scope} % Node: f_a!b
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (207.64bp,175.0bp) -- (164.64bp,175.0bp) -- (164.64bp,153.0bp) -- (207.64bp,153.0bp) -- cycle; \draw (186.14bp,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 (176.14bp,106.0bp) ellipse (11.0bp and 11.0bp); \draw (176.14bp,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 (248.64bp,117.0bp) -- (205.64bp,117.0bp) -- (205.64bp,95.0bp) -- (248.64bp,95.0bp) -- cycle; \draw (227.14bp,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 (216.14bp,48.0bp) ellipse (11.0bp and 11.0bp); \draw (216.14bp,48.0bp) node {$d$}; \end{scope} % Node: f_!a
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (54.64bp,233.0bp) -- (11.64bp,233.0bp) -- (11.64bp,211.0bp) -- (54.64bp,211.0bp) -- cycle; \draw (33.143bp,222.0bp) node {$f_{\lnot a}$}; \end{scope} % Node: c4
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (33.14bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (33.143bp,164.0bp) node {$c$}; \end{scope} % Node: f_!ac
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (54.64bp,117.0bp) -- (11.64bp,117.0bp) -- (11.64bp,95.0bp) -- (54.64bp,95.0bp) -- cycle; \draw (33.143bp,106.0bp) node {$f_{\lnot ac}$}; \end{scope} % Node: e5
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (33.14bp,48.0bp) ellipse (11.0bp and 11.0bp); \draw (33.143bp,48.0bp) node {$e$}; \end{scope} % Node: f_!a!c
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (105.64bp,175.0bp) -- (62.64bp,175.0bp) -- (62.64bp,153.0bp) -- (105.64bp,153.0bp) -- cycle; \draw (84.143bp,164.0bp) node {$f_{\lnot a\lnot c}$}; \end{scope} % Node: d6
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (84.14bp,106.0bp) ellipse (11.0bp and 11.0bp); \draw (84.143bp,106.0bp) node {$d$}; \end{scope} %
\end{tikzpicture} } \end{center}
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