my ($u_set1, $u_set2, $common) = extract_common($set1, $set2);
my $psetc = powerset($common);
my $pset1 = product($psetc, powerset($u_set1));
my $pset2 = product($psetc, powerset($u_set2));
my $pset = union($pset1, $pset2);