To justify if non-Abelian relation compositions can be discovered by DihEdral in an ideal situation, we generate a synthetic dataset called FAMILY.
we first generated two generations of people with equal number of male and females in each generation, and randomly assigned spouse edges within each generation and child and parent edges between the two generations, after which the sibling, parent_in_law and   3 where r 3 is treated as the composition of r 1 and r 2 .