The documentation says that the partial order of D-classes can be obtained by the transitive closure of the output relations. However, it seems that the reflexive closure is also need. For manual example
gap> S:=Semigroup( Transformation( [ 2, 4, 1, 2 ] ), > Transformation( [ 3, 3, 4, 1 ] ) );; gap> PartialOrderOfDClasses(S); [ [ 3 ], [ 2, 3 ], [ 3, 4 ], [ 4 ] ]
(1,1) is missing, while the (3,3) explicitly appears in the output. This also contradicts the documentation saying that only the immediately below relations are returned, hinting that basically the Hasse diagram of the partial order is meant to be returned. From random examples it seems that PartialOrderOfDClasses misses some maximal elements.
So it is not clear what is returned exactly.