(1) Enumerator: P1 -enum< P2 is the enumerator that takes each problem element of P1 to generate a number of new elements, which are put into P2. Therefore the cardinality of P2 is usually larger than that of P1.
(2) Eliminator: P1 >elim- P2 is the eliminator that eliminates non-solution elements of P1 and put the rest into P2. Therefore the cardinality of P2 is usually smaller than that of P1.