It is known that interaction combinators can implement any interaction net system efficiently. Now, let us define a modification of interaction combinators, which, instead of two types of fan cells, has an infinite number of fan-cells, labelled with unique integers. That system works exactly like the previous: two nodes with identical labels annihilate; two nodes with different labels duplicate. In other words, interaction combinators are a subset of that system, with only 2 possible ids.
How can you compile that new system to the former, without losing efficiency?