such that Q j ⊆ S j and the union of the remaining chemical environments that did not match S j but still match S 0 as Q \j ⊆ S 0 . We can therefore see that Q 0 can be rewritten as Q 0 = Q j ∪ Q \j resulting in the more specialized chemical environments matching S j to be split off from S 0 . It is important to note that, as S 0 was never modified, all of the patterns a ∈ A will still match S 0 .