To best illustrate the generation algorithm, we will additionally show how it generates the BW-s2(α) regulariser. The algorithm starts by first creating a list of all possible component combinations. Since we demand all matrix elements to be tensor contractions only featuring the Fock matrix, the first order doubles amplitudes and the ERI tensor, these tensor compositions have a straightforward form. Introducing a notational shorthand, where we denote the Fock matrix as f , amplitudes as t and the ERI tensor as V , the list of valid tensor combinations can be written as V , V t, V tt, . . ., f t, f tt, . . .. The BW-s2(α) regulariser is therefore classified as V t.