These properties describe functions on finite sequences, without asserting that every function satisfies them. Encodings are selected automatically. The two-input property has linear time dependence on the first sequence's length and computable time and word-capacity coefficients depending only on the second sequence's length. The ordinary one-input property instead uses a constant word-capacity coefficient. Natural payload magnitudes are included in $inputMagnitude$, not in the sequence-length time measure.

Polynomial time below means polynomial in sequence length, under that same constant-times-input-magnitude word-capacity convention. It is a word-RAM notion, not a claim about polynomial time in a binary serialization. The degree is an upper bound on the time exponent, not a claim of optimality.