Aい-い N ⇒ Aい-い の
If what is referred to by N in the phrase "A(い)-い N" is known to the participants of the conversation, N can be replaced by の(one).
A: その ふるい じてんしゃは だれのですか。 Whose is that old bicycle?
B: その ふるいのは アリさんのです。 That old one is Ali's.