What happens when functional dependency is circular?

Question

I am trying to decompose the following relationships in to 3NF:

A -> BCD
BC -> DE
C -> D
D -> A

So I eliminated the redundancy to get the canonical cover:

A -> BC
B -> E
C -> D
D -> A

And now I am trying to decompose this into 3NF.

Should I decompose into r1(A, B, C) r2(B, D), r3(C, D). Then what do I do with D -> A?

The fact that A -> B -> D -> A is throwing me off.