Specific BCNF decomposition

问题

I'm trying to do a BCNF decomposition of the following relation:

R(A,B,C,D,E,F)

with functional dependencies:

A -> DF
B -> AC
F -> E

I get the superkey to B, and by following the decomposition algorithm for BCNF I get the following decomposition:

R1{ADF}, R2{ABC} R3{FE}

However, I suspect that R3 is not correct. Can anyone explain why, and where my error is?

来源：https://stackoverflow.com/questions/22437018/specific-bcnf-decomposition