3NF synthesis reduction algorithm

Question

I am working for a DBMS class and came across 3NF synthesis algorithm here http://cis.csuohio.edu/~matos/notes/cis-611/ClassNotes/13-3NF-Synthesis.html

I am stuck with canonical cover computation. The problem is as follows: Reduce the following FD to 3NF:

FD1 : AB→C
FD2 : C→D
FD3 : D→B
FD4 : B→E

The canonical cover is

FD1 : A→C
FD2 : C→D
FD3 : D→B
FD4 : B→E

After computing, the relations are merged {(A,C), (C,D), (D,B,E)}. The synthesis algorithm is lossless, but from the method, isn't the FD1 from the question not satisfied?

Answer 1

I know Its late But canonical cover is A→B A→C B→D B→E A→F

so R1(ABCF) and R2(BDE)