I'm learning the BCNF conversion algorithm and I'm not sure if I understood correctly of what happens when after you decompose the initial relation you still have a subscheme that is not in BCNF.
For example:
Given these Relation scheme and set of dependencies:
R=(ABCD),F={A->C,BC->A,C->D)
I know that both A->C and C->D violate BCNF and I choose to work with A->C.
I decompose it to R1 ({ACD},{A->CD,C->D,AC->D)} and R2 ({AB},{Ø}).
At this point I still have R1 that violates BCNF, so I decompose R1 to R3 ({CD},{C->D}) and R4 ({AC},{A->C}).
This is is the part I'm not sure I'm doing correctly.