R(ABCDE)
F = {AB->C, C->D, D->E, E->A}
AB+ = ABCDE
EB+ = ABCDE
DB+ = ABCDE
CB+ = ABCDE
CK ={ AB, CB, DB, EB}
AB->C (no problem for BCNF)
C->D, D->E, E->A (3NF but not BCNF)
Decompose relation R as:
i. R1(ABC) (CK: AB) [BCNF] {AB->C}
R2(ACDE) (CK: C,D,E) [BCNF] {C->D, D->E, E->A}
C is CK for R2 and common attribute b/w R1 and R2.
Hence, this BCNF decomposition is losselss and Depedency Preserving!