Consider a database R = {Ra} with Ra = {A1, A2, A3, A4, A5, A6} and the dependencies F = {A1 → A2, A2 → A3, A3 → A4, A4 → A2, A3 → A5}.
Consider R1 = {A1, A2}, R2 = {A2, A3, A4}, R3 = {A1, A2, A5}, R4 = {A3, A4}.
How can I tell if R1,R2,R3,R4 is a losseless-join decomposition