Is there a dependency preserving, lossless BCNF decomposition for this relational schema?

R(A,B,C) where {AB -> C , C -> A}. The candidate keys are {A,B} and {C,B}. This is in 3NF but not BCNF because of {C->A} . Now it seems like this can't even be split into a lossless BCNF, let alone a dependency preserving one. Is there some way to prove it? Is there some result that says that if the result of the 3NF algorithm does not give you a BCNF decomposition, then a further BCNF decomposition is not possible? Edit: I have since figured out that every schema can be split into a lossless BCNF one. It is preserving dependency that is uncertain. Here the lossless decomposition would be R(B,C), R(C,A)