Modifying Relation to BCNF

[Soham1087]

I came across the following experiment while studying DBMS and normalization. Regarding the following issue:


Consider the relation R(b,e,s,t,r,o,n,g) with functional dependencies

b,s -> e,r,o,n
b -> t
b -> g
n -> b
o -> r

(a) identify candidate keys

(b) identify prime attributes

(c) state the highest normal form of this table


I think that (a) would be {b, s} since they identify all attributes without redundancy.

(b) would also be {b, s} since they compose the candidate keys of (a).
For a number of factors, (c) would be 1-NF. Due to the existence of the partial dependency n -> b, 2-NF is not satisfied. The aforementioned functional dependency is partial since it only depends on b and not s. Since o -> r implies that one non-prime characteristic depends on another non-prime property, it does not meet 3-NF. Due to 3-NF's unsatisfactoriness, BCNF is not satisfied.
Last but not least, if I changed the table till it was in BCNF, It would divide the relation R into:

R1(b, e, s, r, o, n) with b, s -> e, r, o, n

and,

R2(b, t, g) with b -> t and b -> g

while satisfying BCNF by removing the n->b and o->r?

Regarding fulfilling BCNF, the last section is where I am most perplexed. Any advice you could provide me would be highly appreciated on all steps!