BReduce is an option for B0, B00, B1, B11 determining whether reductions to A0 and B0 will be done.
Overview, A0, B0, B00, B1, B11.
By default B_0 is not expressed in terms of A_0.
B0[0, s, s]\text{B}_0(0,s,s)
With BReduce -> True, transformation is done.
B0[0, s, s, BReduce -> True]-\frac{(2-D) \;\text{A}_0(s)}{2 s}