  Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are
presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed
that the sequences are generated independently of each other by two
B-processes. We are interested in the question of whether the sequences
represent a typical realization of two different processes or of the same one.
We demonstrate that this is impossible to decide, in the sense that every
discrimination procedure is bound to err with non-negligible frequency when
presented with sequences from some B-processes. This contrasts earlier positive
results on B-processes, in particular those showing that there are consistent
$\bar d$-distance estimates for this class of processes.
