  Regular $g$-measures are discrete-time processes determined by conditional
expectations with respect to the past. One-dimensional Gibbs measures, on the
other hand, are fields determined by simultaneous conditioning on past and
future. For the Markovian and exponentially continuous cases both theories are
known to be equivalent. Its equivalence for more general cases was an open
problem. We present a simple example settling this issue in a negative way:
there exist $g$-measures that are continuous and non-null but are not Gibbsian.
Our example belongs, in fact, to a well-studied family of processes with rather
nice attributes: It is a chain with variable-length memory, characterized by
the absence of phase coexistence and the existence of a visible renewal scheme.
