  In this paper, we build the unfolding approach from acyclic
sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of
infinite rank, which can be regard as an improvement of that in the
skew-symmetrizable case. Using this approach, we give a positive answer to the
problem by Berenstein, Fomin and Zelevinsky in \cite{fz3} which asks whether an
acyclic sign-skew-symmetric matrix is always totally sign-skew-symmetric. As
applications, the positivity for cluster algebras in acyclic
sign-skew-symmetric case is given; further, the $F$-polynomials of cluster
algebras are proved to have constant term 1 in acyclic sign-skew-symmetric
case.
