  We give a necessary and sufficient condition for the fundamental group of a
finite graph of groups with infinite cyclic edge groups to be acylindrically
hyperbolic, from which it follows that a finitely generated group splitting
over Z cannot be simple. We also give a necessary and sufficient condition
(when the vertex groups are torsion free) for the fundamental group to be
balanced, where a group is said to be balanced if $x^m$ conjugate to $x^n$
implies that $|m|=|n|$ for all infinite order elements $x$.
