  Happel and Seidel gave a classification of piecewise hereditary Nakayama
algebras, where the relations are given by some power of the radical.
  Here we explore what happens for general relations. We develop techniques for
showing that a given algebra is not piecewise hereditary, illustrating them on
numerous mid-sized examples. Then we observe cases where the property of being
non-piecewise hereditary can be extended to other (larger) Nakayama algebras.
While a complete classification remains elusive, we are able to identify two
types of patterns of relations preventing piecewise heredity, indicating that
for large quivers many Nakayama algebras are non-piecewise hereditary.
