  In 2017, Michael Cuntz gave a definition of reducibility of quiddity cycles
of frieze patterns: It is reducible if it can be written as a sum of two other
quiddity cycles. We discuss the commutativity and associativity of this sum
operator for quiddity cycles and its equivalence classes, respectively. We show
that the sum is neither commutative nor associative, but we may circumvent this
issue by passing to equivalence classes. We also address the question whether a
decomposition of quiddity cycles into irreducible factors is unique and we
answer it in the negative by giving counterexamples. We conclude that even
under stronger assumptions, there is no canonical decomposition.
