  We study the relation between simple-minded systems and two-term tilting
complexes for self-injective Nakayama algebras. More precisely, we show that
any simple-minded system of a self-injective Nakayama algebra is the image of
the set of simple modules under a stable equivalence, which is given by the
restriction of a standard derived equivalence induced by a two-term tilting
complex. We achieve this by exploiting and connecting the mutation theories
from the combinatorics of Brauer tree, configurations of stable translations
quivers of type A, and triangulations of a punctured convex regular polygon.
