NPA · ω-regular
Infinitely often a, or eventually always c
A nondeterministic parity automaton that forks between two conditions on its first symbol. Nondeterminism is a convenience here — NPA = DPA — unlike under Büchi.
The author’s examples, run
(a) → accept(c) → accept(ab) → acceptab(c) → accept(ac) → accept(b) → reject(bc) → rejectabc(b) → reject