Can a quiver algebra with acyclic quiver be derived equivalent to a quiver algebra with non-acyclic quiver?

(I moved this question from another thread Derived equivalences of Dyck paths , where the question was originally aksed when I thought the answer was elementary/well known but the question now doesnt fit so good anymore and I started a new thread. For Nakayama algebras the answer should be that acyclic ones can not be derived equivalent to non-acyclic ones as noted by Jeremy Rickard in that thread)