  We consider cyclic proof systems in which derivations are graphs rather than
trees. Such systems typically come with a condition that isolates which
derivations are admitted as 'proofs', known as a the soundness condition. This
soundness condition frequently takes the form of either a global trace
condition, a property dependent on all infinite paths in the proof-graph, or a
reset condition, a 'local' condition depending on the simple cycles only which,
as a result, is typically stable under more proof transformations. In this
article we present a general method for constructing cyclic proof systems with
reset condition from cyclic proof with global trace conditions. In contrast to
previous approaches, this method of generation is entirely independent of
logic's semantics, only relying on combinatorial aspects of the notion of
'trace' and 'progress'. We apply this method to present reset proof systems for
three cyclic proof systems from the literature: cyclic arithmetic, cyclic
G\"odel's T and cyclic tableaux for the modal {\mu}-calculus.
