Consider this example, I did my pseudocode in python
findCycle(G): for each edge e in E(G): if isThereCycle(G-e): G = G - e return G
assume isthereCycle returns whether the graph $G$ has a cycle.
Input is a graph $G$ that contains a cycle, and the function should return a path of that cycle.
We go through each edge then remove it and see if a cycle still exists without that edge, until we are left with a graph with a single path that is a cycle. (Assume removing the edge (G - e) doesn't mutate the graph unless we do G = G - e).
I want to return a path. Is what I'm returning a path?