  In a seminal paper, Stallings introduced folding of morphisms of graphs. One
consequence of folding is the representation of finitely-generated subgroups of
a finite-rank free group as immersions of finite graphs. Stallings's methods
allow one to construct this representation algorithmically, giving effective,
algorithmic answers and proofs to classical questions about subgroups of free
groups. Recently Dani--Levcovitz used Stallings-like methods to study subgroups
of right-angled Coxeter groups, which act geometrically on CAT(0) cube
complexes. In this paper we extend their techniques to fundamental groups of
non-positively curved cube complexes.
