  The Hanna Neumann conjecture states that if F is a free group, then for all
finitely generated subgroups H,K <= F, rank(H intersect K) - 1 <= [ rank(H)-1 ]
[ rank(K)-1 ] In this paper, we show that if one of the subgroups, say H, has a
generating set consisting of only positive words, then H is not part of any
counterexample to the conjecture. We further show that if H <= F({a,b}) is part
of a counterexample to the conjecture, then its folding Gamma_H must contain
source and/or sink vertices.
