A walk in a graph is a finite or infinite sequence of edges which joins a sequence of vertices. A trail is a walk in which all edges are distinct. Note that a trial may visit a vertex multiple times as long as no edge is revisited.
Given a directed graph $G=(V,E)$ where the weight of each edge may be negative. Let $s,t \in V$ be our source and destination vertices, respectively. We are asked to find the shortest $s-t$ trail in $G$.
This problem seems harder than the elementary shortest path problem. But I failed to reduce it to this problem. I've also tried to do reductions from Hamiltonian cycle or feedback arc set, however I failed again. Could you please shed some light upon it?