Find the shortest s-t trail(edge disjoint path) in a graph with negative weight edges 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?
The longest path problem can be reduced to this problem. Let $G = (V,E)$ be an instance of longest $s,t$-path problem. For each vertex $v \in V$ create two vertices, $v_{in}$ and $v_{out}$, and a directed edge with weight $-1$ from $v_{in}$ to $v_{out}$. For each edge $(u, v) \in E$, create an edge from $u_{out}$ to $v_{in}$ with weight $0$. Now each trial in this graph corresponds to a simple path in the graph $G$, and the edges with weight $-1$ count its length.