The time-complexity of coverability in unary 1-VASS

A 1-dimensional Vector Addition System with States (1-VASS) can be seen as an directed and integer weighted graph that is equipped with a non-negative integer counter. A configuration of a 1-VASS is a pair $(q, x)$ that is the current node $q$ and the current non-negative counter value $x$. A run in a 1-VASS is a sequence of configurations $(q_0, x_0), (q_1, x_1), \ldots, (q_k, x_k)$ where for each $i \in \{ 1, \ldots, k\}$, there is an edge from $x_{i-1}$ to $x_i$ with weight $x_i - x_{i-1}$. Let $n$ the size of a 1-VASS, encoded in unary, that is the number of states plus the absolute value of all weights. The coverability problem asks whether there is a run from $(p, 0)$ to $(q, x)$ in $\mathcal{V}$, where $x \geq 0$; the input consists of a 1-VASS $\mathcal{V}$, an initial state $p$, and a target state $q$. There is a straightforward $\mathcal{O}(n^2)$-time algorithm for coverability in 1-VASS. Is there an $o(n^2)$-time algorithm for coverability in 1-VASS?