Complexity of fixed VAS reachability

A vector addition system is a finite set of vectors $V = \{ v_1,v_2,\ldots,v_n \} \in \mathbb{Z}^d$ with $d \in \mathbb{N}$. Given two positions $s,t \in \mathbb{N}^d$, a run of $V$ from $s$ to $t$ is a sequence $s = c_0, c_1, c_2, \ldots, c_m = t$ of positions $c_i \in \mathbb{N}^d$ where each position is obtained by adding an element of $V$ to the previous one: $c_{i} - c_{i-1} \in V$ for every $1 \leq i \leq m$. Is the following statement correct: Conjecture: For every vector addition system $V$, there exists a constant $C_V$ such that for every pair of positions $s$ and $t$, if there exists at least one run of $V$ from $s$ to $t$, one of these runs has a length smaller than $C_V \cdot \big(||s|| + ||t|| \big)$.