Continuous reachability in ordered data VAS

Data VAS is a finite set of finitely supported functions from ordered data set $\mathbb{D}$ to $\mathbb{Z}^k$, where k is a dimension. A configuration/marking is a finitely supported function from $\mathbb{D}$ to $\mathbb{N}^k$. From a configuration $m$ there is a step to $m'$ if there is a vector $x\in \text{VAS}$ and $\pi$ an ordered preserving bijection (permutation) form $\mathbb{D}$ to $\mathbb{D}$ such that $m+x\circ \pi=m'$. The reachability relation is a transitive closure of the step relation. The reachability problem is undecidable, that is why we are looking for different relaxation of it. Continuous reachability is a continuous version of the reachability. First, markings are finitely/supported functions from $\mathbb{D}$ to $\mathbb{Q}_{\geq 0}^k$. Further there is a continuous step from $m$ to $m'$ if there are: $x\in \text{VAS}$, an order preserving data permutation $\pi$, and a factor $a\in \mathbb{Q}_{\geq 0}$ such that $m+a\cdot x\circ \pi=m'$. A transitive closure of continuous step is a continuous reachability relation.