This paper focus on the decidability of the position based routing in mobile ad hoc system. Based on the Abstract State Machines theory, we provide a formal model ASM PBRAgent for mobile ad hoc system, on which the position based routing runs as a query. In the result, it is shown that the problem of position based routing is PSPACE-complete when the arity of each node?s outgoing edges has a fixed upper bound, and the Yao-graph topology is an instance; on the other hand, the problem is EXPSPACE-complete if there is no fixed upper bound on the arity.