A workflow net N may be extended as another workflow net N´ by adding nodes and arcs. N´ is intuitively called a subclass of N under protocol inheritance if we cannot distinguish those behaviors when removing the added transitions. Protocol inheritance problem is to decide whether N´ is a subclass of N under protocol inheritance. It is known that the problem is decidable but is intractable. Even if N is a subnet of N´, N´ is not always a subclass of N under protocol inheritance. In this paper, limiting our analysis to protocol inheritance between acyclic extended free-choice workflow nets and their subnets, we gave a necessary and sufficient condition on the problem. Based on the condition, we also constructed a polynomial time procedure for solving the problem.