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Analysis of cryptographic protocols in a symbolic model is relative to adeduction system that models the possible actions of an attacker regarding anexecution of this protocol. We present in this paper a transformation algorithmfor such deduction systems provided the equational theory has the finitevariant property. the termination of this transformation entails thedecidability of the ground reachability problems. We prove that it is necessaryto add one other condition to obtain the decidability of non-ground problems,and provide one new such criterion.

On the Decidability of (ground) Reachability Problems for Cryptographic Protocols (extended version)