We study the control reachability problem in the Dolev-Yao model of cryptographic protocols when principals are represented by tailrecursive processes with generated names. We propose a conservative approximation of the problem by reduction to a non-standard collapsed operational semantics and we introduce checkable syntactic conditions entailing the equivalence of the standard and the collapsed semantics. Then we introduce a conservative and decidable set-based analysis of the collapsed operational semantics and we characterize a situation where the analysis is exact. Finally, we describe how our framework can be used to specify secrecy and freshness properties of cryptographic protocols.