Deadlock detection in recursive programs that admit dy-namic resource creation is extremely complex and solutions either give imprecise answers or do not scale. We define an algorithm for detecting deadlocks of linear recursive pro-grams of a basic model. The theory that underpins the algorithm is a generalization of the theory of permutations of names to so-called muta-tions, which transform tuples by introducing duplicates and fresh names. Our algorithm realizes the back-end of deadlock analyzers for object-oriented programming languages, once the association programs/basic-model-programs has been defined as front-end.