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This paper describes how to verify cryptographic protocols by a general-purpose program transformation technique with unfolding. The questions of representation and analysis of the protocols as prefix rewriting grammars are discussed. In these aspects Higman and Turchin embeddings on computational paths are considered, and a refinement of Turchin's relation is presented that allows to algorithmically decide the empty word problem for prefix rewriting grammars.

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The paper studies the subsequence relation through a notion of an intransitive binary relation on words in traces generated by prefix-rewriting systems. The relation was introduced in 1988 by V.F. Turchin for loop approximation in supercompilation. We study properties of this relation and introduce some refinements of the subsequence relation that inherit the useful features of Turchin's relation.

Supercompilation is a program transformation technique that was first described by V. F. Turchin in the 1970s. In supercompilation, Turchin's relation as a similarity relation on call-stack configurations is used both for call-by-value and call-by-name semantics to terminate unfolding of the program being transformed. In this paper, we give a formal grammar model of call-by-name stack behaviour. We classify the model in terms of the Chomsky hierarchy and then formally prove that Turchin's relation can terminate all computations generated by the model.