About Connections Between Syntactical and Computational Complexity

We prove in this paper three kinds of results: 1/ It is undecidable whether a term rewriting system preserves recognizability. 2/ ground term rewriting systems with recognizable control are as powerfull as general rewriting systems. 3/ Influence on decidability and complexity of termination of syntactical restrictions on term rewriting systems reduced to one or two rules.

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