Natural Termination

Two techniques are examined for showing termination of rewrite systems when simpli cation ordering are insu cient. The rst approach generalizes the various path orderings and the conditions under which they work. Examples of its use are given and a brief description of an implementation is presented. The second approach uses restricted derivations, called \forward closures", for proving termination of orthogonal and overlaying systems. Both approaches allow the use of \natural" interpretations under which rules rewrite terms to terms of the same value.

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