Deciding unique termination of permutative rewriting systems: Choose your term algebra carefully
Some problems are considered related to unique termination of rewriting systems for classes of terms equal under some equational theory. It is shown that the approach of Peterson and Stickel  to such problems fails to cope with a rather simple equational theory which is very natural in the context of axiomatic specifications of abstract data types.
One can circumvent the problem by choosing a different axiomatic specification (with a different underlying term algebra) using only associative and commutative equations for which the techniques in  work nicely.
It is argued that we ought to try finding systematic ways of choosing the "right" term algebra for axiomatisations in order to be able to cope with the equational theory needed.
Some tools are presented to deal with the particular equational theory mentionned above, and some of the difficulties encountered in this approach are highlighted.
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