Context-Sensitive AC-Rewriting

Context-sensitive rewriting was introduced in and consists of syntactical restrictions imposed on a Term Rewriting System indicating how reductions can be performed. So context-sensitive rewriting is a restriction of the usual rewrite relation which reduces the reduction space and allows for a finer control of the reductions of a term. In this paper we extend the concept of context-sensitive rewriting to the framework rewriting modulo an associative-commutative theory in two ways: by restricting reductions and restricting AC-steps, and we then study this new relation with respect to the property of termination.