Efficient Strong Sequentiality Using Replacement Restrictions

Huet and L evy deened the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of re-dexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and L evy give an algorithm to compute indices for the general case, there are many proposals to deene subclasses of strongly sequential rewrite systems for which this can be done more eeciently. In this paper, we show that sometimes it is possible to enlarge such classes by only introducing xed replacement restrictions, without forcing any sensible modiication of the corresponding index reduction strategy.