Overlapping Leaf Permutative Equations

Leaf permutative equations often appear in equational reasoning, and lead to dumb repetitions through rather trivial though profuse variants of clauses. These variants can be compacted by performing inferences modulo a theory E of leaf permutative equations, using group-theoretic constructions, as proposed in [1]. However, this requires some tasks that happen to be NP-complete (see [7]), unless restrictions are imposed on E. A natural restriction is orthogonality, which allows the use of powerful group-theoretic algorithms to solve some of the required tasks. If sufficient, this restriction is however not necessary. We therefore investigate what kind of overlapping can be allowed in E while retaining the complexity obtained under orthogonality.