Permutative rewriting and unification

Permutative rewriting provides a way of analyzing deduction modulo a theory defined by leaf-permutative equations. Our analysis naturally leads to the definition of the class of unify-stable axiom sets, in order to enforce a simple reduction strategy. We then give a uniform unification algorithm modulo theories E axiomatized this way. We prove that it computes complete sets of unifiers of simply exponential cardinality, and that the E-unification decision problem belongs to NP.