Rigid E-Unification is a special type of unification which arises naturally when
extending Andrew's method of matings to logic with equality. We study the rigid E-Unification
problem in the presence of subsorts. We present an order sorted method
for the computation of order sorted rigid-E-unifiers. The method is based on an unsorted
one which we refine and extend to handle sort information. Our approach is to
incorporate the sort information within the method so as to leverage it. We show via
examples how the order sorted method is able to detect failures due to sort conflicts
at an early stage in the construction of potential rigid E Unifiers. The algorithm presented
here is NP-complete, as is the unsorted one. This is significant, specially due to
the complications presented by the sort information.Information Systems Working Papers Serie