Basic Completion with E-cycle Simplification

We give a new simplification method, called E-cycle Simplification, for Basic Completion inference systems. We prove the completeness of Basic Completion with E-cycle Simplification. We prove that E-cycle Simplification is strictly stronger than the only previously known complete simplification method for Basic Completion, Basic Simplification, in the sense that every derivation involving Basic Simplification is a derivation involving E-cycle Simplification, but not vice versa. E-cycle Simplification is simple to perform, and does not use the reducibilityrelative-to condition. We believe this new method captures exactly what is needed for completeness. ECC implements our method.