Recording Completion for Finding and Certifying Proofs in Equational   Logic
  When we want to answer/certify whether a given equation is entailed by an equational system we face the following problems: (1) It is hard to find a conversion (but easy to certify a given one). (2) Under the assumption that Knuth-Bendix completion is successful, it is easy to decide the existence of a conversion but hard to certify this decision. In this paper we introduce recording completion, which overcomes both problems. 
Thomas Sternagel and Ren\'e Thiemann and Harald Zankl and Christian   Sternagel
cs.LO