Proving termination of membership equational programs

Advanced typing, matching, and evaluation strategy features, as well as very general conditional rules, are routinely used in equational programming languages such as, for example, ASF+SDF, OBJ, CAFEOBJ, MAUDE, and equational subsets of ELAN and CASL. Proving termination of equational programs having such expressive features is important but nontrivial, because some of those features may not be supported by standard termination methods and tools, such as MU-TERM, CiME, APROVE, TTT, TERMPTATION, etc. Yet, use of the features may be essential to ensure termination. We present a sequence of theory transformations that can be used to bridge the gap between expressive equational programs and termination tools, prove the correctness of such transformations, and discuss a prototype tool performing the transformations on MAUDE equational programs and sending the resulting transformed theories to some of the aforementioned tools.