General A-and Ax-uniication via Optimized Combination Procedures General A-and Ax-uniication via Optimized Combination Procedures

In a recent paper BS91] we introduced a new uniication algorithm for the combination of disjoint equational theories. Among other consequences we mentioned (1) that the algorithm provides us with a decision procedure for the solvability of general A-and AI-uniication problems and (2) that Kapur and Narendran's result about the NP-decidability of the solvability of general AC-and ACI-uniication problems (see KN91]) may be obtained from our results. In BS91] we did not give detailled proofs for these two consequences. In the present paper we will treat these problems in more detail. Moreover, we will use the two examples of general A-and AI-uniication for a case study of possible optimizations of the basic combination procedure.