Proving non-termination by finite automata

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic. 1998 ACM Subject Classification D.1.1 Applicative (Functional) Programming, D.3.1 Formal Definitions and Theory, F.4.1 Mathematical Logic, F.4.2 Grammars and Other Rewriting Systems, I.1.1 Expressions and Their Representation, I.1.3 Languages and Systems