Polynomial interpretations are one of the most popular techniques for automated termination analysis and the search for such interpretations is a main bottleneck in most termination provers. We show that one can obtain speedups in orders of magnitude by encoding this task as a SAT problem and by applying modern SAT solvers.

Context-sensitive rewriting (CSR) is a restriction of rewriting which forbids reductions on selected arguments of functions. Proving termination of CSR is an interesting problem with several applications in the fields of term rewriting and programming languages. Several methods have been developed for proving termination of CSR. The new version of MU-TERM which we present here implements all currently known techniques. Furthermore, we show how to combine them to furnish MU-TERM with an expert which is able to automatically perform the termination proofs. Finally, we provide a first experimental evaluation of the tool.

Abstract. We describe a new approach to proving termination with size change graphs. This is the first decision procedure for size change termination (SCT) which makes direct use of global ranking functions. It handles a well-defined and significant subset of SCT instances, designed to be amenable to a SAT-based solution. We have implemented the approach using a state-of-the-art Boolean satisfaction solver. Experimentation indicates that the approach is a viable alternative to the complete SCT decision procedure based on closure computation and local ranking functions. Our approach has the extra benefit of producing an explicit witness to prove termination in the form of a global ranking function. 1

Abstract. This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair method. We address two main inter-related issues and encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (1) the combined search for a lexicographic path order together with an argument filtering to orient a set of inequalities; and (2) how the choice of the argument filtering influences the set of inequalities that have to be oriented. We have implemented our contributions in the termination prover AProVE. Extensive experiments show that by our encoding and the application of SAT solvers one obtains speedups in orders of magnitude as well as increased termination proving power. 1

We introduce a propositional encoding of the recursive path order with status (RPO). RPO is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. Our encoding allows us to apply SAT solvers in order to determine whether a given term rewrite system is RPO-terminating. Furthermore, to apply RPO within the dependency pair framework, we combined our novel encoding for RPO with an existing encoding for argument filters. We implemented our contributions in the termination prover AProVE. Our experiments show that due to our encoding, combining termination provers with SAT solvers improves the performance of RPO-implementations by orders of magnitude.

Abstract. This paper presents two new approaches to prove termination of rewrite systems with the Knuth-Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic and the resulting formula is tested for satisfiability. Any satisfying assignment represents a weight function and a precedence such that the induced Knuth-Bendix order orients the rules of the encoded rewrite system from left to right. 1

This paper introduces a propositional encoding of the recursive path order (RPO) on terms which is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. The proposed encoding allows us to use SAT solvers in order to determine whether a given term rewrite system is RPO terminating. An implementation is described.

Abstract. This paper describes the application of a partial order constraint solver to a telecommunications feature subscription configuration problem. Partial order constraints are encoded to propositional logic and solved using a state-of-the-art Boolean satisfaction solver. The encoding is based on a symbol-based approach: symbols are viewed as variables which take integer values and are interpreted as indices in the order. Experimental evaluation indicates that partial order constraints are a viable alternative to previous solutions which apply constraint programming techniques and integer linear programming. 1

Abstract. Bounded model checking (BMC) is a technique for overcoming the state explosion problem which has gained wide industrial acceptance. Bounded model checking is typically applied only for linear-time properties, with a few exceptions, which search for a counter-example in the form of a tree-like structure with a pre-determined shape. We suggest a new approach to bounded model checking for universal branching-time logic, in which we encode an arbitrary graph and allow the SAT solver to choose both the states and edges of the graph. This significantly reduces the size of the counter-example produced by BMC. A dynamic completeness criterion is presented which can be used to halt the bounded model checking when it becomes clear that no counterexample can exist. Thus, verification of the checked property can also be achieved. Experiments show that our approach outperforms another recent encoding for µ-calculus on complex ACTL properties. 1

of Computer Science. The generous financial help of the Technion is gratefully acknowledged. Contents Abstract 1