Term rewriting and all that
Reasoning About Recursively Defined Data Structures
Journal of the ACM (JACM)
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Journal of Automated Reasoning
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theory decision by decomposition
Journal of Symbolic Computation
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
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If a rewrite-based inference system is guaranteed to terminate on the axioms of a theory T and any set of ground literals, then any theorem-proving strategy based on that inference system is a rewrite-based decision procedure for T-satisfiability. In this paper, we consider the class of theories defining recursive data structures, that might appear out of reach for this approach, because they are defined by an infinite set of axioms. We overcome this obstacle by designing a problem reduction that allows us to prove a general termination result for all these theories. We also show that the theorem-proving strategy decides satisfiability problems in any combination of these theories with other theories decided by the rewrite-based approach.