Normalized rewriting: an alternative to rewriting modulo a set of equations
Journal of Symbolic Computation
Term rewriting and all that
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Dependency Pairs for Equational Rewriting
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Tyrolean termination tool: Techniques and features
Information and Computation
Dependency Pairs for Rewriting with Non-free Constructors
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Proving Termination by Bounded Increase
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
On the implementation of construction functions for non-free concrete data types
ESOP'07 Proceedings of the 16th European conference on Programming
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Proving Termination of Integer Term Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
A Term Rewriting Approach to the Automated Termination Analysis of Imperative Programs
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Automated termination proofs for haskell by term rewriting
ACM Transactions on Programming Languages and Systems (TOPLAS)
WFLP'11 Proceedings of the 20th international conference on Functional and constraint logic programming
Termination of context-sensitive rewriting with built-in numbers and collection data structures
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
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This paper defines an expressive class of constrained equational rewrite systems that supports the use of semantic data structures (e.g., sets or multisets) and contains built-in numbers, thus extending our previous work presented at CADE 2007 [6]. These rewrite systems, which are based on normalized rewriting on constructor terms, allow the specification of algorithms in a natural and elegant way. Built-in numbers are helpful for this since numbers are a primitive data type in every programming language. We develop a dependency pair framework for these rewrite systems, resulting in a flexible and powerful method for showing termination that can be automated effectively. Various powerful techniques are developed within this framework, including a subterm criterion and reduction pairs that need to consider only subsets of the rules and equations. It is well-known from the dependency pair framework for ordinary rewriting that these techniques are often crucial for a successful automatic termination proof. Termination of a large collection of examples can be established using the presented techniques.