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The unified higher-order dependency pair framework
In recent years, two higher-order extensions of the powerful dependency pair
approach for termination analysis of first-order term rewriting have been
defined: the static and the dynamic approach. Both approaches offer distinct
advantages and disadvantages. However, a grand unifying theory is thus far
missing, and both approaches lack the modularity present in the dependency pair
framework commonly used in first-order rewriting. Moreover, neither approach
can be used to prove non-termination.
In this paper, we aim to address this gap by defining a higher-order
dependency pair framework, integrating both approaches into a shared formal
setup. The framework has been implemented in the (fully automatic) higher-order
termination tool WANDA