Termination by Abstraction

Abstraction can be used very effectively to decompose and simplify termination arguments. If a symbolic computation is nonterminating, then there is an infinite computation with a top redex, such that all redexes are immortal, but all children of redexes are mortal. This suggests applying weakly-monotonic well-founded relations in abstraction-based termination methods, expressed here within an abstract framework for term-based proofs. Lexicographic combinations of orderings may be used to match up with multiple levels of abstraction.

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