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Non-Termination

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AProVE Help SystemTechniquesTechniques working on SCCsNon-Termination

Description

The idea of non-termination analysis is to find a counter-example to the termination of the given SCC P over R. The analysis works on reachability pairs (s, t) of terms s and t, where s →+P ∪ R t. If s and t are semi-unifiable, i.e. there are substitution σ1 and σ2, such that sσ1σ2 equals tσ1 the reachability pair (s, t) is a counter-example to the termination of P over R.

The algorithm starts with all pairs (l, r) where l → r ∈ P and uses narrowing with rules from P ∪ R to compute further reachability pairs. For efficiency reasons AProVE only checks for the special cases of σ1 = id (matching) and σ2 = id (unification).

Application and Configuration

The user can limit the number of times a certain rule is applied when searching for a counter-example.

This technique is especially useful to avoid waste of time in incomplete proofs where termination is already destroyed by a transformation, e.g. from context-sensitive rewrite systems to ordinary term rewriting.