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Non Overlappingness Check

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AProVE Help SystemTechniquesTechniques working on SCCsNon Overlappingness Check

Description

This method works analogous to the non overlappingness check on a TRS. If an SCC P over a non overlapping TRS R is given and P does not overlap with R then instead of proving absence of infinite P-chains over R it is sufficient to prove absence of infinite innermost P-chains over R.

Application and Configuration

There is no configuration possible.
For proving termination one should always integrate this technique as the check costs nearly no time and restricting chains to innermost chains eases the proof afterwards. This technique should also be used when using the non overlappingness check on a TRS before. This is because the removal of rules on SCCs may delete some rules of R that could not be deleted with the corresponding removal technique on TRS before.