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Size Change Principle

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AProVE Help SystemTechniquesTechniques working on SCCsSize Change Principle

Description

Given an SCC P over a TRS R this techniques tries to find a set of symbols DP, an argument filtering π, and a Ce-compatible order > satisfying Here, U(DP,π) are the usable rules of DP regarding the argument filtering π. Furthermore, one may only compare π(s) > / ≥ π(t) if for building π(t) one only needs to filter constructors or usable symbols. (The usable symbols are the root symbols of the left hand sides of the usable rules.)
If a solution is found then the complete SCC is terminating. See [TG '03, TGSK '04] for references.

Application and Configuration

One can choose between different orders and configure these in more detail pressing the Configure button. However, this order will only be used for orienting the rules. The size-change graphs will always be built with regard to. the embedding order. Beside the order the user can choose between different heuristics for the argument filtering and the set of usable symbols DP which both effect the size-change graphs and the constraints arising from rule orientation.
Processing SCCs by the size-change principle can be used as fast preprocessing and as powerful way to prove termination of many SCCs depending on the size limits. Useful settings are (0,0) or (1,0) for fast processing and (2,2) or (2,3) for more power. Here, the (x,y) denotes a filter size limit of x and a DP size limit of y.