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
In every infinite sequence of extended size-change graphs for the DPs
built with (>, π, DP) there is an infinite descent
π(l) ≥ π(r) for all rules l → r ∈ U(DP, π)
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.
The Filter size determines how many symbols occurring in the DPs may be
argument filtered. When trying to orient the usable rules the filtering of these
symbols will be extended to filtering on all symbols. In this second step there is
no limit on how many symbols are filtered.
The DP size is the limit on how much symbols occurring in the DPs may
be usable.
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.