Proof Orders for Decreasing Diagrams

Bertram Felgenhauer, Vincent Van Oostrom, Marc Herbstritt
2013 International Conference on Rewriting Techniques and Applications  
We present and compare some well-founded proof orders for decreasing diagrams. These proof orders order a conversion above another conversion if the latter is obtained by filling any peak in the former by a (locally) decreasing diagram. Therefore each such proof order entails the decreasing diagrams technique for proving confluence. The proof orders differ with respect to monotonicity and complexity. Our results are developed in the setting of involutive monoids. We extend these results to
more » ... n a decreasing diagrams technique for confluence modulo. ACM Subject Classification F.4 Mathematical Logic and Formal Languages Keywords and phrases involutive monoid, confluence modulo, decreasing diagram, proof order Digital Object Identifier 10.4230/LIPIcs.RTA.2013.174 ▸ Example 1. The rewrite relation → on objects {a, . . . , j} as presented on the left in Figure 1 is the union of the family of rewrite relations ( → ) ∈L on its right, indexed by concrete labels L = { , m, κ} and having individual rewrite relations: → κ = {(b, c), (j, i)} → = {(d,
doi:10.4230/lipics.rta.2013.174 dblp:conf/rta/FelgenhauerO13 fatcat:y5dqm24cvzcfxfkzg7swi5ipde