Decreasing Diagrams II

This theory formalizes a commutation version of decreasing diagrams for Church-Rosser modulo. The proof follows Felgenhauer and van Oostrom (RTA 2013). The theory also provides important specializations, in particular van Oostrom’s conversion version (TCS 2008) of decreasing diagrams. We follow the development described in [1]: Conversions are mapped to Greek strings, and we prove that whenever a local peak (or cliff) is replaced by a joining sequence from a locally decreasing diagram, then the corresponding Greek strings become smaller in a specially crafted well-founded order on Greek strings. Once there are no more local peaks or cliffs are left, the result is a valley that establishes the Church-Rosser modulo property. As special cases we provide non-commutation versions and the conversion version of decreasing diagrams by van Oostrom [3]. We also formalize extended decreasingness [2].