  We present some contributions to the theory of infinitary rewriting for
weakly orthogonal term rewrite systems, in which critical pairs may occur
provided they are trivial. We show that the infinitary unique normal form
property fails by an example of a weakly orthogonal TRS with two collapsing
rules. By translating this example, we show that this property also fails for
the infinitary lambda-beta-eta-calculus. As positive results we obtain the
following: Infinitary confluence, and hence the infinitary unique normal forms
property, holds for weakly orthogonal TRSs that do not contain collapsing
rules. To this end we refine the compression lemma. Furthermore, we establish
the triangle and diamond properties for infinitary multi-steps (complete
developments) in weakly orthogonal TRSs, by refining an earlier
cluster-analysis for the finite case.
