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 (UNinf)

fails by a simple example of a weakly orthogonal TRS with two

collapsing rules. By translating this example, we show that UNinf

also fails for the infinitary lambda-beta-eta-calculus.

As positive results we obtain the following: Infinitary confluence,

and hence UNinf, holds for weakly orthogonal TRSs that do not contain

collapsing rules. To this end we refine the compression lemma.

Furthermore, we consider the triangle and diamond properties

for infinitary developments in weakly orthogonal TRSs,

by refining an earlier cluster-analysis for the finite case.