### Weak Convergence and Uniform Normalization in Infinitary Rewriting

Jakob Grue Simonsen
We study infinitary term rewriting systems containing finitely many rules. For these, we show that if a weakly convergent reduction is not strongly convergent, it contains a term that reduces to itself in one step (but the step itself need not be part of the reduction). Using this result, we prove the starkly surprising result that for any orthogonal system with finitely many rules, the system is weakly normalizing under weak convergence if{f} it is...