Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitary Term Rewriting for Weakly Orthogonal Systems: Properties and
  Counterexamples   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.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th