1. I n t r o d u c t i o n Many term rewriting systems and their modifications are considered in logic, automated theorem proving, and programming language [2,3,4,6,8,9]. A fundamental property of term rewriting systems is the confluence property. A few sufficient criteria for the confluence are well known [2,3,4,5,8,9]. However, if a term rewriting system is nonterminating and nonlinear, we kn...

It is well known that confluence and strong normalization are preserved when combining algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual contraction rule for η, or recursion together with the usual contraction rule for surjective pairing. We show that confluence and strong normalization are modular prop...

The confluence model explains birth-order differences in intellectual performance by quantifying the changing dynamics within the family. Wichman, Rodgers, and MacCallum (2006) claimed that these differences are a between-family phenomenon--and hence are not directly related to birth order itself. The study design and analyses presented by Wichman et al. nevertheless suffer from crucial shortco...

The confluence of untyped λ-calculus with unconditional rewriting is now well understood. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether betareduction is allo...

Benzo[a]pyrene (BaP) is potent rodent carcinogen and a reputed human carcinogen. Although much is known about its metabolic activation leading to DNA damage, the mechanisms of its actions are not as well understood at a cellular level. In addressing this, we have established an in vitro model that follows the progression toward neoplastic transformation induced by BaP. The model uses immortal n...

Amongst the iron-based superconductors, LiFeAs is unrivalled in simplicity of its crystal structure and phase diagram. However, our understanding this canonical compound suffers from conflict between mutually incompatible descriptions material's electronic structure, as derived contradictory interpretations photoemission record. Here, we explore challenge interpretation such experiments. By com...

background: abnormal angulation of the lunate can be an indication of intercarpal pathology. on magnetic resonance images (mris) the lunate often looks dorsally angulated, even in healthy wrists. the tilt on individual slices can also be different and might be misinterpreted as pathological, contributing to inaccurate diagnoses and unnecessary surgery. the primary aim of this study was to deter...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

The confluence of untyped λ-calculus with unconditional rewriting is now well understood. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether betareduction is allo...