Semantic Labelling for Termination of Combinatory Reduction Systems

We give a method of proving termination of Klop s higher-order rewrit- ing format, combinatory reduction system (CRS). Our method called higher-order semantic labelling is an extension of Zantema s semantic labelling for rst-order term rewriting systems. We systematically dene the labelling by using the com- plete algebraic semantics of CRS.