Matches in DBpedia 2014 for { ?s ?p In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system (ARS), that is, one in which there are no infinite reduction sequences, is confluent if it is locally confluent. In fact a terminating ARS is confluent precisely when it is locally confluent.Equivalently, for every binary relation with no decreasing infinite chains and satisfying a weak version of the diamond property, there is a unique minimal element in every connected component of the relation considered as a graph.Today, this is seen as a purely combinatorial result based on well-foundedness due to a proof of Gérard Huet in 1980. Newman's original proof was considerably more complicated.. }
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- Newman's_lemma abstract "In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system (ARS), that is, one in which there are no infinite reduction sequences, is confluent if it is locally confluent. In fact a terminating ARS is confluent precisely when it is locally confluent.Equivalently, for every binary relation with no decreasing infinite chains and satisfying a weak version of the diamond property, there is a unique minimal element in every connected component of the relation considered as a graph.Today, this is seen as a purely combinatorial result based on well-foundedness due to a proof of Gérard Huet in 1980. Newman's original proof was considerably more complicated.".