RG and also do not destroy the termination property. Choosing (1 . y, X-I . (:z: . y)) as the critical pair (Cl, C2) in the completion procedure, we detect that (d 1 , d2 ) = (y, :z:-1 . (x . y)) and RG U {d 2 --+ d1 } is again a Noetherian rrs.
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