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Curien (1985) defines a translation of the Ac-calculus in the Pure Combinatory Categorical Logic and establishes an equivalence theorem between these two theories. The rewriting system SUBST simulates in particular the substitution of the Xe-calculus. This system is locally confluent. We shall show here that it is also noetherian.doi:10.1016/0304-3975(86)90035-6 fatcat:63swrohasfam7jzo2b7twwvmme