@MISC{Marche_theword, author = {Claude Marche}, title = {The Word Problem of ACD-Ground theories is Undecidable}, year = {} }

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We prove that there exists an ACD-ground theory --- an equational theory defined by a set of ground equations plus the associativity and commutativity of two binary symbols and +, and the distributivity of over + --- for which the word problem is undecidable. 1 Introduction Equations are ubiquitous in mathematics and the sciences. The word problem of a given a set of equations (that is the problem of deciding if an identity is a consequence of the equations), or equivalently of its equational theory, is undecidable in general. But there are known classes of equational theories which have a decidable word problem, in particular, ground equational theories. The most famous examples of theories with undecidable word problem are given by sets of ground equations over word algebras. Such theories can be considered as associative-ground theories over a certain term algebra, whose signature contains only constants besides the binary (associative) symbol. Their word problem is known to be...