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This work provides an example of a finitely presented semigroup [Formula: see text] with zero containing an infinite ideal of the form [Formula: see text], where [Formula: see text] is a generator of [Formula: see text], such that every word in generators representing an element of [Formula: see text] is square free (i.e. any word of the type [Formula: see text], for non-empty [Formula: see text], equals zero in [Formula: see text]).