Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $mathfrak{C}$(including context-free), every completely regular semigroup that is a union of finitely many finitely generated groups with word problem in $mathfrak{C}$ also has word problem in $mathfrak{C}$. We give an example to show that not all completely regular semigroups with context-free word problem can be so constructed.
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