Well quasi-orders, unavoidable sets, and derivation systems

Let I be a finite set of words and ⇒* I be the derivation relation generated by the set of productions {e → u |u ∈ I}. Let L ∈ I be the set of words u such that e ⇒* I u. We prove that the set I is unavoidable if and only if the relation ⇒* I is a well quasi-order on the set L ∈ I . This result generalizes a theorem of [Ehrenfeucht et al., Theor. Comput. Sci. 27(1983) 311-332]. Further generalizations are investigated.

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