Abstract
We denote by [Formula: see text] the class of tree languages generated by chain-free distributed regular tree grammars of [Formula: see text] components cooperating with terminal strategy. Dányi and Fülöp [2] showed that the hierarchy [Formula: see text], [Formula: see text] contains an infinite proper hierarchy. We improve their result showing that for each [Formula: see text], [Formula: see text].
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