About complexity of a language
(I completely removed the previous answer, which was applicable only to this particular example).

Your grammars seem to be known as ground term rewriting systems nowadays.

They are rather old. They might be introduced by W.S. Brainard: Tree generating regular systems. Inform. and Control 14 (1969) 217-231.

Concerning your question. I googled a paper of a good old collegue. Joost Engelfriet: Derivation trees of ground term rewriting systems. If my hunch, that this is the correct model, is correct, I like to cite Theorem 4 of that paper:


  For every extended ground tree grammar $G$ a regular tree grammar $G'$ with $L(G') = L(G)$ can effectively be constructed.


It is in the section called "New proofs for old results", so that must be a known result.