Symbol different term rewrite systems

We propose the construction of an EGTRS which approximates the reduction of a given term rewrite system. We present heuristics which build such approximations or candidates for such approximations, and hence face the following problem: is it decidable for any term rewrite system R and ground tree transducer (A,B), whether (A,B) is an upper approximation of R? We introduce the notion of a symbol different term rewrite system, and show that for symbol different term rewrite systems the above problem is decidable. On the other hand, it is undecidable for any linear symbol different term rewrite system R and deterministic bottom-up tree automaton A, whether the ground tree transducer (A,A) is a lower approximation of R.