Restricted ground tree transducers

We consider restricted versions of ground tree transducers: total, deterministic, and symmetric subclasses and all other subclasses created by applying any combination of these restrictions. We present the inclusion diagram of the tree transformation classes induced by these restricted ground tree transducers. We show that the following four classes of term relations are the same: (i) tree transformations induced by symmetric deterministic ground tree transducers, (ii) congruence relations on term algebras induced by reduced ground term rewriting systems, (iii) congruence relations on term algebras induced by convergent ground term rewriting systems, and (iv) finitely generated congruence relations on term algebras. As a by-product of our results, we obtain a new ground completion algorithm. Moreover, we show that the following three classes of term relations on term algebras with at least one non-nullary function symbol are also the same: (i) tree transformations induced by total symmetric deterministic ground tree transducers, (ii) congruence relations on term algebras of finite index, (iii) finitely generated congruence relations on term algebras of which the trunk is the whole set of terms.