If your term rewrite rules are sufficiently flexible, then the answer is that this problem is undecidable. The reason is that one can reduce the halting problem for Turing machines to the question of whether a certain term generates another with respect to a certain system.
The idea of the proof is to use terms to represent the configuration of a Turing machine computation. For example, the term $a(b(H_s(c(b(a(.))))))$ would represent the Turing machine having tape $abcba$, with the head on the "c" in state $s$. Now, you write down term rewrite rules that correspond to the steps of computation, so that $b(H_s(c(t)))\to H_u(b(a(t))$ would be a rule, where $t$ is a wildcard for any further subterm, if the Turing machine was supposed to move left when reading symbol $c$ in state $s$, writing $a$ over the $c$ and changing to state $u$. If you also add rules that if a halt state is achieved, then the terms begin to absorb their arguments and containing terms into a constant "halt" term. Thus, the system has the property that the given Turing machine halts if and only if we can generate this "halt" term from the term corresponding to the initial configuration of the machine. Since we cannot decide the halting problem, it now follows that we cannot decide the generation problem for this term rewrite system.
Notice that the type of rules I used in this argument are somewhat more complicated than the example rules in your question. For example, in the Turing machine computation step, we have preserved the (unknown) subterm $t$. So this argument applies only to systems in which such rules are allowed.
This kind of rewrite system is somewhat easier to think about in terms of strings, with rewrite rules about substrings, and this is known as a semi-Thue system. I also wrote this MathOverflow answer on the same topic, showing that the special case where the terms on each side of the rewrite rules have the same length is decidable, but NP-hard.
Lastly, I would like to object to the "congruent" terminology, since I find that word to suggest a symmetric relation, but the term-rewrite-generation relation is not generally symmetric, unless you allow the rules to be applied backwards.