Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in the proof tree. Moreover, explicit handling of the case split rule may cause recomputation of the same tasks in multiple branches of the proof tree. In this paper, we propose a symbolic algorithm that significantly reduces such a redundancy. In particular, we encode a string constraint as a regular language and proof rules as rational transducers. This allows to perform similar steps in the proof tree only once, alleviating the state space explosion. In our preliminary experimental results, we validated that our technique (implemented in a Python prototype) works in many practical cases where other state-of-the-art solvers, such as CVC4 or Z3 fail to provide an answer.