Triple Graph Grammars (TGGs) are a rule-based technique with a formal background for specifying bidirectional model transformation. In practical scenarios, the unidirectional rules needed for the forward and backward transformations are automatically derived from the TGG rules in the specification, and the overall transformation process is governed by a control algorithm. Current implementations either have a worst case exponential runtime complexity or pose such strong restrictions on the class of supported TGGs that practical real-world applications become infeasible. This paper, therefore, introduces a new class of TGGs together with a control algorithm that drops a number of practice-relevant restrictions for TGG rules and still has a polynomial runtime complexity.