We explore the architecture of recurrent neural networks (RNNs) by studying the complexity of string sequences it is able to memorize. Symbolic sequences of different complexity are generated to simulate RNN training and study parameter configurations with a view to the network's capability of learning and inference. We compare Long Short-Term Memory (LSTM) networks and gated recurrent units (GRUs). We find that an increase in RNN depth does not necessarily result in better memorization capability when the training time is constrained. Our results also indicate that the learning rate and the number of units per layer are among the most important hyper-parameters to be tuned. Generally, GRUs outperform LSTM networks on low-complexity sequences while on high-complexity sequences LSTMs perform better.