Reducibility and Artificial Neural Networks

I have read (here and here ) about the computational power of neural networks and a doubt came up.

There is a way to reduce an ANN to another ANN (not taking into count the training algorithm) ? e.g. Reduce a Recurrent Neural Network to a Multilayer Perceptron, meaning that if I have a trained RNN, I can get a MP that maps the same inputs given to the RNN to the same outputs produced by the RNN.

And if exists an answer to the above question, we can show the equivalence between neural networks, e.g., all problems solved by an Multilayer Perceptron can be solved by a Recurrent Neural Network but the opposite is not true, i.e., $MP \subset RNN$ (I do not know if this is true, is just an example). So, if we obtain this relationship between all neural networks, we can get a neural network $X$ that is more powerful than others, so, we can throw away all other neural networks because $X$ can solve any problem that other NN can. Is this reasoning correct ?

Thanks.