Is it possible to simplify the logic circuit?

Question

Electronics

There are 4 bits at the input, 5 bits at the output (4 + overflow bit), it is necessary to add one to the number at the input. Here's what happened:

Is it possible to simplify the circuit in terms of the number of elements, if you use only NAND with two inputs and inverters, or is this already the limit? (So ​​far, 12 NAND and 4 inverters are used).