Maybe, should not prefill it, but just say that basically aut[i, j] = nielsen(TerminalSymbol() + i, TerminalSymbol() + j)

Also now it is bad that x_i -> x_i(x_j)^{-1} means x_j -> x_j^{-1}, x_i -> x_i x_j, x_j -> x_j^{-1}. How could one change that?