Is the language for the following grammar is correct? $L= \{a^i b^j c^k d^l : i,j,k,l \geqslant0 \text{ and }i+k=j+l\}$

Question

I tried to solve it like this:

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\begin{align} A &\to aAd+S+\epsilon \\ S &\to PQR \\ P &\to aPb+\epsilon \\ Q &\to bQc+\epsilon \\ R &\to cRd+\epsilon \end{align}