Finding a Context- free grammar (CFG) for the language [duplicate]

This question already has an answer here:

  • How to prove that a language is context-free? 2 answers
  • How to convert PDA to CFG 2 answers

I am trying to find a CFG for the language A below. I have spent hours on this but still could not find the answer. I also came up with the idea that this may not a context- free language but there is actually a PDA that recognizes it. I would very much appreciate if anyone can help me with this.

                    A= {0^a 1^b 0^c 1^d | a+b < c+d, a,b,c,d>=1}