How to minimize computing time of nonlinear system observability analysis? (Symbolic variables)

Hello,

It's been almost three weeks since I'm working with this and I can't see how to make this code work better. I'm checking the observability of a nonlinear system but as far as I have got is to have the jacobi matrix (stated as "dO" in the code, and was computed in separated columns and each one took hours) but when I try to get the rank of it, or from a part of it, all it does is that Matlab stops working or even the whole computer gets slower or stops working (I'm working on a laptop with Core i5 and 8 GB RAM and in two desktop Core i7 16GB RAM).

I think this is because of the weight of the terms of the derivates which makes it heavier and harder to process, I looked up for a way to lower the weight of the symbolic variables (when I type 'whos' in the command window it says it's 112 bytes) or to assign them a type of variable but I haven't been able to make this work. Is there anything else I can do?

Thanks

(The code's attached, thanks)