F0=0, F1=1, F2=1, F3=2, F4=3 ....
I have one doubt :
Did you mean
gcd(Fn,Fn−1) calls gcd(Fn−1,Fn−2) calls⋯gcd(F1,F0)=1?
If so then i don't think any pair of (Fn,Fn−1) where n>2 will call upto (1,0). It will stop at F3,F2
gcd(8,5) calls gcd(5,3) calls gcd(3,2) calls gcd(2,1) which is equal to 1
gcd(2,1) : n=2 , m=1 n%m==0 so function returns m and does not call gcd(1,0).
Though this doesn't matter here but still I wanted to clarify.
This example would never have crossed my mind. Thanks a lot :)