@Arjun sir,
why have you taken fib(0) and fib(1) as 0,although there are no recursive calls,but there will be one call fib(0) for 0 and fib(1) for 1,the initial function call which should be included.
I think it should be:-
T(n)= T(n-1)+T(n-2) +1 // the 1 is initial function call.
T(0)=T(1)=1, as base condition ,although answer reamins same.
Please check once