# Time complexity of mutually recursive functions

Suppose I have two mutually recursive functions like this:

f1(x)
{
.//some code
.
.
f1(x-1)+g1(x-1);

}

g1(y)
{
.
.//some code
g1(y-1)+f1(y-1);
..

}


How can I calculate time complexities in such cases?

If we set up recurrences, $T_1(n) = T_1(n-1) + T_2(n-1)$ and $T_2(n) = T_1(n-1) + T_2(n-1)$. So from there we can get that $T_1(n) = T_2(n)$, which implies that $T_1(n) = 2T_1(n-1)$. So for this, the two functions would be $O(2^n)$.