This is how far I have gotten:
$$T(n) = T(n-1) + O(1)$$ $$T(n-2) = T(T(n-2)) + O(1)) + O(1)$$ $$T(n-2) = T(n-2) + O(2)$$ $$T(n-3) = T(T(n-3) + O(1)) + O(2)$$ $$T(n-3) = T(n-3) + O(3)$$
Finally emerging with this pattern: $$T(n) = T(n-k) + O(k).$$
Solving for $k$ yields $k = n-1$.
$T(n) = T(n-n-1) + O(n-1)$
$T(n) = O(n)$
Can someone verify my answer and tell me if this is right or wrong?