A recurrence $T(n)$ is algorithmic if for every sufficiently large threshold constant $n_0>0,$ which of the following properties hold?

Select all that apply.

For all $n{n}_0,$ every path of recursion terminates in a defined base case within a finite number of recursive invocations

For all $n{n}_0,$ every path of recursion terminates in a defined base case within a finite number of recursive invocations

$T(n)=aT(\frac{n}{b})+f(n),$ where $a>0$ and $b>1$

For all $n>n_0,$ we have $T(n)=O(n)$

For all $T(n)=(1)n,we$ have $T(n)=(1)$