What is the asymptotic time complexity of the following algo

What is the asymptotic time complexity of the following algorithm? (Show the 5 step process to derive your results)

Procedure proc(<x₁,x₂,x₃....x_n>  

if n = 1 then return (1)

else

for i <-- 1 to m do

y_i <--X_3i-1

z_i <-- X_3i

return( proc(<y₁,y₂....y_m>)+ proc(<z₁,z₂......z_m>))

Solution

O(n)->As it depends on size of n and number of loops runs on the size of n. i.e m=n/3.

where O(n/3)=O(n). constant 3 is removed.(Rule of assymtotic construction).

therfore it is a linear time.