For the following algorithms, describe the loop invariant$($s$)$ and prove that they are sound and complete.

$($a$)$

Algorithm $1$: findMin

Input: $a$ : A non$-$empty array of integers $($indexed starting at $1)$

Output: The smallest element in the array

begin

minlarr$$

for ilarr$1$ to len$(a)$ do

if minlarra$[i]mina[i]$ then

minlarra$[i]$

end

end

return min

end