Are these functions of license requirements (in this problem) possible norms?

${\color{#D61F06}\text{This problem's question: }}$ Are these functions of license requirements (in this problem) norms ?

See definition of license requirements below.

If these license requirements do not make a vector space, then choose the no answer.

Note: negative licenses are considered no license for these two functions.

First function of license requirements is total licenses is the sum of all licenses held, e.g., if a household has one dog and one bird that this function returns a value of 2 and for a household without pets this function returns 0.

Second function of license requirements max type is count for the type of pet of which the household the most: in the previous examples, the answers would be 1 and 0.

A normed vector space has only one norm. Consider each possible norm separately. If either offered norm works, then select both ; if only one works, then select that one; otherwise select no .

LICENSE REQUIREMENTS

An unnamed city requires every household to have a pet license of the appropriate type for each dog, cat, bird or reptile that the household has as a pet. The head of the household is responsible for acquiring the licenses. Pet shops can issue them on behalf of the city. The licenses are free and unlimited in quantity; but, any of these animal types without a license may be confiscated.

One is not required to have any pets. Negative licenses exist for some strange reason. One might talk about merging, separating or replicating households