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Perhaps more than, even, I would say, very likely, if not obvious, but only if the account is kept in the quaternary number system.

For some reason, I didn't see a fairly obvious and simple answer here. Naturally, it is possible in a quaternary number system, for example, in which the numbers go in increasing order 0, 1, 2, 3, 10, 11, 12, 13, 20, 21 and so on.

Of course it is possible. It all depends on how we define the addition operation and on which set. For example, in mathematics, there is such a concept as “residue classes”. Roughly speaking, for the layman, the class of deductions is all such numbers that are divisible by some number with the same remainder. For example, in the classes of triple deductions, 4=10=13=301, because all these numbers, when divided by a triple, will give one in the remainder. 2+2=4, and 4=10, so the equality you presented may be correct.

But in the numbers we've been used to since school, this equality is certainly not true. On the Internet, you can often find various “proofs” 2+2=5, 2*2=5 etc. But as a rule, they contain gross mathematical errors.