One Step Decryption For Multiple Chained Encryptions If we have a encrypting function f(x, y) (x for input, y for key) and let's say we composite this function n times inside itself with the same y (like f(f(f(x, y), y), y)) and set the output to be z. Does there exist another function g(v) so that g(z)=x? Can this be proven for any kind of encryption function f(x, y) stacked inside itself any times? Thanks.
By definition, there exists such a function.  Your function $g(z)$ could be simply a table of all the possible values of $f(f(f(x, y), y), y)$ mapped back to one of the possible values of $x$.

I think that what you're asking is whether there is an efficient algorithm for unwinding this chaining.  Generally, with cryptographic algorithms, the answer is no, and this is intentional (see RichieFrame's comment about nonlinearity).

There are exceptions, though.  For example, with "raw" RSA, $f(x, y) = x^y \mod n$, for whatever $n$ is used alongside $y$ as the public key.  Then:

$f(f(f(x, y), y), y) = ((x^y)^y)^y \mod n = x^{y^3} \mod n$

Let $d$ be the private key (exponent) corresponding to $y$.  Then, you have:

$g(z) = z^{d^3} \mod n = x \mod n$.

In general, this property is something to avoid, because it often allows attackers to modify the contents of an encrypted message (to something useful) without being able to decrypt the message.  In the case of "raw" RSA, it leads to attacks; real RSA implementations use padding to make RSA not have this property.

Closely related: malleability