The only existing well-defined systems are the inventions of human intelligence. One proposal about such systems is that they arise through certain uses of language and its immediate derivates such as writing. This proposal requires that language be a well-defined system. If true, then a language in term must come from a well-defined source. But neither genes nor cultural transmission are well-defined.
Any user has access, in principle, to an infinite set of sentences.
In practice, all but a finite subset of these are not usable to the listeners, either because they require too much production time, are too complex, are false or are meaningless. Recall the hydrocarbon series example. As one attempts to stick more legal language pieces onto the sentence, one encounters flexible constraints. An approximation always requires leaving somethings out of account. The average man has little knowledge of the muscular mechanisms of walking, yet knows how to walk.