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The occurrence of some cycles has been actually ruled out. You can easily find the relevant references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles".

The current state of research excludes none of the two cases. The occurrence of some small cycles has been actually ruled out. You can easily find the relevant references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles".

The occurrence of some cycles has been actually ruled out. You can easily find the references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles".

By the way, I guess that this is the reason for the downvotes, since, otherwise, this seems to me a reasonable question.

The occurrence of some cycles has been actually ruled out. You can easily find the relevant references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles".

The occurrence of some cycles has been actually ruled out. You can easily find the references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles" (by the way, I guess that this is the reason for the downvotes, since, otherwise, this seems to me a reasonable question).

The occurrence of some cycles has been actually ruled out. You can easily find the references in the Wikipedia page devoted to Collatz conjecture (the same that you linked), at the section "Cycles".

By the way, I guess that this is the reason for the downvotes, since, otherwise, this seems to me a reasonable question.