Method for proving the collatz conjecture, would this work?

[firlz]

Would it be possible to prove the collatz conjecture indirectly by demonstrating rules that apply to 'Collatz-like' conjectures? (I call anything where you simply change the values in the 3n+1 part of the conjecture to other values, holding everything else the same a Collatz-like conjecture)

For instance if you could demonstrate that

A. all infinitely increasing sequences of a Collatz-like conjecture follow [insert rule].
B. all sequences that loop in a Collatz-like conjecture either contain '1' as part of the loop, or else [insert condition].
C. when set to 3n+1, A requires that there be no infinitely increasing sequences, and B requires that all loops contain '1'.

Would this prove the conjecture true? (I cannot think of an A and B that are both true and lead to C, but if someone found it, would it prove the conjecture?)

Conversely if you had A and B as above, but instead of C had
D. When set to 3n+1, A requires that there be at least one infinitely increasing set
or
E. When set to 3n+1, B requires that there be at least one set that loops and does not contain '1'

would you be able to disprove the conjecture?

 

[mfb]

A. all infinitely increasing sequences of a Collatz-like conjecture follow [insert rule].
B. all sequences that loop in a Collatz-like conjecture either contain '1' as part of the loop, or else [insert condition].
C. when set to 3n+1, A requires that there be no infinitely increasing sequences, and B requires that all loops contain '1'.

Would this prove the conjecture true?

Sure. It would be a more powerful proof, with the Collatz conjecture as special case.