The Collatz conjecture is a major open problem in math and computer science. The conjec$-$

ture is that the following lines of code always eventually terminate for any positive integer

x given as input:

c$($x$)=$

if x$=1$

print "done!"

else if x is even

return c$($x$/2)$

else

return c$(3$x$+1)$

Your goal in this problem is to prove the proposition in the box. $($This type of proposition