3n+1 Termination?

Study the following program. Assuming that the arg[ 1] is a non-negative integer, does it terminate?

Build it. Run it a few times.

Demonstrating that in billion of such runs, it terminated each time is not good enough. Demonstrating that in one specific example run with initial value x0 for x, the loop will reassign that value to x again is a valid counter example.

// 3n+1 

#include <iostream>
using namespace std;
#include <stdlib.h>

int main(int argc, char * argv []) {
  int x = atoi(argv[1]);
  int y;
  cout << x;

  /*@ x is the given input integer, x > 0 */
  while (x > 1) {
    cout << x << '\n';
    x = (x % 2 == 0? x / 2 : 3*x + 1);
  }
}