Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:

public class CyclicPair2 {
	CyclicPair2 next;

    public static void main(String[] args) {
        Random.args = args;
        CyclicPair2 one = new CyclicPair2();
        CyclicPair2 two = new CyclicPair2();
		int rand = Random.random();
        if (rand != 0) {
            one.next = two;
            two.next = one;
        } else {
            one.next = two;
        }

        if (rand == 0) {
            one.run();
        }
    }

    public void run() {
       CyclicPair2 current = this;
       while (current != null)
           current = current.next;
    }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
CyclicPair2.main([Ljava/lang/String;)V: Graph of 152 nodes with 0 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Proven termination by absence of SCCs

(4) TRUE