The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 116).

(0) Obligation:

Need to prove time_complexity of the following program:

public class CyclicPair {
	CyclicPair next;

	public static void main(String[] args) {
		Random.args = args;
		CyclicPair one = new CyclicPair();
		CyclicPair two = new CyclicPair();
		int i = Random.random();
		if (i == 0) { //two cyclic
			two.next = two;
		} else {      //one cyclic
			one.next = one;
		}

		while (two.next == two && one.next == one) {
			one.next = two;      //one: o1, two: o2 | o1: (next=o2), o2: (next=o2)
			two.next = one;      //one: o1, two: o2 | o1: (next=o2), o2: (next=o1)
			one.next = two.next; //one: o2, two: o2 | o1: (next=o1), o2: (next=o1)
			two.next = two;
		}
	}
}


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

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

(1) JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
CyclicPair.main([Ljava/lang/String;)V: Graph of 135 nodes with 0 SCCs.

(3) TerminationGraphToComplexityProof (EQUIVALENT transformation)

Proven constant complexity by absence of SCCs and edges with non-constant weight

(4) BOUNDS(CONSTANT, 116)

(5) JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Constructed TerminationGraph.

(6) Obligation:

Termination Graph based on JBC Program:
CyclicPair.main([Ljava/lang/String;)V: Graph of 134 nodes with 0 SCCs.