Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: NonPeriodic

public class NonPeriodic {

    public static void main(String args[]) {
	int x = 1, y = 0;

	if (args.length >= 1) {
	    y = -1*args[0].length();
	}

	// does not terminate for x = 1 and y = 1
	while (y > 0)
	    if (x > 0) x = x - 1;
	    else {
		y = y + 1;
		x = y;
	    }
    }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
NonPeriodic.main([Ljava/lang/String;)V: Graph of 75 nodes with 0 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Proven termination by absence of SCCs

(4) TRUE