(0) Obligation:

Need to prove time_complexity of the following program:
package RetVal;

public class RetVal {
	public static void main(int i) {
		int x = i % 2;
		int y = ret(x);
		test(x,y);
	}

	public static int ret(int x) {
		if (x == 0) return 1;
		else return 0;
	}

	public static boolean test(int x, int y) {
		while (x == y) {
			x--;
			y--;
		}
		return true;
	}
}


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

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
RetVal.RetVal.main(I)V: Graph of 61 nodes with 0 SCCs.


(3) TerminationGraphToComplexityProof (EQUIVALENT transformation)

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

(4) BOUNDS(CONSTANT, 50)

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

Constructed TerminationGraph.

(6) Obligation:

Termination Graph based on JBC Program:
RetVal.RetVal.main(I)V: Graph of 57 nodes with 0 SCCs.


(7) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(24)) transformation)

Extracted set of 32 edges for the analysis of TIME complexity. Kept leaves.

(8) Obligation:

Set of 32 edges based on JBC Program.
Performed SCC analyses:
  • Used field analysis yielded the following read fields:

Considered paths: nonterm paths and paths from start to sinks