Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:

package simple.whileDecr;

public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		WhileDecr.decrease(args.length);
	}

}


package simple.whileDecr;

public class WhileDecr {

	// this example does acutally terminate.
	
	public static void decrease(int i) {
		while (i > 5) {
			i--;
		}
	}
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
simple.whileDecr.Main.main([Ljava/lang/String;)V: Graph of 39 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: simple.whileDecr.Main.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses:

• Used field analysis yielded the following read fields:
  
• Marker field analysis yielded the following relations that could be markers:
  

(5) SCCToIntTRSProof (SOUND transformation)

Transformed FIGraph SCCs to intTRSs. Log:

Generated rules. Obtained 7 IRules

P rules:
f110_0_decrease_ConstantStackPush(EOS, i11, i11) → f113_0_decrease_LE(EOS, i11, i11, 5)
f113_0_decrease_LE(EOS, i26, i26, matching1) → f117_0_decrease_LE(EOS, i26, i26, 5) | =(matching1, 5)
f117_0_decrease_LE(EOS, i26, i26, matching1) → f122_0_decrease_Inc(EOS, i26) | &&(>(i26, 5), =(matching1, 5))
f122_0_decrease_Inc(EOS, i26) → f126_0_decrease_JMP(EOS, +(i26, -1)) | >(i26, 0)
f126_0_decrease_JMP(EOS, i28) → f149_0_decrease_Load(EOS, i28)
f149_0_decrease_Load(EOS, i28) → f105_0_decrease_Load(EOS, i28)
f105_0_decrease_Load(EOS, i11) → f110_0_decrease_ConstantStackPush(EOS, i11, i11)

Combined rules. Obtained 1 IRules

P rules:
f110_0_decrease_ConstantStackPush(EOS, x0, x0) → f110_0_decrease_ConstantStackPush(EOS, -(x0, 1), -(x0, 1)) | >(x0, 5)

Filtered ground terms:

f110_0_decrease_ConstantStackPush(x1, x2, x3) → f110_0_decrease_ConstantStackPush(x2, x3)
Cond_f110_0_decrease_ConstantStackPush(x1, x2, x3, x4) → Cond_f110_0_decrease_ConstantStackPush(x1, x3, x4)

Filtered duplicate terms:

f110_0_decrease_ConstantStackPush(x1, x2) → f110_0_decrease_ConstantStackPush(x2)
Cond_f110_0_decrease_ConstantStackPush(x1, x2, x3) → Cond_f110_0_decrease_ConstantStackPush(x1, x3)

Prepared 1 rules for path length conversion:

P rules:
f110_0_decrease_ConstantStackPush(x0) → f110_0_decrease_ConstantStackPush(-(x0, 1)) | >(x0, 5)

Finished conversion. Obtained 1 rules.

P rules:
f110_0_decrease_ConstantStackPush(x0) → f110_0_decrease_ConstantStackPush(-(x0, 1)) | >(x0, 5)

(6) Obligation:

Rules:
f110_0_decrease_ConstantStackPush(x0) → f110_0_decrease_ConstantStackPush(-(x0, 1)) | >(x0, 5)

(7) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f110_0_decrease_ConstantStackPush(x2)] = x2

Therefore the following rule(s) have been dropped:

f110_0_decrease_ConstantStackPush(x0) → f110_0_decrease_ConstantStackPush(-(x0, 1)) | >(x0, 5)

(8) YES