Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaA10 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x != y) {
            if (x > y) {
                y++;
            } else {
                x++;
            }
        }
    }
}


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:
PastaA10.main([Ljava/lang/String;)V: Graph of 182 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: PastaA10.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 16 IRules

P rules:
f316_0_main_Load(EOS, i18, i44, i18) → f324_0_main_EQ(EOS, i18, i44, i18, i44)
f324_0_main_EQ(EOS, i18, i44, i18, i44) → f341_0_main_EQ(EOS, i18, i44, i18, i44)
f341_0_main_EQ(EOS, i18, i44, i18, i44) → f354_0_main_Load(EOS, i18, i44) | !(=(i18, i44))
f354_0_main_Load(EOS, i18, i44) → f363_0_main_Load(EOS, i18, i44, i18)
f363_0_main_Load(EOS, i18, i44, i18) → f375_0_main_LE(EOS, i18, i44, i18, i44)
f375_0_main_LE(EOS, i18, i44, i18, i44) → f390_0_main_LE(EOS, i18, i44, i18, i44)
f375_0_main_LE(EOS, i18, i44, i18, i44) → f391_0_main_LE(EOS, i18, i44, i18, i44)
f390_0_main_LE(EOS, i18, i44, i18, i44) → f402_0_main_Inc(EOS, i18, i44) | <=(i18, i44)
f402_0_main_Inc(EOS, i18, i44) → f416_0_main_JMP(EOS, +(i18, 1), i44) | >=(i18, 0)
f416_0_main_JMP(EOS, i52, i44) → f461_0_main_Load(EOS, i52, i44)
f461_0_main_Load(EOS, i52, i44) → f308_0_main_Load(EOS, i52, i44)
f308_0_main_Load(EOS, i18, i44) → f316_0_main_Load(EOS, i18, i44, i18)
f391_0_main_LE(EOS, i18, i44, i18, i44) → f405_0_main_Inc(EOS, i18, i44) | >(i18, i44)
f405_0_main_Inc(EOS, i18, i44) → f418_0_main_JMP(EOS, i18, +(i44, 1)) | >=(i44, 0)
f418_0_main_JMP(EOS, i18, i53) → f469_0_main_Load(EOS, i18, i53)
f469_0_main_Load(EOS, i18, i53) → f308_0_main_Load(EOS, i18, i53)

Combined rules. Obtained 2 IRules

P rules:
f316_0_main_Load(EOS, x0, x1, x0) → f316_0_main_Load(EOS, +(x0, 1), x1, +(x0, 1)) | &&(>(+(x0, 1), 0), >(x1, x0))
f316_0_main_Load(EOS, x0, x1, x0) → f316_0_main_Load(EOS, x0, +(x1, 1), x0) | &&(<(x1, x0), >(+(x1, 1), 0))

Filtered ground terms:

f316_0_main_Load(x1, x2, x3, x4) → f316_0_main_Load(x2, x3, x4)
Cond_f316_0_main_Load(x1, x2, x3, x4, x5) → Cond_f316_0_main_Load(x1, x3, x4, x5)
Cond_f316_0_main_Load1(x1, x2, x3, x4, x5) → Cond_f316_0_main_Load1(x1, x3, x4, x5)

Filtered duplicate terms:

f316_0_main_Load(x1, x2, x3) → f316_0_main_Load(x2, x3)
Cond_f316_0_main_Load(x1, x2, x3, x4) → Cond_f316_0_main_Load(x1, x3, x4)
Cond_f316_0_main_Load1(x1, x2, x3, x4) → Cond_f316_0_main_Load1(x1, x3, x4)

Prepared 2 rules for path length conversion:

P rules:
f316_0_main_Load(x1, x0) → f316_0_main_Load(x1, +(x0, 1)) | &&(>(+(x0, 1), 0), >(x1, x0))
f316_0_main_Load(x1, x0) → f316_0_main_Load(+(x1, 1), x0) | &&(<(x1, x0), >(+(x1, 1), 0))

Finished conversion. Obtained 2 rules.

P rules:
f316_0_main_Load(x0, x1) → f316_0_main_Load(x0, +(x1, 1)) | &&(<(x1, x0), >(x1, -1))
f316_0_main_Load(x2, x3) → f316_0_main_Load(+(x2, 1), x3) | &&(>(x2, -1), >(x3, x2))

(6) Obligation:

Rules:
f316_0_main_Load(x0, x1) → f316_0_main_Load(x0, +(x1, 1)) | &&(<(x1, x0), >(x1, -1))
f316_0_main_Load(x2, x3) → f316_0_main_Load(+(x2, 1), x3) | &&(>(x2, -1), >(x3, x2))

(7) TerminationGraphProcessor (SOUND transformation)

Constructed the termination graph and obtained 2 non-trivial SCCs.

(8) Complex Obligation (AND)

(9) Obligation:

Rules:
f316_0_main_Load(x2, x3) → f316_0_main_Load(+(x2, 1), x3) | &&(>(x2, -1), >(x3, x2))

(10) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f316_0_main_Load(x3, x5)] = -x3 + x5

Therefore the following rule(s) have been dropped:

f316_0_main_Load(x0, x1) → f316_0_main_Load(+(x0, 1), x1) | &&(>(x0, -1), >(x1, x0))

(11) YES

(12) Obligation:

Rules:
f316_0_main_Load(x0, x1) → f316_0_main_Load(x0, +(x1, 1)) | &&(<(x1, x0), >(x1, -1))

(13) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f316_0_main_Load(x3, x5)] = x3 - x5

Therefore the following rule(s) have been dropped:

f316_0_main_Load(x0, x1) → f316_0_main_Load(x0, +(x1, 1)) | &&(<(x1, x0), >(x1, -1))

(14) YES