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 PastaB10 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x + y > 0) {
            if (x > 0) {
                x--;
            } else if (y > 0) {
                y--;
            } else {
                continue;
            }            
        }
    }
}


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:
PastaB10.main([Ljava/lang/String;)V: Graph of 187 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: PastaB10.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 22 IRules

P rules:
f309_0_main_Load(EOS, i18, i45, i18) → f315_0_main_IntArithmetic(EOS, i18, i45, i18, i45)
f315_0_main_IntArithmetic(EOS, i18, i45, i18, i45) → f327_0_main_LE(EOS, i18, i45, +(i18, i45)) | &&(>=(i18, 0), >=(i45, 0))
f327_0_main_LE(EOS, i18, i45, i55) → f336_0_main_LE(EOS, i18, i45, i55)
f336_0_main_LE(EOS, i18, i45, i55) → f347_0_main_Load(EOS, i18, i45) | >(i55, 0)
f347_0_main_Load(EOS, i18, i45) → f363_0_main_LE(EOS, i18, i45, i18)
f363_0_main_LE(EOS, matching1, i45, matching2) → f377_0_main_LE(EOS, 0, i45, 0) | &&(=(matching1, 0), =(matching2, 0))
f363_0_main_LE(EOS, i62, i45, i62) → f378_0_main_LE(EOS, i62, i45, i62)
f377_0_main_LE(EOS, matching1, i45, matching2) → f390_0_main_Load(EOS, 0, i45) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
f390_0_main_Load(EOS, matching1, i45) → f405_0_main_LE(EOS, 0, i45, i45) | =(matching1, 0)
f405_0_main_LE(EOS, matching1, matching2, matching3) → f425_0_main_LE(EOS, 0, 0, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
f405_0_main_LE(EOS, matching1, i72, i72) → f426_0_main_LE(EOS, 0, i72, i72) | =(matching1, 0)
f425_0_main_LE(EOS, matching1, matching2, matching3) → f475_0_main_Load(EOS, 0, 0) | &&(&&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0)), =(matching3, 0))
f475_0_main_Load(EOS, matching1, matching2) → f301_0_main_Load(EOS, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
f301_0_main_Load(EOS, i18, i45) → f309_0_main_Load(EOS, i18, i45, i18)
f426_0_main_LE(EOS, matching1, i72, i72) → f477_0_main_Inc(EOS, 0, i72) | &&(>(i72, 0), =(matching1, 0))
f477_0_main_Inc(EOS, matching1, i72) → f1243_0_main_JMP(EOS, 0, +(i72, -1)) | &&(>(i72, 0), =(matching1, 0))
f1243_0_main_JMP(EOS, matching1, i235) → f1253_0_main_Load(EOS, 0, i235) | =(matching1, 0)
f1253_0_main_Load(EOS, matching1, i235) → f301_0_main_Load(EOS, 0, i235) | =(matching1, 0)
f378_0_main_LE(EOS, i62, i45, i62) → f393_0_main_Inc(EOS, i62, i45) | >(i62, 0)
f393_0_main_Inc(EOS, i62, i45) → f408_0_main_JMP(EOS, +(i62, -1), i45) | >(i62, 0)
f408_0_main_JMP(EOS, i68, i45) → f456_0_main_Load(EOS, i68, i45)
f456_0_main_Load(EOS, i68, i45) → f301_0_main_Load(EOS, i68, i45)

Combined rules. Obtained 2 IRules

P rules:
f309_0_main_Load(EOS, 0, x1, 0) → f309_0_main_Load(EOS, 0, -(x1, 1), 0) | >(x1, 0)
f309_0_main_Load(EOS, x0, x1, x0) → f309_0_main_Load(EOS, -(x0, 1), x1, -(x0, 1)) | &&(&&(>(+(x1, 1), 0), >(x0, 0)), >(+(x0, x1), 0))

Filtered ground terms:

f309_0_main_Load(x1, x2, x3, x4) → f309_0_main_Load(x2, x3, x4)
Cond_f309_0_main_Load(x1, x2, x3, x4, x5) → Cond_f309_0_main_Load(x1, x4)
Cond_f309_0_main_Load1(x1, x2, x3, x4, x5) → Cond_f309_0_main_Load1(x1, x3, x4, x5)

Filtered duplicate terms:

f309_0_main_Load(x1, x2, x3) → f309_0_main_Load(x2, x3)
Cond_f309_0_main_Load1(x1, x2, x3, x4) → Cond_f309_0_main_Load1(x1, x3, x4)

Prepared 2 rules for path length conversion:

P rules:
f309_0_main_Load(x1, 0) → f309_0_main_Load(-(x1, 1), 0) | >(x1, 0)
f309_0_main_Load(x1, x0) → f309_0_main_Load(x1, -(x0, 1)) | &&(&&(>(+(x1, 1), 0), >(x0, 0)), >(+(x0, x1), 0))

Finished conversion. Obtained 2 rules.

P rules:
f309_0_main_Load(x0, c0) → f309_0_main_Load(-(x0, 1), 0) | &&(>(x0, 0), =(0, c0))
f309_0_main_Load(x1, x2) → f309_0_main_Load(x1, -(x2, 1)) | &&(&&(>(x2, 0), >(x1, -1)), >(+(x2, x1), 0))

(6) Obligation:

Rules:
f309_0_main_Load(x0, c0) → f309_0_main_Load(-(x0, 1), 0) | &&(>(x0, 0), =(0, c0))
f309_0_main_Load(x1, x2) → f309_0_main_Load(x1, -(x2, 1)) | &&(&&(>(x2, 0), >(x1, -1)), >(+(x2, x1), 0))

(7) TerminationGraphProcessor (SOUND transformation)

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

(8) Complex Obligation (AND)

(9) Obligation:

Rules:
f309_0_main_Load(x2, x3) → f309_0_main_Load(x2, -(x3, 1)) | &&(&&(>(x3, 0), >(x2, -1)), >(+(x3, x2), 0))

(10) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f309_0_main_Load(x3, x5)] = x3 + x5

Therefore the following rule(s) have been dropped:

f309_0_main_Load(x0, x1) → f309_0_main_Load(x0, -(x1, 1)) | &&(&&(>(x1, 0), >(x0, -1)), >(+(x1, x0), 0))

(11) YES

(12) Obligation:

Rules:
f309_0_main_Load(x0, x1) → f309_0_main_Load(-(x0, 1), 0) | &&(>(x0, 0), =(0, x1))

(13) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f309_0_main_Load(x3, x5)] = x3 + c6·x5

Therefore the following rule(s) have been dropped:

f309_0_main_Load(x0, x1) → f309_0_main_Load(-(x0, 1), 0) | &&(>(x0, 0), =(0, x1))

(14) YES