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 PastaB16 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x > 0) {
            while (y > 0) {
                y--;
            }
            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:
PastaB16.main([Ljava/lang/String;)V: Graph of 180 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: PastaB16.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 14 IRules

P rules:
f358_0_main_LE(EOS, i62, i53, i62) → f365_0_main_LE(EOS, i62, i53, i62)
f365_0_main_LE(EOS, i62, i53, i62) → f380_0_main_Load(EOS, i62, i53) | >(i62, 0)
f380_0_main_Load(EOS, i62, i53) → f390_0_main_LE(EOS, i62, i53, i53)
f390_0_main_LE(EOS, i62, matching1, matching2) → f396_0_main_LE(EOS, i62, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
f390_0_main_LE(EOS, i62, i70, i70) → f397_0_main_LE(EOS, i62, i70, i70)
f396_0_main_LE(EOS, i62, matching1, matching2) → f406_0_main_Inc(EOS, i62, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
f406_0_main_Inc(EOS, i62, matching1) → f418_0_main_JMP(EOS, +(i62, -1), 0) | &&(>(i62, 0), =(matching1, 0))
f418_0_main_JMP(EOS, i73, matching1) → f450_0_main_Load(EOS, i73, 0) | =(matching1, 0)
f450_0_main_Load(EOS, i73, matching1) → f351_0_main_Load(EOS, i73, 0) | =(matching1, 0)
f351_0_main_Load(EOS, i18, i53) → f358_0_main_LE(EOS, i18, i53, i18)
f397_0_main_LE(EOS, i62, i70, i70) → f407_0_main_Inc(EOS, i62, i70) | >(i70, 0)
f407_0_main_Inc(EOS, i62, i70) → f420_0_main_JMP(EOS, i62, +(i70, -1)) | >(i70, 0)
f420_0_main_JMP(EOS, i62, i74) → f459_0_main_Load(EOS, i62, i74)
f459_0_main_Load(EOS, i62, i74) → f380_0_main_Load(EOS, i62, i74)

Combined rules. Obtained 2 IRules

P rules:
f390_0_main_LE(EOS, x0, 0, 0) → f390_0_main_LE(EOS, -(x0, 1), 0, 0) | >(x0, 1)
f390_0_main_LE(EOS, x0, x1, x1) → f390_0_main_LE(EOS, x0, -(x1, 1), -(x1, 1)) | >(x1, 0)

Filtered ground terms:

f390_0_main_LE(x1, x2, x3, x4) → f390_0_main_LE(x2, x3, x4)
Cond_f390_0_main_LE(x1, x2, x3, x4, x5) → Cond_f390_0_main_LE(x1, x3)
Cond_f390_0_main_LE1(x1, x2, x3, x4, x5) → Cond_f390_0_main_LE1(x1, x3, x4, x5)

Filtered duplicate terms:

f390_0_main_LE(x1, x2, x3) → f390_0_main_LE(x1, x3)
Cond_f390_0_main_LE1(x1, x2, x3, x4) → Cond_f390_0_main_LE1(x1, x2, x4)

Prepared 2 rules for path length conversion:

P rules:
f390_0_main_LE(x0, 0) → f390_0_main_LE(-(x0, 1), 0) | >(x0, 1)
f390_0_main_LE(x0, x1) → f390_0_main_LE(x0, -(x1, 1)) | >(x1, 0)

Finished conversion. Obtained 2 rules.

P rules:
f390_0_main_LE(x0, c0) → f390_0_main_LE(-(x0, 1), 0) | &&(>(x0, 1), =(0, c0))
f390_0_main_LE(x1, x2) → f390_0_main_LE(x1, -(x2, 1)) | >(x2, 0)

(6) Obligation:

Rules:
f390_0_main_LE(x0, c0) → f390_0_main_LE(-(x0, 1), 0) | &&(>(x0, 1), =(0, c0))
f390_0_main_LE(x1, x2) → f390_0_main_LE(x1, -(x2, 1)) | >(x2, 0)

(7) TerminationGraphProcessor (SOUND transformation)

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

(8) Complex Obligation (AND)

(9) Obligation:

Rules:
f390_0_main_LE(x2, x3) → f390_0_main_LE(x2, -(x3, 1)) | >(x3, 0)

(10) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f390_0_main_LE(x3, x5)] = x5

Therefore the following rule(s) have been dropped:

f390_0_main_LE(x0, x1) → f390_0_main_LE(x0, -(x1, 1)) | >(x1, 0)

(11) YES

(12) Obligation:

Rules:
f390_0_main_LE(x0, x1) → f390_0_main_LE(-(x0, 1), 0) | &&(>(x0, 1), =(0, x1))

(13) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f390_0_main_LE(x3, x5)] = x3 + c6·x5

Therefore the following rule(s) have been dropped:

f390_0_main_LE(x0, x1) → f390_0_main_LE(-(x0, 1), 0) | &&(>(x0, 1), =(0, x1))

(14) YES