Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:

public class Duplicate{

  public static int round (int x) {

    if (x % 2 == 0) return x;
    else return x+1;
  }


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

    while ((x > y) && (y > 2)) {
      x++;
      y = 2*y;

    }
  }
}


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:
Duplicate.main([Ljava/lang/String;)V: Graph of 184 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: Duplicate.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 15 IRules

P rules:
f362_0_main_Load(EOS, i18, i48, i18) → f370_0_main_LE(EOS, i18, i48, i18, i48)
f370_0_main_LE(EOS, i18, i48, i18, i48) → f388_0_main_LE(EOS, i18, i48, i18, i48)
f388_0_main_LE(EOS, i18, i48, i18, i48) → f401_0_main_Load(EOS, i18, i48) | >(i18, i48)
f401_0_main_Load(EOS, i18, i48) → f410_0_main_ConstantStackPush(EOS, i18, i48, i48)
f410_0_main_ConstantStackPush(EOS, i18, i48, i48) → f424_0_main_LE(EOS, i18, i48, i48, 2)
f424_0_main_LE(EOS, i18, i65, i65, matching1) → f439_0_main_LE(EOS, i18, i65, i65, 2) | =(matching1, 2)
f439_0_main_LE(EOS, i18, i65, i65, matching1) → f464_0_main_Inc(EOS, i18, i65) | &&(>(i65, 2), =(matching1, 2))
f464_0_main_Inc(EOS, i18, i65) → f477_0_main_ConstantStackPush(EOS, +(i18, 1), i65) | >=(i18, 0)
f477_0_main_ConstantStackPush(EOS, i70, i65) → f493_0_main_Load(EOS, i70, i65, 2)
f493_0_main_Load(EOS, i70, i65, matching1) → f505_0_main_IntArithmetic(EOS, i70, 2, i65) | =(matching1, 2)
f505_0_main_IntArithmetic(EOS, i70, matching1, i65) → f517_0_main_Store(EOS, i70, *(2, i65)) | &&(>(i65, 1), =(matching1, 2))
f517_0_main_Store(EOS, i70, i74) → f526_0_main_JMP(EOS, i70, i74)
f526_0_main_JMP(EOS, i70, i74) → f559_0_main_Load(EOS, i70, i74)
f559_0_main_Load(EOS, i70, i74) → f351_0_main_Load(EOS, i70, i74)
f351_0_main_Load(EOS, i18, i48) → f362_0_main_Load(EOS, i18, i48, i18)

Combined rules. Obtained 1 IRules

P rules:
f362_0_main_Load(EOS, x0, x1, x0) → f362_0_main_Load(EOS, +(x0, 1), *(2, x1), +(x0, 1)) | &&(&&(>(x1, 2), >(+(x0, 1), 0)), <(x1, x0))

Filtered ground terms:

f362_0_main_Load(x1, x2, x3, x4) → f362_0_main_Load(x2, x3, x4)
Cond_f362_0_main_Load(x1, x2, x3, x4, x5) → Cond_f362_0_main_Load(x1, x3, x4, x5)

Filtered duplicate terms:

f362_0_main_Load(x1, x2, x3) → f362_0_main_Load(x2, x3)
Cond_f362_0_main_Load(x1, x2, x3, x4) → Cond_f362_0_main_Load(x1, x3, x4)

Prepared 1 rules for path length conversion:

P rules:
f362_0_main_Load(x1, x0) → f362_0_main_Load(*(2, x1), +(x0, 1)) | &&(&&(>(x1, 2), >(+(x0, 1), 0)), <(x1, x0))

Finished conversion. Obtained 1 rules.

P rules:
f362_0_main_Load(x0, x1) → f362_0_main_Load(*(2, x0), +(x1, 1)) | &&(&&(>(x1, x0), >(x0, 2)), >(x1, -1))

(6) Obligation:

Rules:
f362_0_main_Load(x0, x1) → f362_0_main_Load(*(2, x0), +(x1, 1)) | &&(&&(>(x1, x0), >(x0, 2)), >(x1, -1))

(7) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f362_0_main_Load(x3, x5)] = -x3 + x5

Therefore the following rule(s) have been dropped:

f362_0_main_Load(x0, x1) → f362_0_main_Load(*(2, x0), +(x1, 1)) | &&(&&(>(x1, x0), >(x0, 2)), >(x1, -1))

(8) YES