/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 357 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 126 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 24 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 59 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 17 ms]
(18) IntTRS
(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
(20) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
public class DivWithoutMinus{
  // adaption of the algorithm from [Kolbe 95]
  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    int y = Random.random();
    int z = y;
    int res = 0;

    while (z > 0 && (y == 0 || y > 0 && x > 0))	{

      if (y == 0) {
        res++;
        y = z;
      }
      else {
        x--;
        y--;
      }
    }
  }
}



public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



----------------------------------------

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
public class DivWithoutMinus{
  // adaption of the algorithm from [Kolbe 95]
  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    int y = Random.random();
    int z = y;
    int res = 0;

    while (z > 0 && (y == 0 || y > 0 && x > 0))	{

      if (y == 0) {
        res++;
        y = z;
      }
      else {
        x--;
        y--;
      }
    }
  }
}



public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
DivWithoutMinus.main([Ljava/lang/String;)V: Graph of 202 nodes with 1 SCC.





----------------------------------------

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
----------------------------------------

(6)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: DivWithoutMinus.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:

----------------------------------------

(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 26 IRulesP rules:
f1492_0_main_LE(EOS(STATIC_1492), i82, i246, i266, i266) -> f1494_0_main_LE(EOS(STATIC_1494), i82, i246, i266, i266) :|: TRUE
f1494_0_main_LE(EOS(STATIC_1494), i82, i246, i266, i266) -> f1496_0_main_Load(EOS(STATIC_1496), i82, i246, i266) :|: i266 > 0
f1496_0_main_Load(EOS(STATIC_1496), i82, i246, i266) -> f1500_0_main_EQ(EOS(STATIC_1500), i82, i246, i266, i246) :|: TRUE
f1500_0_main_EQ(EOS(STATIC_1500), i82, i268, i266, i268) -> f1503_0_main_EQ(EOS(STATIC_1503), i82, i268, i266, i268) :|: TRUE
f1500_0_main_EQ(EOS(STATIC_1500), i82, matching1, i266, matching2) -> f1506_0_main_EQ(EOS(STATIC_1506), i82, 0, i266, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f1503_0_main_EQ(EOS(STATIC_1503), i82, i268, i266, i268) -> f1509_0_main_Load(EOS(STATIC_1509), i82, i268, i266) :|: i268 > 0
f1509_0_main_Load(EOS(STATIC_1509), i82, i268, i266) -> f1513_0_main_LE(EOS(STATIC_1513), i82, i268, i266, i268) :|: TRUE
f1513_0_main_LE(EOS(STATIC_1513), i82, i268, i266, i268) -> f1517_0_main_Load(EOS(STATIC_1517), i82, i268, i266) :|: i268 > 0
f1517_0_main_Load(EOS(STATIC_1517), i82, i268, i266) -> f1520_0_main_LE(EOS(STATIC_1520), i82, i268, i266, i82) :|: TRUE
f1520_0_main_LE(EOS(STATIC_1520), i275, i268, i266, i275) -> f1528_0_main_LE(EOS(STATIC_1528), i275, i268, i266, i275) :|: TRUE
f1528_0_main_LE(EOS(STATIC_1528), i275, i268, i266, i275) -> f1543_0_main_Load(EOS(STATIC_1543), i275, i268, i266) :|: i275 > 0
f1543_0_main_Load(EOS(STATIC_1543), i275, i268, i266) -> f1549_0_main_NE(EOS(STATIC_1549), i275, i268, i266, i268) :|: TRUE
f1549_0_main_NE(EOS(STATIC_1549), i275, i268, i266, i268) -> f1615_0_main_Inc(EOS(STATIC_1615), i275, i268, i266) :|: i268 > 0
f1615_0_main_Inc(EOS(STATIC_1615), i275, i268, i266) -> f1618_0_main_Inc(EOS(STATIC_1618), i275 + -1, i268, i266) :|: TRUE
f1618_0_main_Inc(EOS(STATIC_1618), i284, i268, i266) -> f1621_0_main_JMP(EOS(STATIC_1621), i284, i268 + -1, i266) :|: TRUE
f1621_0_main_JMP(EOS(STATIC_1621), i284, i285, i266) -> f1695_0_main_Load(EOS(STATIC_1695), i284, i285, i266) :|: TRUE
f1695_0_main_Load(EOS(STATIC_1695), i284, i285, i266) -> f1491_0_main_Load(EOS(STATIC_1491), i284, i285, i266) :|: TRUE
f1491_0_main_Load(EOS(STATIC_1491), i82, i246, i247) -> f1492_0_main_LE(EOS(STATIC_1492), i82, i246, i247, i247) :|: TRUE
f1506_0_main_EQ(EOS(STATIC_1506), i82, matching1, i266, matching2) -> f1510_0_main_Load(EOS(STATIC_1510), i82, 0, i266) :|: TRUE && matching1 = 0 && matching2 = 0
f1510_0_main_Load(EOS(STATIC_1510), i82, matching1, i266) -> f1515_0_main_NE(EOS(STATIC_1515), i82, 0, i266, 0) :|: TRUE && matching1 = 0
f1515_0_main_NE(EOS(STATIC_1515), i82, matching1, i266, matching2) -> f1519_0_main_Inc(EOS(STATIC_1519), i82, i266) :|: TRUE && matching1 = 0 && matching2 = 0
f1519_0_main_Inc(EOS(STATIC_1519), i82, i266) -> f1524_0_main_Load(EOS(STATIC_1524), i82, i266) :|: TRUE
f1524_0_main_Load(EOS(STATIC_1524), i82, i266) -> f1530_0_main_Store(EOS(STATIC_1530), i82, i266, i266) :|: TRUE
f1530_0_main_Store(EOS(STATIC_1530), i82, i266, i266) -> f1545_0_main_JMP(EOS(STATIC_1545), i82, i266, i266) :|: TRUE
f1545_0_main_JMP(EOS(STATIC_1545), i82, i266, i266) -> f1612_0_main_Load(EOS(STATIC_1612), i82, i266, i266) :|: TRUE
f1612_0_main_Load(EOS(STATIC_1612), i82, i266, i266) -> f1491_0_main_Load(EOS(STATIC_1491), i82, i266, i266) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f1492_0_main_LE(EOS(STATIC_1492), i82:0, 0, i266:0, i266:0) -> f1492_0_main_LE(EOS(STATIC_1492), i82:0, i266:0, i266:0, i266:0) :|: i266:0 > 0
f1492_0_main_LE(EOS(STATIC_1492), i82:0, i246:0, i266:0, i266:0) -> f1492_0_main_LE(EOS(STATIC_1492), i82:0 - 1, i246:0 - 1, i266:0, i266:0) :|: i266:0 > 0 && i246:0 > 0 && i82:0 > 0
Filtered constant ground arguments:
   f1492_0_main_LE(x1, x2, x3, x4, x5) -> f1492_0_main_LE(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1492_0_main_LE(x1, x2, x3, x4) -> f1492_0_main_LE(x1, x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f1492_0_main_LE(i82:0, cons_0, i266:0) -> f1492_0_main_LE(i82:0, i266:0, i266:0) :|: i266:0 > 0 && cons_0 = 0
f1492_0_main_LE(i82:0, i246:0, i266:0) -> f1492_0_main_LE(i82:0 - 1, i246:0 - 1, i266:0) :|: i246:0 > 0 && i82:0 > 0 && i266:0 > 0

----------------------------------------

(8)
Obligation:
Rules:
f1492_0_main_LE(i82:0, cons_0, i266:0) -> f1492_0_main_LE(i82:0, i266:0, i266:0) :|: i266:0 > 0 && cons_0 = 0
f1492_0_main_LE(x, x1, x2) -> f1492_0_main_LE(x - 1, x1 - 1, x2) :|: x1 > 0 && x > 0 && x2 > 0

----------------------------------------

(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(10)
Obligation:
Rules:
f1492_0_main_LE(i82:0, cons_0, i266:0) -> f1492_0_main_LE(i82:0, i266:0, i266:0) :|: i266:0 > 0 && cons_0 = 0
f1492_0_main_LE(x, x1, x2) -> f1492_0_main_LE(arith, arith1, x2) :|: x1 > 0 && x > 0 && x2 > 0 && arith = x - 1 && arith1 = x1 - 1

----------------------------------------

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1492_0_main_LE(i82:0, cons_0, i266:0) -> f1492_0_main_LE(i82:0, i266:0, i266:0) :|: i266:0 > 0 && cons_0 = 0
(2) f1492_0_main_LE(x, x1, x2) -> f1492_0_main_LE(arith, arith1, x2) :|: x1 > 0 && x > 0 && x2 > 0 && arith = x - 1 && arith1 = x1 - 1

Arcs:
(1) -> (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1492_0_main_LE(i82:0, cons_0, i266:0) -> f1492_0_main_LE(i82:0, i266:0, i266:0) :|: i266:0 > 0 && cons_0 = 0
(2) f1492_0_main_LE(x, x1, x2) -> f1492_0_main_LE(arith, arith1, x2) :|: x1 > 0 && x > 0 && x2 > 0 && arith = x - 1 && arith1 = x1 - 1

Arcs:
(1) -> (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(14)
Obligation:
Rules:
f1492_0_main_LE(i82:0:0, cons_0, i266:0:0) -> f1492_0_main_LE(i82:0:0, i266:0:0, i266:0:0) :|: i266:0:0 > 0 && cons_0 = 0
f1492_0_main_LE(x:0, x1:0, x2:0) -> f1492_0_main_LE(x:0 - 1, x1:0 - 1, x2:0) :|: x1:0 > 0 && x:0 > 0 && x2:0 > 0

----------------------------------------

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1492_0_main_LE(VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f1492_0_main_LE(i82:0:0, c, i266:0:0) -> f1492_0_main_LE(i82:0:0, i266:0:0, i266:0:0) :|: c = 0 && (i266:0:0 > 0 && cons_0 = 0)
f1492_0_main_LE(x:0, x1:0, x2:0) -> f1492_0_main_LE(c1, c2, x2:0) :|: c2 = x1:0 - 1 && c1 = x:0 - 1 && (x1:0 > 0 && x:0 > 0 && x2:0 > 0)

----------------------------------------

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1492_0_main_LE(x, x1, x2)] = -1 + x

The following rules are decreasing:
f1492_0_main_LE(x:0, x1:0, x2:0) -> f1492_0_main_LE(c1, c2, x2:0) :|: c2 = x1:0 - 1 && c1 = x:0 - 1 && (x1:0 > 0 && x:0 > 0 && x2:0 > 0)
The following rules are bounded:
f1492_0_main_LE(x:0, x1:0, x2:0) -> f1492_0_main_LE(c1, c2, x2:0) :|: c2 = x1:0 - 1 && c1 = x:0 - 1 && (x1:0 > 0 && x:0 > 0 && x2:0 > 0)

----------------------------------------

(18)
Obligation:
Rules:
f1492_0_main_LE(i82:0:0, c, i266:0:0) -> f1492_0_main_LE(i82:0:0, i266:0:0, i266:0:0) :|: c = 0 && (i266:0:0 > 0 && cons_0 = 0)

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1492_0_main_LE ] = -1*f1492_0_main_LE_2

The following rules are decreasing:
f1492_0_main_LE(i82:0:0, c, i266:0:0) -> f1492_0_main_LE(i82:0:0, i266:0:0, i266:0:0) :|: c = 0 && (i266:0:0 > 0 && cons_0 = 0)

The following rules are bounded:
f1492_0_main_LE(i82:0:0, c, i266:0:0) -> f1492_0_main_LE(i82:0:0, i266:0:0, i266:0:0) :|: c = 0 && (i266:0:0 > 0 && cons_0 = 0)


----------------------------------------

(20)
YES