/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 416 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 105 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 50 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 69 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
(20) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class DivMinus2 {
  public static int div(int x, int y) {
    int res = 0;
    while (x >= y && y > 0) {
      x = minus(x,y);
      res = res + 1;
    }
    return res;
  }

  public static int minus(int x, int y) {
    while (y != 0) {
      if (y > 0)  {
        y--;
        x--;
      } else  {
        y++;
        x++;
      }
    }
    return x;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    div(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 DivMinus2 {
  public static int div(int x, int y) {
    int res = 0;
    while (x >= y && y > 0) {
      x = minus(x,y);
      res = res + 1;
    }
    return res;
  }

  public static int minus(int x, int y) {
    while (y != 0) {
      if (y > 0)  {
        y--;
        x--;
      } else  {
        y++;
        x++;
      }
    }
    return x;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    div(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:
DivMinus2.main([Ljava/lang/String;)V: Graph of 210 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: DivMinus2.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 31 IRulesP rules:
f945_0_div_Load(EOS(STATIC_945), i189, i190, i189) -> f947_0_div_LT(EOS(STATIC_947), i189, i190, i189, i190) :|: TRUE
f947_0_div_LT(EOS(STATIC_947), i189, i190, i189, i190) -> f956_0_div_LT(EOS(STATIC_956), i189, i190, i189, i190) :|: i189 >= i190
f956_0_div_LT(EOS(STATIC_956), i189, i190, i189, i190) -> f977_0_div_Load(EOS(STATIC_977), i189, i190) :|: i189 >= i190
f977_0_div_Load(EOS(STATIC_977), i189, i190) -> f982_0_div_LE(EOS(STATIC_982), i189, i190, i190) :|: TRUE
f982_0_div_LE(EOS(STATIC_982), i204, i203, i203) -> f989_0_div_LE(EOS(STATIC_989), i204, i203, i203) :|: TRUE
f989_0_div_LE(EOS(STATIC_989), i204, i203, i203) -> f998_0_div_Load(EOS(STATIC_998), i204, i203) :|: i203 > 0
f998_0_div_Load(EOS(STATIC_998), i204, i203) -> f1002_0_div_Load(EOS(STATIC_1002), i203, i204) :|: TRUE
f1002_0_div_Load(EOS(STATIC_1002), i203, i204) -> f1003_0_div_InvokeMethod(EOS(STATIC_1003), i203, i204, i203) :|: TRUE
f1003_0_div_InvokeMethod(EOS(STATIC_1003), i203, i204, i203) -> f1005_0_minus_Load(EOS(STATIC_1005), i203, i204, i203) :|: TRUE
f1005_0_minus_Load(EOS(STATIC_1005), i203, i204, i203) -> f1047_0_minus_Load(EOS(STATIC_1047), i203, i204, i203) :|: TRUE
f1047_0_minus_Load(EOS(STATIC_1047), i203, i214, i215) -> f1049_0_minus_EQ(EOS(STATIC_1049), i203, i214, i215, i215) :|: TRUE
f1049_0_minus_EQ(EOS(STATIC_1049), i203, i224, i223, i223) -> f1050_0_minus_EQ(EOS(STATIC_1050), i203, i224, i223, i223) :|: TRUE
f1049_0_minus_EQ(EOS(STATIC_1049), i203, i214, matching1, matching2) -> f1051_0_minus_EQ(EOS(STATIC_1051), i203, i214, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f1050_0_minus_EQ(EOS(STATIC_1050), i203, i224, i223, i223) -> f1053_0_minus_Load(EOS(STATIC_1053), i203, i224, i223) :|: i223 > 0
f1053_0_minus_Load(EOS(STATIC_1053), i203, i224, i223) -> f1055_0_minus_LE(EOS(STATIC_1055), i203, i224, i223, i223) :|: TRUE
f1055_0_minus_LE(EOS(STATIC_1055), i203, i224, i223, i223) -> f1057_0_minus_Inc(EOS(STATIC_1057), i203, i224, i223) :|: i223 > 0
f1057_0_minus_Inc(EOS(STATIC_1057), i203, i224, i223) -> f1061_0_minus_Inc(EOS(STATIC_1061), i203, i224, i223 + -1) :|: TRUE
f1061_0_minus_Inc(EOS(STATIC_1061), i203, i224, i225) -> f1066_0_minus_JMP(EOS(STATIC_1066), i203, i224 + -1, i225) :|: TRUE
f1066_0_minus_JMP(EOS(STATIC_1066), i203, i226, i225) -> f1097_0_minus_Load(EOS(STATIC_1097), i203, i226, i225) :|: TRUE
f1097_0_minus_Load(EOS(STATIC_1097), i203, i226, i225) -> f1047_0_minus_Load(EOS(STATIC_1047), i203, i226, i225) :|: TRUE
f1051_0_minus_EQ(EOS(STATIC_1051), i203, i214, matching1, matching2) -> f1054_0_minus_Load(EOS(STATIC_1054), i203, i214) :|: TRUE && matching1 = 0 && matching2 = 0
f1054_0_minus_Load(EOS(STATIC_1054), i203, i214) -> f1056_0_minus_Return(EOS(STATIC_1056), i203, i214) :|: TRUE
f1056_0_minus_Return(EOS(STATIC_1056), i203, i214) -> f1059_0_div_Store(EOS(STATIC_1059), i203, i214) :|: TRUE
f1059_0_div_Store(EOS(STATIC_1059), i203, i214) -> f1063_0_div_Load(EOS(STATIC_1063), i214, i203) :|: TRUE
f1063_0_div_Load(EOS(STATIC_1063), i214, i203) -> f1068_0_div_ConstantStackPush(EOS(STATIC_1068), i214, i203) :|: TRUE
f1068_0_div_ConstantStackPush(EOS(STATIC_1068), i214, i203) -> f1099_0_div_IntArithmetic(EOS(STATIC_1099), i214, i203) :|: TRUE
f1099_0_div_IntArithmetic(EOS(STATIC_1099), i214, i203) -> f1102_0_div_Store(EOS(STATIC_1102), i214, i203) :|: TRUE
f1102_0_div_Store(EOS(STATIC_1102), i214, i203) -> f1104_0_div_JMP(EOS(STATIC_1104), i214, i203) :|: TRUE
f1104_0_div_JMP(EOS(STATIC_1104), i214, i203) -> f1114_0_div_Load(EOS(STATIC_1114), i214, i203) :|: TRUE
f1114_0_div_Load(EOS(STATIC_1114), i214, i203) -> f940_0_div_Load(EOS(STATIC_940), i214, i203) :|: TRUE
f940_0_div_Load(EOS(STATIC_940), i189, i190) -> f945_0_div_Load(EOS(STATIC_945), i189, i190, i189) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f1049_0_minus_EQ(EOS(STATIC_1049), i203:0, i214:0, 0, 0) -> f1049_0_minus_EQ(EOS(STATIC_1049), i203:0, i214:0, i203:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0
f1049_0_minus_EQ(EOS(STATIC_1049), i203:0, i224:0, i223:0, i223:0) -> f1049_0_minus_EQ(EOS(STATIC_1049), i203:0, i224:0 - 1, i223:0 - 1, i223:0 - 1) :|: i223:0 > 0
Filtered constant ground arguments:
   f1049_0_minus_EQ(x1, x2, x3, x4, x5) -> f1049_0_minus_EQ(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1049_0_minus_EQ(x1, x2, x3, x4) -> f1049_0_minus_EQ(x1, x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f1049_0_minus_EQ(i203:0, i214:0, cons_0) -> f1049_0_minus_EQ(i203:0, i214:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0 && cons_0 = 0
f1049_0_minus_EQ(i203:0, i224:0, i223:0) -> f1049_0_minus_EQ(i203:0, i224:0 - 1, i223:0 - 1) :|: i223:0 > 0

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

(8)
Obligation:
Rules:
f1049_0_minus_EQ(i203:0, i214:0, cons_0) -> f1049_0_minus_EQ(i203:0, i214:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0 && cons_0 = 0
f1049_0_minus_EQ(x, x1, x2) -> f1049_0_minus_EQ(x, x1 - 1, x2 - 1) :|: x2 > 0

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

(10)
Obligation:
Rules:
f1049_0_minus_EQ(i203:0, i214:0, cons_0) -> f1049_0_minus_EQ(i203:0, i214:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0 && cons_0 = 0
f1049_0_minus_EQ(x, x1, x2) -> f1049_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1049_0_minus_EQ(i203:0, i214:0, cons_0) -> f1049_0_minus_EQ(i203:0, i214:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0 && cons_0 = 0
(2) f1049_0_minus_EQ(x, x1, x2) -> f1049_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1049_0_minus_EQ(i203:0, i214:0, cons_0) -> f1049_0_minus_EQ(i203:0, i214:0, i203:0) :|: i214:0 >= i203:0 && i203:0 > 0 && cons_0 = 0
(2) f1049_0_minus_EQ(x, x1, x2) -> f1049_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f1049_0_minus_EQ(i203:0:0, i214:0:0, cons_0) -> f1049_0_minus_EQ(i203:0:0, i214:0:0, i203:0:0) :|: i214:0:0 >= i203:0:0 && i203:0:0 > 0 && cons_0 = 0
f1049_0_minus_EQ(x:0, x1:0, x2:0) -> f1049_0_minus_EQ(x:0, x1:0 - 1, x2:0 - 1) :|: x2:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1049_0_minus_EQ(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f1049_0_minus_EQ(i203:0:0, i214:0:0, c) -> f1049_0_minus_EQ(i203:0:0, i214:0:0, i203:0:0) :|: c = 0 && (i214:0:0 >= i203:0:0 && i203:0:0 > 0 && cons_0 = 0)
f1049_0_minus_EQ(x:0, x1:0, x2:0) -> f1049_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1049_0_minus_EQ(x, x1, x2)] = x + x1 - x2

The following rules are decreasing:
f1049_0_minus_EQ(i203:0:0, i214:0:0, c) -> f1049_0_minus_EQ(i203:0:0, i214:0:0, i203:0:0) :|: c = 0 && (i214:0:0 >= i203:0:0 && i203:0:0 > 0 && cons_0 = 0)
The following rules are bounded:
f1049_0_minus_EQ(i203:0:0, i214:0:0, c) -> f1049_0_minus_EQ(i203:0:0, i214:0:0, i203:0:0) :|: c = 0 && (i214:0:0 >= i203:0:0 && i203:0:0 > 0 && cons_0 = 0)

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

(18)
Obligation:
Rules:
f1049_0_minus_EQ(x:0, x1:0, x2:0) -> f1049_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1049_0_minus_EQ(x, x1, x2)] = x2

The following rules are decreasing:
f1049_0_minus_EQ(x:0, x1:0, x2:0) -> f1049_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0
The following rules are bounded:
f1049_0_minus_EQ(x:0, x1:0, x2:0) -> f1049_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(20)
YES