/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 97 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 387 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 140 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 25 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 61 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) PolynomialOrderProcessor [EQUIVALENT, 0 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:
f1193_0_div_Load(EOS(STATIC_1193), i225, i226, i225) -> f1195_0_div_LT(EOS(STATIC_1195), i225, i226, i225, i226) :|: TRUE
f1195_0_div_LT(EOS(STATIC_1195), i225, i226, i225, i226) -> f1198_0_div_LT(EOS(STATIC_1198), i225, i226, i225, i226) :|: i225 >= i226
f1198_0_div_LT(EOS(STATIC_1198), i225, i226, i225, i226) -> f1213_0_div_Load(EOS(STATIC_1213), i225, i226) :|: i225 >= i226
f1213_0_div_Load(EOS(STATIC_1213), i225, i226) -> f1218_0_div_LE(EOS(STATIC_1218), i225, i226, i226) :|: TRUE
f1218_0_div_LE(EOS(STATIC_1218), i246, i245, i245) -> f1225_0_div_LE(EOS(STATIC_1225), i246, i245, i245) :|: TRUE
f1225_0_div_LE(EOS(STATIC_1225), i246, i245, i245) -> f1236_0_div_Load(EOS(STATIC_1236), i246, i245) :|: i245 > 0
f1236_0_div_Load(EOS(STATIC_1236), i246, i245) -> f1239_0_div_Load(EOS(STATIC_1239), i245, i246) :|: TRUE
f1239_0_div_Load(EOS(STATIC_1239), i245, i246) -> f1240_0_div_InvokeMethod(EOS(STATIC_1240), i245, i246, i245) :|: TRUE
f1240_0_div_InvokeMethod(EOS(STATIC_1240), i245, i246, i245) -> f1241_0_minus_Load(EOS(STATIC_1241), i245, i246, i245) :|: TRUE
f1241_0_minus_Load(EOS(STATIC_1241), i245, i246, i245) -> f1281_0_minus_Load(EOS(STATIC_1281), i245, i246, i245) :|: TRUE
f1281_0_minus_Load(EOS(STATIC_1281), i245, i255, i256) -> f1284_0_minus_EQ(EOS(STATIC_1284), i245, i255, i256, i256) :|: TRUE
f1284_0_minus_EQ(EOS(STATIC_1284), i245, i262, i261, i261) -> f1288_0_minus_EQ(EOS(STATIC_1288), i245, i262, i261, i261) :|: TRUE
f1284_0_minus_EQ(EOS(STATIC_1284), i245, i255, matching1, matching2) -> f1290_0_minus_EQ(EOS(STATIC_1290), i245, i255, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f1288_0_minus_EQ(EOS(STATIC_1288), i245, i262, i261, i261) -> f1292_0_minus_Load(EOS(STATIC_1292), i245, i262, i261) :|: i261 > 0
f1292_0_minus_Load(EOS(STATIC_1292), i245, i262, i261) -> f1296_0_minus_LE(EOS(STATIC_1296), i245, i262, i261, i261) :|: TRUE
f1296_0_minus_LE(EOS(STATIC_1296), i245, i262, i261, i261) -> f1301_0_minus_Inc(EOS(STATIC_1301), i245, i262, i261) :|: i261 > 0
f1301_0_minus_Inc(EOS(STATIC_1301), i245, i262, i261) -> f1306_0_minus_Inc(EOS(STATIC_1306), i245, i262, i261 + -1) :|: TRUE
f1306_0_minus_Inc(EOS(STATIC_1306), i245, i262, i263) -> f1311_0_minus_JMP(EOS(STATIC_1311), i245, i262 + -1, i263) :|: TRUE
f1311_0_minus_JMP(EOS(STATIC_1311), i245, i264, i263) -> f1338_0_minus_Load(EOS(STATIC_1338), i245, i264, i263) :|: TRUE
f1338_0_minus_Load(EOS(STATIC_1338), i245, i264, i263) -> f1281_0_minus_Load(EOS(STATIC_1281), i245, i264, i263) :|: TRUE
f1290_0_minus_EQ(EOS(STATIC_1290), i245, i255, matching1, matching2) -> f1294_0_minus_Load(EOS(STATIC_1294), i245, i255) :|: TRUE && matching1 = 0 && matching2 = 0
f1294_0_minus_Load(EOS(STATIC_1294), i245, i255) -> f1299_0_minus_Return(EOS(STATIC_1299), i245, i255) :|: TRUE
f1299_0_minus_Return(EOS(STATIC_1299), i245, i255) -> f1303_0_div_Store(EOS(STATIC_1303), i245, i255) :|: TRUE
f1303_0_div_Store(EOS(STATIC_1303), i245, i255) -> f1308_0_div_Load(EOS(STATIC_1308), i255, i245) :|: TRUE
f1308_0_div_Load(EOS(STATIC_1308), i255, i245) -> f1313_0_div_ConstantStackPush(EOS(STATIC_1313), i255, i245) :|: TRUE
f1313_0_div_ConstantStackPush(EOS(STATIC_1313), i255, i245) -> f1339_0_div_IntArithmetic(EOS(STATIC_1339), i255, i245) :|: TRUE
f1339_0_div_IntArithmetic(EOS(STATIC_1339), i255, i245) -> f1340_0_div_Store(EOS(STATIC_1340), i255, i245) :|: TRUE
f1340_0_div_Store(EOS(STATIC_1340), i255, i245) -> f1341_0_div_JMP(EOS(STATIC_1341), i255, i245) :|: TRUE
f1341_0_div_JMP(EOS(STATIC_1341), i255, i245) -> f1347_0_div_Load(EOS(STATIC_1347), i255, i245) :|: TRUE
f1347_0_div_Load(EOS(STATIC_1347), i255, i245) -> f1189_0_div_Load(EOS(STATIC_1189), i255, i245) :|: TRUE
f1189_0_div_Load(EOS(STATIC_1189), i225, i226) -> f1193_0_div_Load(EOS(STATIC_1193), i225, i226, i225) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f1284_0_minus_EQ(EOS(STATIC_1284), i245:0, i255:0, 0, 0) -> f1284_0_minus_EQ(EOS(STATIC_1284), i245:0, i255:0, i245:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0
f1284_0_minus_EQ(EOS(STATIC_1284), i245:0, i262:0, i261:0, i261:0) -> f1284_0_minus_EQ(EOS(STATIC_1284), i245:0, i262:0 - 1, i261:0 - 1, i261:0 - 1) :|: i261:0 > 0
Filtered constant ground arguments:
   f1284_0_minus_EQ(x1, x2, x3, x4, x5) -> f1284_0_minus_EQ(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1284_0_minus_EQ(x1, x2, x3, x4) -> f1284_0_minus_EQ(x1, x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f1284_0_minus_EQ(i245:0, i255:0, cons_0) -> f1284_0_minus_EQ(i245:0, i255:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0 && cons_0 = 0
f1284_0_minus_EQ(i245:0, i262:0, i261:0) -> f1284_0_minus_EQ(i245:0, i262:0 - 1, i261:0 - 1) :|: i261:0 > 0

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

(8)
Obligation:
Rules:
f1284_0_minus_EQ(i245:0, i255:0, cons_0) -> f1284_0_minus_EQ(i245:0, i255:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0 && cons_0 = 0
f1284_0_minus_EQ(x, x1, x2) -> f1284_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:
f1284_0_minus_EQ(i245:0, i255:0, cons_0) -> f1284_0_minus_EQ(i245:0, i255:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0 && cons_0 = 0
f1284_0_minus_EQ(x, x1, x2) -> f1284_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) f1284_0_minus_EQ(i245:0, i255:0, cons_0) -> f1284_0_minus_EQ(i245:0, i255:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0 && cons_0 = 0
(2) f1284_0_minus_EQ(x, x1, x2) -> f1284_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) f1284_0_minus_EQ(i245:0, i255:0, cons_0) -> f1284_0_minus_EQ(i245:0, i255:0, i245:0) :|: i255:0 >= i245:0 && i245:0 > 0 && cons_0 = 0
(2) f1284_0_minus_EQ(x, x1, x2) -> f1284_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!

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

(14)
Obligation:
Rules:
f1284_0_minus_EQ(i245:0:0, i255:0:0, cons_0) -> f1284_0_minus_EQ(i245:0:0, i255:0:0, i245:0:0) :|: i255:0:0 >= i245:0:0 && i245:0:0 > 0 && cons_0 = 0
f1284_0_minus_EQ(x:0, x1:0, x2:0) -> f1284_0_minus_EQ(x:0, x1:0 - 1, x2:0 - 1) :|: x2:0 > 0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1284_0_minus_EQ(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f1284_0_minus_EQ(i245:0:0, i255:0:0, c) -> f1284_0_minus_EQ(i245:0:0, i255:0:0, i245:0:0) :|: c = 0 && (i255:0:0 >= i245:0:0 && i245:0:0 > 0 && cons_0 = 0)
f1284_0_minus_EQ(x:0, x1:0, x2:0) -> f1284_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:
[f1284_0_minus_EQ(x, x1, x2)] = x + x1 - x2

The following rules are decreasing:
f1284_0_minus_EQ(i245:0:0, i255:0:0, c) -> f1284_0_minus_EQ(i245:0:0, i255:0:0, i245:0:0) :|: c = 0 && (i255:0:0 >= i245:0:0 && i245:0:0 > 0 && cons_0 = 0)
The following rules are bounded:
f1284_0_minus_EQ(i245:0:0, i255:0:0, c) -> f1284_0_minus_EQ(i245:0:0, i255:0:0, i245:0:0) :|: c = 0 && (i255:0:0 >= i245:0:0 && i245:0:0 > 0 && cons_0 = 0)

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

(18)
Obligation:
Rules:
f1284_0_minus_EQ(x:0, x1:0, x2:0) -> f1284_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:
[f1284_0_minus_EQ(x, x1, x2)] = x2

The following rules are decreasing:
f1284_0_minus_EQ(x:0, x1:0, x2:0) -> f1284_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0
The following rules are bounded:
f1284_0_minus_EQ(x:0, x1:0, x2:0) -> f1284_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(20)
YES