/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 92 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 351 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 155 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 86 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 63 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
(20) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class GCD {
  public static int mod(int a, int b) {
    if(a <= 0 || b <= 0)
      return 0;
    if (a == b) {
      return 0;
    }
    while(a>b) {
      a -= b;
    }
    return a;
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b != 0) {
      tmp = b;
      b = mod(a, b);
      a = tmp;
    }
    return a;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    gcd(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 GCD {
  public static int mod(int a, int b) {
    if(a <= 0 || b <= 0)
      return 0;
    if (a == b) {
      return 0;
    }
    while(a>b) {
      a -= b;
    }
    return a;
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b != 0) {
      tmp = b;
      b = mod(a, b);
      a = tmp;
    }
    return a;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    gcd(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:
GCD.main([Ljava/lang/String;)V: Graph of 222 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: GCD.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 51 IRulesP rules:
f425_0_gcd_EQ(EOS(STATIC_425), i50, i57, i57) -> f428_0_gcd_EQ(EOS(STATIC_428), i50, i57, i57) :|: TRUE
f428_0_gcd_EQ(EOS(STATIC_428), i50, i57, i57) -> f432_0_gcd_Load(EOS(STATIC_432), i50, i57) :|: i57 > 0
f432_0_gcd_Load(EOS(STATIC_432), i50, i57) -> f436_0_gcd_Store(EOS(STATIC_436), i50, i57, i57) :|: TRUE
f436_0_gcd_Store(EOS(STATIC_436), i50, i57, i57) -> f440_0_gcd_Load(EOS(STATIC_440), i50, i57, i57) :|: TRUE
f440_0_gcd_Load(EOS(STATIC_440), i50, i57, i57) -> f446_0_gcd_Load(EOS(STATIC_446), i57, i57, i50) :|: TRUE
f446_0_gcd_Load(EOS(STATIC_446), i57, i57, i50) -> f450_0_gcd_InvokeMethod(EOS(STATIC_450), i57, i50, i57) :|: TRUE
f450_0_gcd_InvokeMethod(EOS(STATIC_450), i57, i50, i57) -> f453_0_mod_Load(EOS(STATIC_453), i57, i50, i57) :|: TRUE
f453_0_mod_Load(EOS(STATIC_453), i57, i50, i57) -> f454_0_mod_LE(EOS(STATIC_454), i57, i50, i57, i50) :|: TRUE
f454_0_mod_LE(EOS(STATIC_454), i57, matching1, i57, matching2) -> f455_0_mod_LE(EOS(STATIC_455), i57, 0, i57, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f454_0_mod_LE(EOS(STATIC_454), i57, i58, i57, i58) -> f456_0_mod_LE(EOS(STATIC_456), i57, i58, i57, i58) :|: TRUE
f455_0_mod_LE(EOS(STATIC_455), i57, matching1, i57, matching2) -> f457_0_mod_ConstantStackPush(EOS(STATIC_457), i57) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
f457_0_mod_ConstantStackPush(EOS(STATIC_457), i57) -> f459_0_mod_Return(EOS(STATIC_459), i57, 0) :|: TRUE
f459_0_mod_Return(EOS(STATIC_459), i57, matching1) -> f461_0_gcd_Store(EOS(STATIC_461), i57, 0) :|: TRUE && matching1 = 0
f461_0_gcd_Store(EOS(STATIC_461), i57, matching1) -> f463_0_gcd_Load(EOS(STATIC_463), 0, i57) :|: TRUE && matching1 = 0
f463_0_gcd_Load(EOS(STATIC_463), matching1, i57) -> f468_0_gcd_Store(EOS(STATIC_468), 0, i57) :|: TRUE && matching1 = 0
f468_0_gcd_Store(EOS(STATIC_468), matching1, i57) -> f471_0_gcd_JMP(EOS(STATIC_471), i57, 0) :|: TRUE && matching1 = 0
f471_0_gcd_JMP(EOS(STATIC_471), i57, matching1) -> f510_0_gcd_Load(EOS(STATIC_510), i57, 0) :|: TRUE && matching1 = 0
f510_0_gcd_Load(EOS(STATIC_510), i57, matching1) -> f424_0_gcd_Load(EOS(STATIC_424), i57, 0) :|: TRUE && matching1 = 0
f424_0_gcd_Load(EOS(STATIC_424), i50, i51) -> f425_0_gcd_EQ(EOS(STATIC_425), i50, i51, i51) :|: TRUE
f456_0_mod_LE(EOS(STATIC_456), i57, i58, i57, i58) -> f458_0_mod_Load(EOS(STATIC_458), i57, i58, i57) :|: i58 > 0
f458_0_mod_Load(EOS(STATIC_458), i57, i58, i57) -> f460_0_mod_GT(EOS(STATIC_460), i57, i58, i57, i57) :|: TRUE
f460_0_mod_GT(EOS(STATIC_460), i57, i58, i57, i57) -> f462_0_mod_Load(EOS(STATIC_462), i57, i58, i57) :|: i57 > 0
f462_0_mod_Load(EOS(STATIC_462), i57, i58, i57) -> f466_0_mod_Load(EOS(STATIC_466), i57, i58, i57, i58) :|: TRUE
f466_0_mod_Load(EOS(STATIC_466), i57, i58, i57, i58) -> f470_0_mod_NE(EOS(STATIC_470), i57, i58, i57, i58, i57) :|: TRUE
f470_0_mod_NE(EOS(STATIC_470), i57, i58, i57, i58, i57) -> f477_0_mod_NE(EOS(STATIC_477), i57, i58, i57, i58, i57) :|: !(i58 = i57)
f470_0_mod_NE(EOS(STATIC_470), i57, i57, i57, i57, i57) -> f479_0_mod_NE(EOS(STATIC_479), i57, i57, i57, i57, i57) :|: i58 = i57
f477_0_mod_NE(EOS(STATIC_477), i57, i58, i57, i58, i57) -> f513_0_mod_Load(EOS(STATIC_513), i57, i58, i57) :|: !(i58 = i57)
f513_0_mod_Load(EOS(STATIC_513), i57, i58, i57) -> f791_0_mod_Load(EOS(STATIC_791), i57, i58, i57) :|: TRUE
f791_0_mod_Load(EOS(STATIC_791), i57, i74, i57) -> f793_0_mod_Load(EOS(STATIC_793), i57, i74, i57, i74) :|: TRUE
f793_0_mod_Load(EOS(STATIC_793), i57, i74, i57, i74) -> f794_0_mod_LE(EOS(STATIC_794), i57, i74, i57, i74, i57) :|: TRUE
f794_0_mod_LE(EOS(STATIC_794), i57, i74, i57, i74, i57) -> f797_0_mod_LE(EOS(STATIC_797), i57, i74, i57, i74, i57) :|: i74 <= i57
f794_0_mod_LE(EOS(STATIC_794), i57, i74, i57, i74, i57) -> f798_0_mod_LE(EOS(STATIC_798), i57, i74, i57, i74, i57) :|: i74 > i57
f797_0_mod_LE(EOS(STATIC_797), i57, i74, i57, i74, i57) -> f802_0_mod_Load(EOS(STATIC_802), i57, i74) :|: i74 <= i57
f802_0_mod_Load(EOS(STATIC_802), i57, i74) -> f805_0_mod_Return(EOS(STATIC_805), i57, i74) :|: TRUE
f805_0_mod_Return(EOS(STATIC_805), i57, i74) -> f807_0_gcd_Store(EOS(STATIC_807), i57, i74) :|: TRUE
f807_0_gcd_Store(EOS(STATIC_807), i57, i74) -> f812_0_gcd_Load(EOS(STATIC_812), i74, i57) :|: TRUE
f812_0_gcd_Load(EOS(STATIC_812), i74, i57) -> f823_0_gcd_Store(EOS(STATIC_823), i74, i57) :|: TRUE
f823_0_gcd_Store(EOS(STATIC_823), i74, i57) -> f828_0_gcd_JMP(EOS(STATIC_828), i57, i74) :|: TRUE
f828_0_gcd_JMP(EOS(STATIC_828), i57, i74) -> f847_0_gcd_Load(EOS(STATIC_847), i57, i74) :|: TRUE
f847_0_gcd_Load(EOS(STATIC_847), i57, i74) -> f424_0_gcd_Load(EOS(STATIC_424), i57, i74) :|: TRUE
f798_0_mod_LE(EOS(STATIC_798), i57, i74, i57, i74, i57) -> f804_0_mod_Load(EOS(STATIC_804), i57, i74, i57) :|: i74 > i57
f804_0_mod_Load(EOS(STATIC_804), i57, i74, i57) -> f806_0_mod_Load(EOS(STATIC_806), i57, i57, i74) :|: TRUE
f806_0_mod_Load(EOS(STATIC_806), i57, i57, i74) -> f808_0_mod_IntArithmetic(EOS(STATIC_808), i57, i57, i74, i57) :|: TRUE
f808_0_mod_IntArithmetic(EOS(STATIC_808), i57, i57, i74, i57) -> f819_0_mod_Store(EOS(STATIC_819), i57, i57, i74 - i57) :|: i74 > 0 && i57 > 0
f819_0_mod_Store(EOS(STATIC_819), i57, i57, i77) -> f825_0_mod_JMP(EOS(STATIC_825), i57, i77, i57) :|: TRUE
f825_0_mod_JMP(EOS(STATIC_825), i57, i77, i57) -> f831_0_mod_Load(EOS(STATIC_831), i57, i77, i57) :|: TRUE
f831_0_mod_Load(EOS(STATIC_831), i57, i77, i57) -> f791_0_mod_Load(EOS(STATIC_791), i57, i77, i57) :|: TRUE
f479_0_mod_NE(EOS(STATIC_479), i57, i57, i57, i57, i57) -> f514_0_mod_ConstantStackPush(EOS(STATIC_514), i57) :|: TRUE
f514_0_mod_ConstantStackPush(EOS(STATIC_514), i57) -> f744_0_mod_Return(EOS(STATIC_744), i57, 0) :|: TRUE
f744_0_mod_Return(EOS(STATIC_744), i57, matching1) -> f757_0_gcd_Store(EOS(STATIC_757), i57, 0) :|: TRUE && matching1 = 0
f757_0_gcd_Store(EOS(STATIC_757), i57, matching1) -> f461_0_gcd_Store(EOS(STATIC_461), i57, 0) :|: TRUE && matching1 = 0
Combined rules. Obtained 6 IRulesP rules:
f425_0_gcd_EQ(EOS(STATIC_425), i57:0, i57:0, i57:0) -> f425_0_gcd_EQ(EOS(STATIC_425), i57:0, 0, 0) :|: i57:0 > 0
f425_0_gcd_EQ(EOS(STATIC_425), 0, i57:0, i57:0) -> f425_0_gcd_EQ(EOS(STATIC_425), i57:0, 0, 0) :|: i57:0 > 0
f794_0_mod_LE(EOS(STATIC_794), i57:0, i74:0, i57:0, i74:0, i57:0) -> f425_0_gcd_EQ(EOS(STATIC_425), i57:0, i74:0, i74:0) :|: i74:0 <= i57:0
f794_0_mod_LE(EOS(STATIC_794), i57:0, i74:0, i57:0, i74:0, i57:0) -> f794_0_mod_LE(EOS(STATIC_794), i57:0, i74:0 - i57:0, i57:0, i74:0 - i57:0, i57:0) :|: i74:0 > i57:0 && i74:0 > 0 && i57:0 > 0
f425_0_gcd_EQ(EOS(STATIC_425), i50:0, i57:0, i57:0) -> f794_0_mod_LE(EOS(STATIC_794), i57:0, i50:0, i57:0, i50:0, i57:0) :|: i57:0 > 0 && i50:0 > 0 && i57:0 > i50:0
f425_0_gcd_EQ(EOS(STATIC_425), i50:0, i57:0, i57:0) -> f794_0_mod_LE(EOS(STATIC_794), i57:0, i50:0, i57:0, i50:0, i57:0) :|: i57:0 > 0 && i50:0 > 0 && i57:0 < i50:0
Filtered constant ground arguments:
   f425_0_gcd_EQ(x1, x2, x3, x4) -> f425_0_gcd_EQ(x2, x3, x4)
   f794_0_mod_LE(x1, x2, x3, x4, x5, x6) -> f794_0_mod_LE(x2, x3, x4, x5, x6)
Filtered duplicate arguments:
   f794_0_mod_LE(x1, x2, x3, x4, x5) -> f794_0_mod_LE(x4, x5)
Finished conversion. Obtained 6 rules.P rules:
f425_0_gcd_EQ(i57:0, i57:0, i57:0) -> f425_0_gcd_EQ(i57:0, 0, 0) :|: i57:0 > 0
f425_0_gcd_EQ(cons_0, i57:0, i57:0) -> f425_0_gcd_EQ(i57:0, 0, 0) :|: i57:0 > 0 && cons_0 = 0
f794_0_mod_LE(i74:0, i57:0) -> f425_0_gcd_EQ(i57:0, i74:0, i74:0) :|: i74:0 <= i57:0
f794_0_mod_LE(i74:0, i57:0) -> f794_0_mod_LE(i74:0 - i57:0, i57:0) :|: i74:0 > 0 && i57:0 > 0 && i74:0 > i57:0
f425_0_gcd_EQ(i50:0, i57:0, i57:0) -> f794_0_mod_LE(i50:0, i57:0) :|: i50:0 > 0 && i57:0 > i50:0 && i57:0 > 0
f425_0_gcd_EQ(i50:0, i57:0, i57:0) -> f794_0_mod_LE(i50:0, i57:0) :|: i50:0 > 0 && i57:0 < i50:0 && i57:0 > 0

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

(8)
Obligation:
Rules:
f425_0_gcd_EQ(i57:0, i57:0, i57:0) -> f425_0_gcd_EQ(i57:0, 0, 0) :|: i57:0 > 0
f425_0_gcd_EQ(x, x1, x1) -> f425_0_gcd_EQ(x1, 0, 0) :|: x1 > 0 && x = 0
f794_0_mod_LE(x2, x3) -> f425_0_gcd_EQ(x3, x2, x2) :|: x2 <= x3
f794_0_mod_LE(x4, x5) -> f794_0_mod_LE(x4 - x5, x5) :|: x4 > 0 && x5 > 0 && x4 > x5
f425_0_gcd_EQ(x6, x7, x7) -> f794_0_mod_LE(x6, x7) :|: x6 > 0 && x7 > x6 && x7 > 0
f425_0_gcd_EQ(x8, x9, x9) -> f794_0_mod_LE(x8, x9) :|: x8 > 0 && x9 < x8 && x9 > 0

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

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

(10)
Obligation:
Rules:
f425_0_gcd_EQ(i57:0, i57:0, i57:0) -> f425_0_gcd_EQ(i57:0, 0, 0) :|: i57:0 > 0
f425_0_gcd_EQ(x, x1, x1) -> f425_0_gcd_EQ(x1, 0, 0) :|: x1 > 0 && x = 0
f794_0_mod_LE(x2, x3) -> f425_0_gcd_EQ(x3, x2, x2) :|: x2 <= x3
f794_0_mod_LE(x4, x5) -> f794_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
f425_0_gcd_EQ(x6, x7, x7) -> f794_0_mod_LE(x6, x7) :|: x6 > 0 && x7 > x6 && x7 > 0
f425_0_gcd_EQ(x8, x9, x9) -> f794_0_mod_LE(x8, x9) :|: x8 > 0 && x9 < x8 && x9 > 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f425_0_gcd_EQ(i57:0, i57:0, i57:0) -> f425_0_gcd_EQ(i57:0, 0, 0) :|: i57:0 > 0
(2) f425_0_gcd_EQ(x, x1, x1) -> f425_0_gcd_EQ(x1, 0, 0) :|: x1 > 0 && x = 0
(3) f794_0_mod_LE(x2, x3) -> f425_0_gcd_EQ(x3, x2, x2) :|: x2 <= x3
(4) f794_0_mod_LE(x4, x5) -> f794_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
(5) f425_0_gcd_EQ(x6, x7, x7) -> f794_0_mod_LE(x6, x7) :|: x6 > 0 && x7 > x6 && x7 > 0
(6) f425_0_gcd_EQ(x8, x9, x9) -> f794_0_mod_LE(x8, x9) :|: x8 > 0 && x9 < x8 && x9 > 0

Arcs:
(3) -> (1), (6)
(4) -> (3), (4)
(5) -> (3)
(6) -> (4)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f794_0_mod_LE(x2, x3) -> f425_0_gcd_EQ(x3, x2, x2) :|: x2 <= x3
(2) f794_0_mod_LE(x4, x5) -> f794_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
(3) f425_0_gcd_EQ(x8, x9, x9) -> f794_0_mod_LE(x8, x9) :|: x8 > 0 && x9 < x8 && x9 > 0

Arcs:
(1) -> (3)
(2) -> (1), (2)
(3) -> (2)

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f794_0_mod_LE(x4:0, x5:0) -> f794_0_mod_LE(x4:0 - x5:0, x5:0) :|: x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0
f794_0_mod_LE(x2:0, x3:0) -> f794_0_mod_LE(x3:0, x2:0) :|: x3:0 > 0 && x3:0 > x2:0 && x2:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f794_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f794_0_mod_LE(x4:0, x5:0) -> f794_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)
f794_0_mod_LE(x2:0, x3:0) -> f794_0_mod_LE(x3:0, x2:0) :|: x3:0 > 0 && x3:0 > x2:0 && x2:0 > 0

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f794_0_mod_LE(x, x1)] = -2 + x1

The following rules are decreasing:
f794_0_mod_LE(x2:0, x3:0) -> f794_0_mod_LE(x3:0, x2:0) :|: x3:0 > 0 && x3:0 > x2:0 && x2:0 > 0
The following rules are bounded:
f794_0_mod_LE(x2:0, x3:0) -> f794_0_mod_LE(x3:0, x2:0) :|: x3:0 > 0 && x3:0 > x2:0 && x2:0 > 0

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

(18)
Obligation:
Rules:
f794_0_mod_LE(x4:0, x5:0) -> f794_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f794_0_mod_LE ] = f794_0_mod_LE_1

The following rules are decreasing:
f794_0_mod_LE(x4:0, x5:0) -> f794_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)

The following rules are bounded:
f794_0_mod_LE(x4:0, x5:0) -> f794_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)


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

(20)
YES