/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 334 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 88 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 64 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 56 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 GCD2 {
  public static int mod(int a, int b) {
    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 && a >= 0 && 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 GCD2 {
  public static int mod(int a, int b) {
    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 && a >= 0 && 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:
GCD2.main([Ljava/lang/String;)V: Graph of 213 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: GCD2.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 42 IRulesP rules:
f337_0_gcd_EQ(EOS(STATIC_337), i19, i45, i45) -> f340_0_gcd_EQ(EOS(STATIC_340), i19, i45, i45) :|: TRUE
f340_0_gcd_EQ(EOS(STATIC_340), i19, i45, i45) -> f344_0_gcd_Load(EOS(STATIC_344), i19, i45) :|: i45 > 0
f344_0_gcd_Load(EOS(STATIC_344), i19, i45) -> f348_0_gcd_LT(EOS(STATIC_348), i19, i45, i19) :|: TRUE
f348_0_gcd_LT(EOS(STATIC_348), i19, i45, i19) -> f352_0_gcd_Load(EOS(STATIC_352), i19, i45) :|: i19 >= 0
f352_0_gcd_Load(EOS(STATIC_352), i19, i45) -> f356_0_gcd_LT(EOS(STATIC_356), i19, i45, i45) :|: TRUE
f356_0_gcd_LT(EOS(STATIC_356), i19, i45, i45) -> f360_0_gcd_Load(EOS(STATIC_360), i19, i45) :|: i45 >= 0
f360_0_gcd_Load(EOS(STATIC_360), i19, i45) -> f364_0_gcd_Store(EOS(STATIC_364), i19, i45, i45) :|: TRUE
f364_0_gcd_Store(EOS(STATIC_364), i19, i45, i45) -> f367_0_gcd_Load(EOS(STATIC_367), i19, i45, i45) :|: TRUE
f367_0_gcd_Load(EOS(STATIC_367), i19, i45, i45) -> f369_0_gcd_Load(EOS(STATIC_369), i45, i45, i19) :|: TRUE
f369_0_gcd_Load(EOS(STATIC_369), i45, i45, i19) -> f371_0_gcd_InvokeMethod(EOS(STATIC_371), i45, i19, i45) :|: TRUE
f371_0_gcd_InvokeMethod(EOS(STATIC_371), i45, i19, i45) -> f373_0_mod_Load(EOS(STATIC_373), i45, i19, i45) :|: TRUE
f373_0_mod_Load(EOS(STATIC_373), i45, i19, i45) -> f375_0_mod_Load(EOS(STATIC_375), i45, i19, i45, i19) :|: TRUE
f375_0_mod_Load(EOS(STATIC_375), i45, i19, i45, i19) -> f376_0_mod_NE(EOS(STATIC_376), i45, i19, i45, i19, i45) :|: TRUE
f376_0_mod_NE(EOS(STATIC_376), i45, i19, i45, i19, i45) -> f379_0_mod_NE(EOS(STATIC_379), i45, i19, i45, i19, i45) :|: !(i19 = i45)
f376_0_mod_NE(EOS(STATIC_376), i45, i45, i45, i45, i45) -> f380_0_mod_NE(EOS(STATIC_380), i45, i45, i45, i45, i45) :|: i19 = i45
f379_0_mod_NE(EOS(STATIC_379), i45, i19, i45, i19, i45) -> f382_0_mod_Load(EOS(STATIC_382), i45, i19, i45) :|: !(i19 = i45)
f382_0_mod_Load(EOS(STATIC_382), i45, i19, i45) -> f514_0_mod_Load(EOS(STATIC_514), i45, i19, i45) :|: TRUE
f514_0_mod_Load(EOS(STATIC_514), i45, i54, i45) -> f534_0_mod_Load(EOS(STATIC_534), i45, i54, i45, i54) :|: TRUE
f534_0_mod_Load(EOS(STATIC_534), i45, i54, i45, i54) -> f898_0_mod_LE(EOS(STATIC_898), i45, i54, i45, i54, i45) :|: TRUE
f898_0_mod_LE(EOS(STATIC_898), i45, i54, i45, i54, i45) -> f901_0_mod_LE(EOS(STATIC_901), i45, i54, i45, i54, i45) :|: i54 <= i45
f898_0_mod_LE(EOS(STATIC_898), i45, i54, i45, i54, i45) -> f902_0_mod_LE(EOS(STATIC_902), i45, i54, i45, i54, i45) :|: i54 > i45
f901_0_mod_LE(EOS(STATIC_901), i45, i54, i45, i54, i45) -> f906_0_mod_Load(EOS(STATIC_906), i45, i54) :|: i54 <= i45
f906_0_mod_Load(EOS(STATIC_906), i45, i54) -> f909_0_mod_Return(EOS(STATIC_909), i45, i54) :|: TRUE
f909_0_mod_Return(EOS(STATIC_909), i45, i54) -> f920_0_gcd_Store(EOS(STATIC_920), i45, i54) :|: TRUE
f920_0_gcd_Store(EOS(STATIC_920), i45, i54) -> f927_0_gcd_Load(EOS(STATIC_927), i54, i45) :|: TRUE
f927_0_gcd_Load(EOS(STATIC_927), i54, i45) -> f934_0_gcd_Store(EOS(STATIC_934), i54, i45) :|: TRUE
f934_0_gcd_Store(EOS(STATIC_934), i54, i45) -> f936_0_gcd_JMP(EOS(STATIC_936), i45, i54) :|: TRUE
f936_0_gcd_JMP(EOS(STATIC_936), i45, i54) -> f956_0_gcd_Load(EOS(STATIC_956), i45, i54) :|: TRUE
f956_0_gcd_Load(EOS(STATIC_956), i45, i54) -> f332_0_gcd_Load(EOS(STATIC_332), i45, i54) :|: TRUE
f332_0_gcd_Load(EOS(STATIC_332), i19, i43) -> f337_0_gcd_EQ(EOS(STATIC_337), i19, i43, i43) :|: TRUE
f902_0_mod_LE(EOS(STATIC_902), i45, i54, i45, i54, i45) -> f908_0_mod_Load(EOS(STATIC_908), i45, i54, i45) :|: i54 > i45
f908_0_mod_Load(EOS(STATIC_908), i45, i54, i45) -> f910_0_mod_Load(EOS(STATIC_910), i45, i45, i54) :|: TRUE
f910_0_mod_Load(EOS(STATIC_910), i45, i45, i54) -> f924_0_mod_IntArithmetic(EOS(STATIC_924), i45, i45, i54, i45) :|: TRUE
f924_0_mod_IntArithmetic(EOS(STATIC_924), i45, i45, i54, i45) -> f933_0_mod_Store(EOS(STATIC_933), i45, i45, i54 - i45) :|: i54 > 0 && i45 > 0
f933_0_mod_Store(EOS(STATIC_933), i45, i45, i74) -> f935_0_mod_JMP(EOS(STATIC_935), i45, i74, i45) :|: TRUE
f935_0_mod_JMP(EOS(STATIC_935), i45, i74, i45) -> f945_0_mod_Load(EOS(STATIC_945), i45, i74, i45) :|: TRUE
f945_0_mod_Load(EOS(STATIC_945), i45, i74, i45) -> f514_0_mod_Load(EOS(STATIC_514), i45, i74, i45) :|: TRUE
f380_0_mod_NE(EOS(STATIC_380), i45, i45, i45, i45, i45) -> f384_0_mod_ConstantStackPush(EOS(STATIC_384), i45) :|: TRUE
f384_0_mod_ConstantStackPush(EOS(STATIC_384), i45) -> f389_0_mod_Return(EOS(STATIC_389), i45, 0) :|: TRUE
f389_0_mod_Return(EOS(STATIC_389), i45, matching1) -> f392_0_gcd_Store(EOS(STATIC_392), i45, 0) :|: TRUE && matching1 = 0
f392_0_gcd_Store(EOS(STATIC_392), i45, matching1) -> f482_0_gcd_Store(EOS(STATIC_482), i45, 0) :|: TRUE && matching1 = 0
f482_0_gcd_Store(EOS(STATIC_482), i45, i19) -> f920_0_gcd_Store(EOS(STATIC_920), i45, i19) :|: TRUE
Combined rules. Obtained 5 IRulesP rules:
f898_0_mod_LE(EOS(STATIC_898), i45:0, i54:0, i45:0, i54:0, i45:0) -> f898_0_mod_LE(EOS(STATIC_898), i45:0, i54:0 - i45:0, i45:0, i54:0 - i45:0, i45:0) :|: i54:0 > i45:0 && i54:0 > 0 && i45:0 > 0
f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i45:0, i45:0) -> f898_0_mod_LE(EOS(STATIC_898), i45:0, i19:0, i45:0, i19:0, i45:0) :|: i45:0 > 0 && i19:0 > -1 && i45:0 > i19:0
f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i45:0, i45:0) -> f898_0_mod_LE(EOS(STATIC_898), i45:0, i19:0, i45:0, i19:0, i45:0) :|: i45:0 > 0 && i19:0 > -1 && i45:0 < i19:0
f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i19:0, i19:0) -> f337_0_gcd_EQ(EOS(STATIC_337), i19:0, 0, 0) :|: i19:0 > 0
f898_0_mod_LE(EOS(STATIC_898), i45:0, i54:0, i45:0, i54:0, i45:0) -> f337_0_gcd_EQ(EOS(STATIC_337), i45:0, i54:0, i54:0) :|: i54:0 <= i45:0
Filtered constant ground arguments:
   f898_0_mod_LE(x1, x2, x3, x4, x5, x6) -> f898_0_mod_LE(x2, x3, x4, x5, x6)
   f337_0_gcd_EQ(x1, x2, x3, x4) -> f337_0_gcd_EQ(x2, x3, x4)
Filtered duplicate arguments:
   f898_0_mod_LE(x1, x2, x3, x4, x5) -> f898_0_mod_LE(x4, x5)
   f337_0_gcd_EQ(x1, x2, x3) -> f337_0_gcd_EQ(x1, x3)
Finished conversion. Obtained 5 rules.P rules:
f898_0_mod_LE(i54:0, i45:0) -> f898_0_mod_LE(i54:0 - i45:0, i45:0) :|: i54:0 > 0 && i45:0 > 0 && i54:0 > i45:0
f337_0_gcd_EQ(i19:0, i45:0) -> f898_0_mod_LE(i19:0, i45:0) :|: i19:0 > -1 && i45:0 > i19:0 && i45:0 > 0
f337_0_gcd_EQ(i19:0, i45:0) -> f898_0_mod_LE(i19:0, i45:0) :|: i19:0 > -1 && i45:0 < i19:0 && i45:0 > 0
f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
f898_0_mod_LE(i54:0, i45:0) -> f337_0_gcd_EQ(i45:0, i54:0) :|: i54:0 <= i45:0

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

(8)
Obligation:
Rules:
f898_0_mod_LE(i54:0, i45:0) -> f898_0_mod_LE(i54:0 - i45:0, i45:0) :|: i54:0 > 0 && i45:0 > 0 && i54:0 > i45:0
f337_0_gcd_EQ(x, x1) -> f898_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
f337_0_gcd_EQ(x2, x3) -> f898_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
f898_0_mod_LE(x4, x5) -> f337_0_gcd_EQ(x5, x4) :|: x4 <= x5

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

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

(10)
Obligation:
Rules:
f898_0_mod_LE(i54:0, i45:0) -> f898_0_mod_LE(arith, i45:0) :|: i54:0 > 0 && i45:0 > 0 && i54:0 > i45:0 && arith = i54:0 - i45:0
f337_0_gcd_EQ(x, x1) -> f898_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
f337_0_gcd_EQ(x2, x3) -> f898_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
f898_0_mod_LE(x4, x5) -> f337_0_gcd_EQ(x5, x4) :|: x4 <= x5

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f898_0_mod_LE(i54:0, i45:0) -> f898_0_mod_LE(arith, i45:0) :|: i54:0 > 0 && i45:0 > 0 && i54:0 > i45:0 && arith = i54:0 - i45:0
(2) f337_0_gcd_EQ(x, x1) -> f898_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
(3) f337_0_gcd_EQ(x2, x3) -> f898_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
(4) f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
(5) f898_0_mod_LE(x4, x5) -> f337_0_gcd_EQ(x5, x4) :|: x4 <= x5

Arcs:
(1) -> (1), (5)
(2) -> (5)
(3) -> (1)
(5) -> (3), (4)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f898_0_mod_LE(i54:0, i45:0) -> f898_0_mod_LE(arith, i45:0) :|: i54:0 > 0 && i45:0 > 0 && i54:0 > i45:0 && arith = i54:0 - i45:0
(2) f337_0_gcd_EQ(x2, x3) -> f898_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
(3) f898_0_mod_LE(x4, x5) -> f337_0_gcd_EQ(x5, x4) :|: x4 <= x5

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f898_0_mod_LE(x4:0, x5:0) -> f898_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(i54:0:0 - i45:0:0, i45:0:0) :|: i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f898_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f898_0_mod_LE(x4:0, x5:0) -> f898_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(c, i45:0:0) :|: c = i54:0:0 - i45:0:0 && (i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0)

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f898_0_mod_LE(x, x1)] = x1

The following rules are decreasing:
f898_0_mod_LE(x4:0, x5:0) -> f898_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0
The following rules are bounded:
f898_0_mod_LE(x4:0, x5:0) -> f898_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(c, i45:0:0) :|: c = i54:0:0 - i45:0:0 && (i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0)

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

(18)
Obligation:
Rules:
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(c, i45:0:0) :|: c = i54:0:0 - i45:0:0 && (i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0)

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

(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f898_0_mod_LE(x, x1)] = x

The following rules are decreasing:
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(c, i45:0:0) :|: c = i54:0:0 - i45:0:0 && (i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0)
The following rules are bounded:
f898_0_mod_LE(i54:0:0, i45:0:0) -> f898_0_mod_LE(c, i45:0:0) :|: c = i54:0:0 - i45:0:0 && (i54:0:0 > 0 && i45:0:0 > 0 && i54:0:0 > i45:0:0)

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

(20)
YES