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


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 98 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 322 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 95 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 75 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 57 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 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 221 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:
f345_0_gcd_EQ(EOS(STATIC_345), i19, i46, i46) -> f348_0_gcd_EQ(EOS(STATIC_348), i19, i46, i46) :|: TRUE
f348_0_gcd_EQ(EOS(STATIC_348), i19, i46, i46) -> f352_0_gcd_Load(EOS(STATIC_352), i19, i46) :|: i46 > 0
f352_0_gcd_Load(EOS(STATIC_352), i19, i46) -> f356_0_gcd_Store(EOS(STATIC_356), i19, i46, i46) :|: TRUE
f356_0_gcd_Store(EOS(STATIC_356), i19, i46, i46) -> f360_0_gcd_Load(EOS(STATIC_360), i19, i46, i46) :|: TRUE
f360_0_gcd_Load(EOS(STATIC_360), i19, i46, i46) -> f364_0_gcd_Load(EOS(STATIC_364), i46, i46, i19) :|: TRUE
f364_0_gcd_Load(EOS(STATIC_364), i46, i46, i19) -> f368_0_gcd_InvokeMethod(EOS(STATIC_368), i46, i19, i46) :|: TRUE
f368_0_gcd_InvokeMethod(EOS(STATIC_368), i46, i19, i46) -> f372_0_mod_Load(EOS(STATIC_372), i46, i19, i46) :|: TRUE
f372_0_mod_Load(EOS(STATIC_372), i46, i19, i46) -> f376_0_mod_LE(EOS(STATIC_376), i46, i19, i46, i19) :|: TRUE
f376_0_mod_LE(EOS(STATIC_376), i46, matching1, i46, matching2) -> f378_0_mod_LE(EOS(STATIC_378), i46, 0, i46, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f376_0_mod_LE(EOS(STATIC_376), i46, i47, i46, i47) -> f379_0_mod_LE(EOS(STATIC_379), i46, i47, i46, i47) :|: TRUE
f378_0_mod_LE(EOS(STATIC_378), i46, matching1, i46, matching2) -> f381_0_mod_ConstantStackPush(EOS(STATIC_381), i46) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
f381_0_mod_ConstantStackPush(EOS(STATIC_381), i46) -> f384_0_mod_Return(EOS(STATIC_384), i46, 0) :|: TRUE
f384_0_mod_Return(EOS(STATIC_384), i46, matching1) -> f386_0_gcd_Store(EOS(STATIC_386), i46, 0) :|: TRUE && matching1 = 0
f386_0_gcd_Store(EOS(STATIC_386), i46, matching1) -> f388_0_gcd_Load(EOS(STATIC_388), 0, i46) :|: TRUE && matching1 = 0
f388_0_gcd_Load(EOS(STATIC_388), matching1, i46) -> f390_0_gcd_Store(EOS(STATIC_390), 0, i46) :|: TRUE && matching1 = 0
f390_0_gcd_Store(EOS(STATIC_390), matching1, i46) -> f392_0_gcd_JMP(EOS(STATIC_392), i46, 0) :|: TRUE && matching1 = 0
f392_0_gcd_JMP(EOS(STATIC_392), i46, matching1) -> f438_0_gcd_Load(EOS(STATIC_438), i46, 0) :|: TRUE && matching1 = 0
f438_0_gcd_Load(EOS(STATIC_438), i46, matching1) -> f340_0_gcd_Load(EOS(STATIC_340), i46, 0) :|: TRUE && matching1 = 0
f340_0_gcd_Load(EOS(STATIC_340), i19, i44) -> f345_0_gcd_EQ(EOS(STATIC_345), i19, i44, i44) :|: TRUE
f379_0_mod_LE(EOS(STATIC_379), i46, i47, i46, i47) -> f382_0_mod_Load(EOS(STATIC_382), i46, i47, i46) :|: i47 > 0
f382_0_mod_Load(EOS(STATIC_382), i46, i47, i46) -> f385_0_mod_GT(EOS(STATIC_385), i46, i47, i46, i46) :|: TRUE
f385_0_mod_GT(EOS(STATIC_385), i46, i47, i46, i46) -> f387_0_mod_Load(EOS(STATIC_387), i46, i47, i46) :|: i46 > 0
f387_0_mod_Load(EOS(STATIC_387), i46, i47, i46) -> f389_0_mod_Load(EOS(STATIC_389), i46, i47, i46, i47) :|: TRUE
f389_0_mod_Load(EOS(STATIC_389), i46, i47, i46, i47) -> f391_0_mod_NE(EOS(STATIC_391), i46, i47, i46, i47, i46) :|: TRUE
f391_0_mod_NE(EOS(STATIC_391), i46, i47, i46, i47, i46) -> f394_0_mod_NE(EOS(STATIC_394), i46, i47, i46, i47, i46) :|: !(i47 = i46)
f391_0_mod_NE(EOS(STATIC_391), i46, i46, i46, i46, i46) -> f396_0_mod_NE(EOS(STATIC_396), i46, i46, i46, i46, i46) :|: i47 = i46
f394_0_mod_NE(EOS(STATIC_394), i46, i47, i46, i47, i46) -> f439_0_mod_Load(EOS(STATIC_439), i46, i47, i46) :|: !(i47 = i46)
f439_0_mod_Load(EOS(STATIC_439), i46, i47, i46) -> f798_0_mod_Load(EOS(STATIC_798), i46, i47, i46) :|: TRUE
f798_0_mod_Load(EOS(STATIC_798), i46, i64, i46) -> f799_0_mod_Load(EOS(STATIC_799), i46, i64, i46, i64) :|: TRUE
f799_0_mod_Load(EOS(STATIC_799), i46, i64, i46, i64) -> f800_0_mod_LE(EOS(STATIC_800), i46, i64, i46, i64, i46) :|: TRUE
f800_0_mod_LE(EOS(STATIC_800), i46, i64, i46, i64, i46) -> f819_0_mod_LE(EOS(STATIC_819), i46, i64, i46, i64, i46) :|: i64 <= i46
f800_0_mod_LE(EOS(STATIC_800), i46, i64, i46, i64, i46) -> f820_0_mod_LE(EOS(STATIC_820), i46, i64, i46, i64, i46) :|: i64 > i46
f819_0_mod_LE(EOS(STATIC_819), i46, i64, i46, i64, i46) -> f827_0_mod_Load(EOS(STATIC_827), i46, i64) :|: i64 <= i46
f827_0_mod_Load(EOS(STATIC_827), i46, i64) -> f833_0_mod_Return(EOS(STATIC_833), i46, i64) :|: TRUE
f833_0_mod_Return(EOS(STATIC_833), i46, i64) -> f835_0_gcd_Store(EOS(STATIC_835), i46, i64) :|: TRUE
f835_0_gcd_Store(EOS(STATIC_835), i46, i64) -> f837_0_gcd_Load(EOS(STATIC_837), i64, i46) :|: TRUE
f837_0_gcd_Load(EOS(STATIC_837), i64, i46) -> f843_0_gcd_Store(EOS(STATIC_843), i64, i46) :|: TRUE
f843_0_gcd_Store(EOS(STATIC_843), i64, i46) -> f845_0_gcd_JMP(EOS(STATIC_845), i46, i64) :|: TRUE
f845_0_gcd_JMP(EOS(STATIC_845), i46, i64) -> f863_0_gcd_Load(EOS(STATIC_863), i46, i64) :|: TRUE
f863_0_gcd_Load(EOS(STATIC_863), i46, i64) -> f340_0_gcd_Load(EOS(STATIC_340), i46, i64) :|: TRUE
f820_0_mod_LE(EOS(STATIC_820), i46, i64, i46, i64, i46) -> f832_0_mod_Load(EOS(STATIC_832), i46, i64, i46) :|: i64 > i46
f832_0_mod_Load(EOS(STATIC_832), i46, i64, i46) -> f834_0_mod_Load(EOS(STATIC_834), i46, i46, i64) :|: TRUE
f834_0_mod_Load(EOS(STATIC_834), i46, i46, i64) -> f836_0_mod_IntArithmetic(EOS(STATIC_836), i46, i46, i64, i46) :|: TRUE
f836_0_mod_IntArithmetic(EOS(STATIC_836), i46, i46, i64, i46) -> f838_0_mod_Store(EOS(STATIC_838), i46, i46, i64 - i46) :|: i64 > 0 && i46 > 0
f838_0_mod_Store(EOS(STATIC_838), i46, i46, i71) -> f844_0_mod_JMP(EOS(STATIC_844), i46, i71, i46) :|: TRUE
f844_0_mod_JMP(EOS(STATIC_844), i46, i71, i46) -> f855_0_mod_Load(EOS(STATIC_855), i46, i71, i46) :|: TRUE
f855_0_mod_Load(EOS(STATIC_855), i46, i71, i46) -> f798_0_mod_Load(EOS(STATIC_798), i46, i71, i46) :|: TRUE
f396_0_mod_NE(EOS(STATIC_396), i46, i46, i46, i46, i46) -> f440_0_mod_ConstantStackPush(EOS(STATIC_440), i46) :|: TRUE
f440_0_mod_ConstantStackPush(EOS(STATIC_440), i46) -> f728_0_mod_Return(EOS(STATIC_728), i46, 0) :|: TRUE
f728_0_mod_Return(EOS(STATIC_728), i46, matching1) -> f740_0_gcd_Store(EOS(STATIC_740), i46, 0) :|: TRUE && matching1 = 0
f740_0_gcd_Store(EOS(STATIC_740), i46, matching1) -> f386_0_gcd_Store(EOS(STATIC_386), i46, 0) :|: TRUE && matching1 = 0
Combined rules. Obtained 6 IRulesP rules:
f800_0_mod_LE(EOS(STATIC_800), i46:0, i64:0, i46:0, i64:0, i46:0) -> f800_0_mod_LE(EOS(STATIC_800), i46:0, i64:0 - i46:0, i46:0, i64:0 - i46:0, i46:0) :|: i64:0 > i46:0 && i64:0 > 0 && i46:0 > 0
f800_0_mod_LE(EOS(STATIC_800), i46:0, i64:0, i46:0, i64:0, i46:0) -> f345_0_gcd_EQ(EOS(STATIC_345), i46:0, i64:0, i64:0) :|: i64:0 <= i46:0
f345_0_gcd_EQ(EOS(STATIC_345), i46:0, i46:0, i46:0) -> f345_0_gcd_EQ(EOS(STATIC_345), i46:0, 0, 0) :|: i46:0 > 0
f345_0_gcd_EQ(EOS(STATIC_345), i19:0, i46:0, i46:0) -> f800_0_mod_LE(EOS(STATIC_800), i46:0, i19:0, i46:0, i19:0, i46:0) :|: i46:0 > 0 && i19:0 > 0 && i46:0 > i19:0
f345_0_gcd_EQ(EOS(STATIC_345), i19:0, i46:0, i46:0) -> f800_0_mod_LE(EOS(STATIC_800), i46:0, i19:0, i46:0, i19:0, i46:0) :|: i46:0 > 0 && i19:0 > 0 && i46:0 < i19:0
f345_0_gcd_EQ(EOS(STATIC_345), 0, i46:0, i46:0) -> f345_0_gcd_EQ(EOS(STATIC_345), i46:0, 0, 0) :|: i46:0 > 0
Filtered constant ground arguments:
   f800_0_mod_LE(x1, x2, x3, x4, x5, x6) -> f800_0_mod_LE(x2, x3, x4, x5, x6)
   f345_0_gcd_EQ(x1, x2, x3, x4) -> f345_0_gcd_EQ(x2, x3, x4)
Filtered duplicate arguments:
   f800_0_mod_LE(x1, x2, x3, x4, x5) -> f800_0_mod_LE(x4, x5)
   f345_0_gcd_EQ(x1, x2, x3) -> f345_0_gcd_EQ(x1, x3)
Finished conversion. Obtained 6 rules.P rules:
f800_0_mod_LE(i64:0, i46:0) -> f800_0_mod_LE(i64:0 - i46:0, i46:0) :|: i64:0 > 0 && i46:0 > 0 && i64:0 > i46:0
f800_0_mod_LE(i64:0, i46:0) -> f345_0_gcd_EQ(i46:0, i64:0) :|: i64:0 <= i46:0
f345_0_gcd_EQ(i46:0, i46:0) -> f345_0_gcd_EQ(i46:0, 0) :|: i46:0 > 0
f345_0_gcd_EQ(i19:0, i46:0) -> f800_0_mod_LE(i19:0, i46:0) :|: i19:0 > 0 && i46:0 > i19:0 && i46:0 > 0
f345_0_gcd_EQ(i19:0, i46:0) -> f800_0_mod_LE(i19:0, i46:0) :|: i19:0 > 0 && i46:0 < i19:0 && i46:0 > 0
f345_0_gcd_EQ(cons_0, i46:0) -> f345_0_gcd_EQ(i46:0, 0) :|: i46:0 > 0 && cons_0 = 0

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

(8)
Obligation:
Rules:
f800_0_mod_LE(i64:0, i46:0) -> f800_0_mod_LE(i64:0 - i46:0, i46:0) :|: i64:0 > 0 && i46:0 > 0 && i64:0 > i46:0
f800_0_mod_LE(x, x1) -> f345_0_gcd_EQ(x1, x) :|: x <= x1
f345_0_gcd_EQ(x2, x2) -> f345_0_gcd_EQ(x2, 0) :|: x2 > 0
f345_0_gcd_EQ(x3, x4) -> f800_0_mod_LE(x3, x4) :|: x3 > 0 && x4 > x3 && x4 > 0
f345_0_gcd_EQ(x5, x6) -> f800_0_mod_LE(x5, x6) :|: x5 > 0 && x6 < x5 && x6 > 0
f345_0_gcd_EQ(x7, x8) -> f345_0_gcd_EQ(x8, 0) :|: x8 > 0 && x7 = 0

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

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

(10)
Obligation:
Rules:
f800_0_mod_LE(i64:0, i46:0) -> f800_0_mod_LE(arith, i46:0) :|: i64:0 > 0 && i46:0 > 0 && i64:0 > i46:0 && arith = i64:0 - i46:0
f800_0_mod_LE(x, x1) -> f345_0_gcd_EQ(x1, x) :|: x <= x1
f345_0_gcd_EQ(x2, x2) -> f345_0_gcd_EQ(x2, 0) :|: x2 > 0
f345_0_gcd_EQ(x3, x4) -> f800_0_mod_LE(x3, x4) :|: x3 > 0 && x4 > x3 && x4 > 0
f345_0_gcd_EQ(x5, x6) -> f800_0_mod_LE(x5, x6) :|: x5 > 0 && x6 < x5 && x6 > 0
f345_0_gcd_EQ(x7, x8) -> f345_0_gcd_EQ(x8, 0) :|: x8 > 0 && x7 = 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f800_0_mod_LE(i64:0, i46:0) -> f800_0_mod_LE(arith, i46:0) :|: i64:0 > 0 && i46:0 > 0 && i64:0 > i46:0 && arith = i64:0 - i46:0
(2) f800_0_mod_LE(x, x1) -> f345_0_gcd_EQ(x1, x) :|: x <= x1
(3) f345_0_gcd_EQ(x2, x2) -> f345_0_gcd_EQ(x2, 0) :|: x2 > 0
(4) f345_0_gcd_EQ(x3, x4) -> f800_0_mod_LE(x3, x4) :|: x3 > 0 && x4 > x3 && x4 > 0
(5) f345_0_gcd_EQ(x5, x6) -> f800_0_mod_LE(x5, x6) :|: x5 > 0 && x6 < x5 && x6 > 0
(6) f345_0_gcd_EQ(x7, x8) -> f345_0_gcd_EQ(x8, 0) :|: x8 > 0 && x7 = 0

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f800_0_mod_LE(i64:0, i46:0) -> f800_0_mod_LE(arith, i46:0) :|: i64:0 > 0 && i46:0 > 0 && i64:0 > i46:0 && arith = i64:0 - i46:0
(2) f345_0_gcd_EQ(x5, x6) -> f800_0_mod_LE(x5, x6) :|: x5 > 0 && x6 < x5 && x6 > 0
(3) f800_0_mod_LE(x, x1) -> f345_0_gcd_EQ(x1, x) :|: x <= x1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f800_0_mod_LE(x:0, x1:0) -> f800_0_mod_LE(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(i64:0:0 - i46:0:0, i46:0:0) :|: i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f800_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f800_0_mod_LE(x:0, x1:0) -> f800_0_mod_LE(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(c, i46:0:0) :|: c = i64:0:0 - i46:0:0 && (i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0)

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f800_0_mod_LE(x, x1)] = x1

The following rules are decreasing:
f800_0_mod_LE(x:0, x1:0) -> f800_0_mod_LE(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
The following rules are bounded:
f800_0_mod_LE(x:0, x1:0) -> f800_0_mod_LE(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(c, i46:0:0) :|: c = i64:0:0 - i46:0:0 && (i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0)

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

(18)
Obligation:
Rules:
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(c, i46:0:0) :|: c = i64:0:0 - i46:0:0 && (i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0)

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

(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f800_0_mod_LE(x, x1)] = x

The following rules are decreasing:
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(c, i46:0:0) :|: c = i64:0:0 - i46:0:0 && (i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0)
The following rules are bounded:
f800_0_mod_LE(i64:0:0, i46:0:0) -> f800_0_mod_LE(c, i46:0:0) :|: c = i64:0:0 - i46:0:0 && (i64:0:0 > 0 && i46:0:0 > 0 && i64:0:0 > i46:0:0)

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

(20)
YES