/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 308 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 92 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 67 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 54 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 9 ms]
(18) IntTRS
(19) RankingReductionPairProof [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 214 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:
f469_0_gcd_EQ(EOS(STATIC_469), i52, i59, i59) -> f470_0_gcd_EQ(EOS(STATIC_470), i52, i59, i59) :|: TRUE
f470_0_gcd_EQ(EOS(STATIC_470), i52, i59, i59) -> f472_0_gcd_Load(EOS(STATIC_472), i52, i59) :|: i59 > 0
f472_0_gcd_Load(EOS(STATIC_472), i52, i59) -> f474_0_gcd_LT(EOS(STATIC_474), i52, i59, i52) :|: TRUE
f474_0_gcd_LT(EOS(STATIC_474), i52, i59, i52) -> f476_0_gcd_Load(EOS(STATIC_476), i52, i59) :|: i52 >= 0
f476_0_gcd_Load(EOS(STATIC_476), i52, i59) -> f478_0_gcd_LT(EOS(STATIC_478), i52, i59, i59) :|: TRUE
f478_0_gcd_LT(EOS(STATIC_478), i52, i59, i59) -> f483_0_gcd_Load(EOS(STATIC_483), i52, i59) :|: i59 >= 0
f483_0_gcd_Load(EOS(STATIC_483), i52, i59) -> f486_0_gcd_Store(EOS(STATIC_486), i52, i59, i59) :|: TRUE
f486_0_gcd_Store(EOS(STATIC_486), i52, i59, i59) -> f487_0_gcd_Load(EOS(STATIC_487), i52, i59, i59) :|: TRUE
f487_0_gcd_Load(EOS(STATIC_487), i52, i59, i59) -> f488_0_gcd_Load(EOS(STATIC_488), i59, i59, i52) :|: TRUE
f488_0_gcd_Load(EOS(STATIC_488), i59, i59, i52) -> f489_0_gcd_InvokeMethod(EOS(STATIC_489), i59, i52, i59) :|: TRUE
f489_0_gcd_InvokeMethod(EOS(STATIC_489), i59, i52, i59) -> f490_0_mod_Load(EOS(STATIC_490), i59, i52, i59) :|: TRUE
f490_0_mod_Load(EOS(STATIC_490), i59, i52, i59) -> f492_0_mod_Load(EOS(STATIC_492), i59, i52, i59, i52) :|: TRUE
f492_0_mod_Load(EOS(STATIC_492), i59, i52, i59, i52) -> f493_0_mod_NE(EOS(STATIC_493), i59, i52, i59, i52, i59) :|: TRUE
f493_0_mod_NE(EOS(STATIC_493), i59, i52, i59, i52, i59) -> f501_0_mod_NE(EOS(STATIC_501), i59, i52, i59, i52, i59) :|: !(i52 = i59)
f493_0_mod_NE(EOS(STATIC_493), i59, i59, i59, i59, i59) -> f502_0_mod_NE(EOS(STATIC_502), i59, i59, i59, i59, i59) :|: i52 = i59
f501_0_mod_NE(EOS(STATIC_501), i59, i52, i59, i52, i59) -> f507_0_mod_Load(EOS(STATIC_507), i59, i52, i59) :|: !(i52 = i59)
f507_0_mod_Load(EOS(STATIC_507), i59, i52, i59) -> f589_0_mod_Load(EOS(STATIC_589), i59, i52, i59) :|: TRUE
f589_0_mod_Load(EOS(STATIC_589), i59, i65, i59) -> f604_0_mod_Load(EOS(STATIC_604), i59, i65, i59, i65) :|: TRUE
f604_0_mod_Load(EOS(STATIC_604), i59, i65, i59, i65) -> f605_0_mod_LE(EOS(STATIC_605), i59, i65, i59, i65, i59) :|: TRUE
f605_0_mod_LE(EOS(STATIC_605), i59, i65, i59, i65, i59) -> f608_0_mod_LE(EOS(STATIC_608), i59, i65, i59, i65, i59) :|: i65 <= i59
f605_0_mod_LE(EOS(STATIC_605), i59, i65, i59, i65, i59) -> f609_0_mod_LE(EOS(STATIC_609), i59, i65, i59, i65, i59) :|: i65 > i59
f608_0_mod_LE(EOS(STATIC_608), i59, i65, i59, i65, i59) -> f611_0_mod_Load(EOS(STATIC_611), i59, i65) :|: i65 <= i59
f611_0_mod_Load(EOS(STATIC_611), i59, i65) -> f617_0_mod_Return(EOS(STATIC_617), i59, i65) :|: TRUE
f617_0_mod_Return(EOS(STATIC_617), i59, i65) -> f631_0_gcd_Store(EOS(STATIC_631), i59, i65) :|: TRUE
f631_0_gcd_Store(EOS(STATIC_631), i59, i65) -> f635_0_gcd_Load(EOS(STATIC_635), i65, i59) :|: TRUE
f635_0_gcd_Load(EOS(STATIC_635), i65, i59) -> f645_0_gcd_Store(EOS(STATIC_645), i65, i59) :|: TRUE
f645_0_gcd_Store(EOS(STATIC_645), i65, i59) -> f647_0_gcd_JMP(EOS(STATIC_647), i59, i65) :|: TRUE
f647_0_gcd_JMP(EOS(STATIC_647), i59, i65) -> f658_0_gcd_Load(EOS(STATIC_658), i59, i65) :|: TRUE
f658_0_gcd_Load(EOS(STATIC_658), i59, i65) -> f462_0_gcd_Load(EOS(STATIC_462), i59, i65) :|: TRUE
f462_0_gcd_Load(EOS(STATIC_462), i52, i53) -> f469_0_gcd_EQ(EOS(STATIC_469), i52, i53, i53) :|: TRUE
f609_0_mod_LE(EOS(STATIC_609), i59, i65, i59, i65, i59) -> f616_0_mod_Load(EOS(STATIC_616), i59, i65, i59) :|: i65 > i59
f616_0_mod_Load(EOS(STATIC_616), i59, i65, i59) -> f618_0_mod_Load(EOS(STATIC_618), i59, i59, i65) :|: TRUE
f618_0_mod_Load(EOS(STATIC_618), i59, i59, i65) -> f633_0_mod_IntArithmetic(EOS(STATIC_633), i59, i59, i65, i59) :|: TRUE
f633_0_mod_IntArithmetic(EOS(STATIC_633), i59, i59, i65, i59) -> f644_0_mod_Store(EOS(STATIC_644), i59, i59, i65 - i59) :|: i65 > 0 && i59 > 0
f644_0_mod_Store(EOS(STATIC_644), i59, i59, i74) -> f646_0_mod_JMP(EOS(STATIC_646), i59, i74, i59) :|: TRUE
f646_0_mod_JMP(EOS(STATIC_646), i59, i74, i59) -> f648_0_mod_Load(EOS(STATIC_648), i59, i74, i59) :|: TRUE
f648_0_mod_Load(EOS(STATIC_648), i59, i74, i59) -> f589_0_mod_Load(EOS(STATIC_589), i59, i74, i59) :|: TRUE
f502_0_mod_NE(EOS(STATIC_502), i59, i59, i59, i59, i59) -> f508_0_mod_ConstantStackPush(EOS(STATIC_508), i59) :|: TRUE
f508_0_mod_ConstantStackPush(EOS(STATIC_508), i59) -> f511_0_mod_Return(EOS(STATIC_511), i59, 0) :|: TRUE
f511_0_mod_Return(EOS(STATIC_511), i59, matching1) -> f513_0_gcd_Store(EOS(STATIC_513), i59, 0) :|: TRUE && matching1 = 0
f513_0_gcd_Store(EOS(STATIC_513), i59, matching1) -> f559_0_gcd_Store(EOS(STATIC_559), i59, 0) :|: TRUE && matching1 = 0
f559_0_gcd_Store(EOS(STATIC_559), i59, i52) -> f631_0_gcd_Store(EOS(STATIC_631), i59, i52) :|: TRUE
Combined rules. Obtained 5 IRulesP rules:
f469_0_gcd_EQ(EOS(STATIC_469), i52:0, i59:0, i59:0) -> f605_0_mod_LE(EOS(STATIC_605), i59:0, i52:0, i59:0, i52:0, i59:0) :|: i59:0 > 0 && i52:0 > -1 && i59:0 > i52:0
f469_0_gcd_EQ(EOS(STATIC_469), i52:0, i59:0, i59:0) -> f605_0_mod_LE(EOS(STATIC_605), i59:0, i52:0, i59:0, i52:0, i59:0) :|: i59:0 > 0 && i52:0 > -1 && i59:0 < i52:0
f605_0_mod_LE(EOS(STATIC_605), i59:0, i65:0, i59:0, i65:0, i59:0) -> f605_0_mod_LE(EOS(STATIC_605), i59:0, i65:0 - i59:0, i59:0, i65:0 - i59:0, i59:0) :|: i65:0 > i59:0 && i65:0 > 0 && i59:0 > 0
f605_0_mod_LE(EOS(STATIC_605), i59:0, i65:0, i59:0, i65:0, i59:0) -> f469_0_gcd_EQ(EOS(STATIC_469), i59:0, i65:0, i65:0) :|: i65:0 <= i59:0
f469_0_gcd_EQ(EOS(STATIC_469), i52:0, i52:0, i52:0) -> f469_0_gcd_EQ(EOS(STATIC_469), i52:0, 0, 0) :|: i52:0 > 0
Filtered constant ground arguments:
   f469_0_gcd_EQ(x1, x2, x3, x4) -> f469_0_gcd_EQ(x2, x3, x4)
   f605_0_mod_LE(x1, x2, x3, x4, x5, x6) -> f605_0_mod_LE(x2, x3, x4, x5, x6)
Filtered duplicate arguments:
   f469_0_gcd_EQ(x1, x2, x3) -> f469_0_gcd_EQ(x1, x3)
   f605_0_mod_LE(x1, x2, x3, x4, x5) -> f605_0_mod_LE(x4, x5)
Finished conversion. Obtained 5 rules.P rules:
f469_0_gcd_EQ(i52:0, i59:0) -> f605_0_mod_LE(i52:0, i59:0) :|: i52:0 > -1 && i59:0 > i52:0 && i59:0 > 0
f469_0_gcd_EQ(i52:0, i59:0) -> f605_0_mod_LE(i52:0, i59:0) :|: i52:0 > -1 && i59:0 < i52:0 && i59:0 > 0
f605_0_mod_LE(i65:0, i59:0) -> f605_0_mod_LE(i65:0 - i59:0, i59:0) :|: i65:0 > 0 && i59:0 > 0 && i65:0 > i59:0
f605_0_mod_LE(i65:0, i59:0) -> f469_0_gcd_EQ(i59:0, i65:0) :|: i65:0 <= i59:0
f469_0_gcd_EQ(i52:0, i52:0) -> f469_0_gcd_EQ(i52:0, 0) :|: i52:0 > 0

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

(8)
Obligation:
Rules:
f469_0_gcd_EQ(i52:0, i59:0) -> f605_0_mod_LE(i52:0, i59:0) :|: i52:0 > -1 && i59:0 > i52:0 && i59:0 > 0
f469_0_gcd_EQ(x, x1) -> f605_0_mod_LE(x, x1) :|: x > -1 && x1 < x && x1 > 0
f605_0_mod_LE(x2, x3) -> f605_0_mod_LE(x2 - x3, x3) :|: x2 > 0 && x3 > 0 && x2 > x3
f605_0_mod_LE(x4, x5) -> f469_0_gcd_EQ(x5, x4) :|: x4 <= x5
f469_0_gcd_EQ(x6, x6) -> f469_0_gcd_EQ(x6, 0) :|: x6 > 0

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

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

(10)
Obligation:
Rules:
f469_0_gcd_EQ(i52:0, i59:0) -> f605_0_mod_LE(i52:0, i59:0) :|: i52:0 > -1 && i59:0 > i52:0 && i59:0 > 0
f469_0_gcd_EQ(x, x1) -> f605_0_mod_LE(x, x1) :|: x > -1 && x1 < x && x1 > 0
f605_0_mod_LE(x2, x3) -> f605_0_mod_LE(arith, x3) :|: x2 > 0 && x3 > 0 && x2 > x3 && arith = x2 - x3
f605_0_mod_LE(x4, x5) -> f469_0_gcd_EQ(x5, x4) :|: x4 <= x5
f469_0_gcd_EQ(x6, x6) -> f469_0_gcd_EQ(x6, 0) :|: x6 > 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f469_0_gcd_EQ(i52:0, i59:0) -> f605_0_mod_LE(i52:0, i59:0) :|: i52:0 > -1 && i59:0 > i52:0 && i59:0 > 0
(2) f469_0_gcd_EQ(x, x1) -> f605_0_mod_LE(x, x1) :|: x > -1 && x1 < x && x1 > 0
(3) f605_0_mod_LE(x2, x3) -> f605_0_mod_LE(arith, x3) :|: x2 > 0 && x3 > 0 && x2 > x3 && arith = x2 - x3
(4) f605_0_mod_LE(x4, x5) -> f469_0_gcd_EQ(x5, x4) :|: x4 <= x5
(5) f469_0_gcd_EQ(x6, x6) -> f469_0_gcd_EQ(x6, 0) :|: x6 > 0

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f605_0_mod_LE(x4, x5) -> f469_0_gcd_EQ(x5, x4) :|: x4 <= x5
(2) f605_0_mod_LE(x2, x3) -> f605_0_mod_LE(arith, x3) :|: x2 > 0 && x3 > 0 && x2 > x3 && arith = x2 - x3
(3) f469_0_gcd_EQ(x, x1) -> f605_0_mod_LE(x, x1) :|: x > -1 && x1 < x && x1 > 0

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f605_0_mod_LE(x2:0, x3:0) -> f605_0_mod_LE(x2:0 - x3:0, x3:0) :|: x2:0 > 0 && x3:0 > 0 && x3:0 < x2:0
f605_0_mod_LE(x4:0, x5:0) -> f605_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f605_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f605_0_mod_LE(x2:0, x3:0) -> f605_0_mod_LE(c, x3:0) :|: c = x2:0 - x3:0 && (x2:0 > 0 && x3:0 > 0 && x3:0 < x2:0)
f605_0_mod_LE(x4:0, x5:0) -> f605_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f605_0_mod_LE(x, x1)] = -2 + x1

The following rules are decreasing:
f605_0_mod_LE(x4:0, x5:0) -> f605_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0
The following rules are bounded:
f605_0_mod_LE(x4:0, x5:0) -> f605_0_mod_LE(x5:0, x4:0) :|: x5:0 > -1 && x5:0 > x4:0 && x4:0 > 0

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

(18)
Obligation:
Rules:
f605_0_mod_LE(x2:0, x3:0) -> f605_0_mod_LE(c, x3:0) :|: c = x2:0 - x3:0 && (x2:0 > 0 && x3:0 > 0 && x3:0 < x2:0)

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f605_0_mod_LE ] = f605_0_mod_LE_1

The following rules are decreasing:
f605_0_mod_LE(x2:0, x3:0) -> f605_0_mod_LE(c, x3:0) :|: c = x2:0 - x3:0 && (x2:0 > 0 && x3:0 > 0 && x3:0 < x2:0)

The following rules are bounded:
f605_0_mod_LE(x2:0, x3:0) -> f605_0_mod_LE(c, x3:0) :|: c = x2:0 - x3:0 && (x2:0 > 0 && x3:0 > 0 && x3:0 < x2:0)


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

(20)
YES