/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 249 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 115 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 37 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 32 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 0 ms]
(18) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class GCD3 {
  public static int mod(int a, int b) {
    if(b == 0) {
      return b;
    }
    if(b < 0) {
      a = -a;
    }
    if(a > 0) {
      while(a>=b) {
        a -= b;
      }
      return a;
    } else {
      while(a < 0) {
        a -= b;
      }
      return a;
    }
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b > 0 && a > 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 GCD3 {
  public static int mod(int a, int b) {
    if(b == 0) {
      return b;
    }
    if(b < 0) {
      a = -a;
    }
    if(a > 0) {
      while(a>=b) {
        a -= b;
      }
      return a;
    } else {
      while(a < 0) {
        a -= b;
      }
      return a;
    }
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b > 0 && a > 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:
GCD3.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: GCD3.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 37 IRulesP rules:
f341_0_gcd_LE(EOS(STATIC_341), i19, i46, i46) -> f352_0_gcd_LE(EOS(STATIC_352), i19, i46, i46) :|: TRUE
f352_0_gcd_LE(EOS(STATIC_352), i19, i46, i46) -> f356_0_gcd_Load(EOS(STATIC_356), i19, i46) :|: i46 > 0
f356_0_gcd_Load(EOS(STATIC_356), i19, i46) -> f360_0_gcd_LE(EOS(STATIC_360), i19, i46, i19) :|: TRUE
f360_0_gcd_LE(EOS(STATIC_360), i47, i46, i47) -> f365_0_gcd_LE(EOS(STATIC_365), i47, i46, i47) :|: TRUE
f365_0_gcd_LE(EOS(STATIC_365), i47, i46, i47) -> f370_0_gcd_Load(EOS(STATIC_370), i47, i46) :|: i47 > 0
f370_0_gcd_Load(EOS(STATIC_370), i47, i46) -> f375_0_gcd_Store(EOS(STATIC_375), i47, i46, i46) :|: TRUE
f375_0_gcd_Store(EOS(STATIC_375), i47, i46, i46) -> f379_0_gcd_Load(EOS(STATIC_379), i47, i46, i46) :|: TRUE
f379_0_gcd_Load(EOS(STATIC_379), i47, i46, i46) -> f383_0_gcd_Load(EOS(STATIC_383), i46, i46, i47) :|: TRUE
f383_0_gcd_Load(EOS(STATIC_383), i46, i46, i47) -> f385_0_gcd_InvokeMethod(EOS(STATIC_385), i46, i47, i46) :|: TRUE
f385_0_gcd_InvokeMethod(EOS(STATIC_385), i46, i47, i46) -> f387_0_mod_Load(EOS(STATIC_387), i46, i47, i46) :|: TRUE
f387_0_mod_Load(EOS(STATIC_387), i46, i47, i46) -> f390_0_mod_NE(EOS(STATIC_390), i46, i47, i46, i46) :|: TRUE
f390_0_mod_NE(EOS(STATIC_390), i46, i47, i46, i46) -> f391_0_mod_Load(EOS(STATIC_391), i46, i47, i46) :|: i46 > 0
f391_0_mod_Load(EOS(STATIC_391), i46, i47, i46) -> f392_0_mod_GE(EOS(STATIC_392), i46, i47, i46, i46) :|: TRUE
f392_0_mod_GE(EOS(STATIC_392), i46, i47, i46, i46) -> f393_0_mod_Load(EOS(STATIC_393), i46, i47, i46) :|: i46 >= 0
f393_0_mod_Load(EOS(STATIC_393), i46, i47, i46) -> f394_0_mod_LE(EOS(STATIC_394), i46, i47, i46, i47) :|: TRUE
f394_0_mod_LE(EOS(STATIC_394), i46, i47, i46, i47) -> f395_0_mod_Load(EOS(STATIC_395), i46, i47, i46) :|: i47 > 0
f395_0_mod_Load(EOS(STATIC_395), i46, i47, i46) -> f464_0_mod_Load(EOS(STATIC_464), i46, i47, i46) :|: TRUE
f464_0_mod_Load(EOS(STATIC_464), i46, i53, i46) -> f466_0_mod_Load(EOS(STATIC_466), i46, i53, i46, i53) :|: TRUE
f466_0_mod_Load(EOS(STATIC_466), i46, i53, i46, i53) -> f467_0_mod_LT(EOS(STATIC_467), i46, i53, i46, i53, i46) :|: TRUE
f467_0_mod_LT(EOS(STATIC_467), i46, i53, i46, i53, i46) -> f482_0_mod_LT(EOS(STATIC_482), i46, i53, i46, i53, i46) :|: i53 < i46
f467_0_mod_LT(EOS(STATIC_467), i46, i53, i46, i53, i46) -> f484_0_mod_LT(EOS(STATIC_484), i46, i53, i46, i53, i46) :|: i53 >= i46
f482_0_mod_LT(EOS(STATIC_482), i46, i53, i46, i53, i46) -> f486_0_mod_Load(EOS(STATIC_486), i46, i53) :|: i53 < i46
f486_0_mod_Load(EOS(STATIC_486), i46, i53) -> f500_0_mod_Return(EOS(STATIC_500), i46, i53) :|: TRUE
f500_0_mod_Return(EOS(STATIC_500), i46, i53) -> f503_0_gcd_Store(EOS(STATIC_503), i46, i53) :|: TRUE
f503_0_gcd_Store(EOS(STATIC_503), i46, i53) -> f505_0_gcd_Load(EOS(STATIC_505), i53, i46) :|: TRUE
f505_0_gcd_Load(EOS(STATIC_505), i53, i46) -> f507_0_gcd_Store(EOS(STATIC_507), i53, i46) :|: TRUE
f507_0_gcd_Store(EOS(STATIC_507), i53, i46) -> f509_0_gcd_JMP(EOS(STATIC_509), i46, i53) :|: TRUE
f509_0_gcd_JMP(EOS(STATIC_509), i46, i53) -> f531_0_gcd_Load(EOS(STATIC_531), i46, i53) :|: TRUE
f531_0_gcd_Load(EOS(STATIC_531), i46, i53) -> f322_0_gcd_Load(EOS(STATIC_322), i46, i53) :|: TRUE
f322_0_gcd_Load(EOS(STATIC_322), i19, i43) -> f341_0_gcd_LE(EOS(STATIC_341), i19, i43, i43) :|: TRUE
f484_0_mod_LT(EOS(STATIC_484), i46, i53, i46, i53, i46) -> f497_0_mod_Load(EOS(STATIC_497), i46, i53, i46) :|: i53 >= i46
f497_0_mod_Load(EOS(STATIC_497), i46, i53, i46) -> f502_0_mod_Load(EOS(STATIC_502), i46, i46, i53) :|: TRUE
f502_0_mod_Load(EOS(STATIC_502), i46, i46, i53) -> f504_0_mod_IntArithmetic(EOS(STATIC_504), i46, i46, i53, i46) :|: TRUE
f504_0_mod_IntArithmetic(EOS(STATIC_504), i46, i46, i53, i46) -> f506_0_mod_Store(EOS(STATIC_506), i46, i46, i53 - i46) :|: i53 > 0 && i46 > 0
f506_0_mod_Store(EOS(STATIC_506), i46, i46, i56) -> f508_0_mod_JMP(EOS(STATIC_508), i46, i56, i46) :|: TRUE
f508_0_mod_JMP(EOS(STATIC_508), i46, i56, i46) -> f522_0_mod_Load(EOS(STATIC_522), i46, i56, i46) :|: TRUE
f522_0_mod_Load(EOS(STATIC_522), i46, i56, i46) -> f464_0_mod_Load(EOS(STATIC_464), i46, i56, i46) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f467_0_mod_LT(EOS(STATIC_467), i46:0, i53:0, i46:0, i53:0, i46:0) -> f467_0_mod_LT(EOS(STATIC_467), i46:0, i53:0 - i46:0, i46:0, i53:0 - i46:0, i46:0) :|: i53:0 >= i46:0 && i53:0 > 0 && i46:0 > 0
f467_0_mod_LT(EOS(STATIC_467), i46:0, i53:0, i46:0, i53:0, i46:0) -> f467_0_mod_LT(EOS(STATIC_467), i53:0, i46:0, i53:0, i46:0, i53:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 < i46:0
Filtered constant ground arguments:
   f467_0_mod_LT(x1, x2, x3, x4, x5, x6) -> f467_0_mod_LT(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f467_0_mod_LT(x1, x2, x3, x4, x5) -> f467_0_mod_LT(x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(i53:0 - i46:0, i46:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 >= i46:0
f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(i46:0, i53:0) :|: i46:0 > 0 && i53:0 < i46:0 && i53:0 > 0

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

(8)
Obligation:
Rules:
f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(i53:0 - i46:0, i46:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 >= i46:0
f467_0_mod_LT(x, x1) -> f467_0_mod_LT(x1, x) :|: x1 > 0 && x < x1 && x > 0

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

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

(10)
Obligation:
Rules:
f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(arith, i46:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 >= i46:0 && arith = i53:0 - i46:0
f467_0_mod_LT(x, x1) -> f467_0_mod_LT(x1, x) :|: x1 > 0 && x < x1 && x > 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(arith, i46:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 >= i46:0 && arith = i53:0 - i46:0
(2) f467_0_mod_LT(x, x1) -> f467_0_mod_LT(x1, x) :|: x1 > 0 && x < x1 && x > 0

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f467_0_mod_LT(i53:0, i46:0) -> f467_0_mod_LT(arith, i46:0) :|: i53:0 > 0 && i46:0 > 0 && i53:0 >= i46:0 && arith = i53:0 - i46:0
(2) f467_0_mod_LT(x, x1) -> f467_0_mod_LT(x1, x) :|: x1 > 0 && x < x1 && x > 0

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f467_0_mod_LT(i53:0:0, i46:0:0) -> f467_0_mod_LT(i53:0:0 - i46:0:0, i46:0:0) :|: i53:0:0 > 0 && i46:0:0 > 0 && i53:0:0 >= i46:0:0
f467_0_mod_LT(x:0, x1:0) -> f467_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f467_0_mod_LT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f467_0_mod_LT(i53:0:0, i46:0:0) -> f467_0_mod_LT(c, i46:0:0) :|: c = i53:0:0 - i46:0:0 && (i53:0:0 > 0 && i46:0:0 > 0 && i53:0:0 >= i46:0:0)
f467_0_mod_LT(x:0, x1:0) -> f467_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0

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

(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f467_0_mod_LT ] = f467_0_mod_LT_1 + 2*f467_0_mod_LT_2

The following rules are decreasing:
f467_0_mod_LT(i53:0:0, i46:0:0) -> f467_0_mod_LT(c, i46:0:0) :|: c = i53:0:0 - i46:0:0 && (i53:0:0 > 0 && i46:0:0 > 0 && i53:0:0 >= i46:0:0)
f467_0_mod_LT(x:0, x1:0) -> f467_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0

The following rules are bounded:
f467_0_mod_LT(i53:0:0, i46:0:0) -> f467_0_mod_LT(c, i46:0:0) :|: c = i53:0:0 - i46:0:0 && (i53:0:0 > 0 && i46:0:0 > 0 && i53:0:0 >= i46:0:0)
f467_0_mod_LT(x:0, x1:0) -> f467_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0


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

(18)
YES