/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 95 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 313 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 93 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 47 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 53 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
(20) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class GCD4 {
  public static int mod(int a, int b) {
    while(a>=b && b > 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 GCD4 {
  public static int mod(int a, int b) {
    while(a>=b && b > 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:
GCD4.main([Ljava/lang/String;)V: Graph of 210 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: GCD4.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 33 IRulesP rules:
f342_0_gcd_LE(EOS(STATIC_342), i19, i46, i46) -> f346_0_gcd_LE(EOS(STATIC_346), i19, i46, i46) :|: TRUE
f346_0_gcd_LE(EOS(STATIC_346), i19, i46, i46) -> f350_0_gcd_Load(EOS(STATIC_350), i19, i46) :|: i46 > 0
f350_0_gcd_Load(EOS(STATIC_350), i19, i46) -> f354_0_gcd_LE(EOS(STATIC_354), i19, i46, i19) :|: TRUE
f354_0_gcd_LE(EOS(STATIC_354), i47, i46, i47) -> f359_0_gcd_LE(EOS(STATIC_359), i47, i46, i47) :|: TRUE
f359_0_gcd_LE(EOS(STATIC_359), i47, i46, i47) -> f364_0_gcd_Load(EOS(STATIC_364), i47, i46) :|: i47 > 0
f364_0_gcd_Load(EOS(STATIC_364), i47, i46) -> f369_0_gcd_Store(EOS(STATIC_369), i47, i46, i46) :|: TRUE
f369_0_gcd_Store(EOS(STATIC_369), i47, i46, i46) -> f373_0_gcd_Load(EOS(STATIC_373), i47, i46, i46) :|: TRUE
f373_0_gcd_Load(EOS(STATIC_373), i47, i46, i46) -> f377_0_gcd_Load(EOS(STATIC_377), i46, i46, i47) :|: TRUE
f377_0_gcd_Load(EOS(STATIC_377), i46, i46, i47) -> f379_0_gcd_InvokeMethod(EOS(STATIC_379), i46, i47, i46) :|: TRUE
f379_0_gcd_InvokeMethod(EOS(STATIC_379), i46, i47, i46) -> f381_0_mod_Load(EOS(STATIC_381), i46, i47, i46) :|: TRUE
f381_0_mod_Load(EOS(STATIC_381), i46, i47, i46) -> f691_0_mod_Load(EOS(STATIC_691), i46, i47, i46) :|: TRUE
f691_0_mod_Load(EOS(STATIC_691), i46, i72, i46) -> f692_0_mod_Load(EOS(STATIC_692), i46, i72, i46, i72) :|: TRUE
f692_0_mod_Load(EOS(STATIC_692), i46, i72, i46, i72) -> f693_0_mod_LT(EOS(STATIC_693), i46, i72, i46, i72, i46) :|: TRUE
f693_0_mod_LT(EOS(STATIC_693), i46, i72, i46, i72, i46) -> f697_0_mod_LT(EOS(STATIC_697), i46, i72, i46, i72, i46) :|: i72 < i46
f693_0_mod_LT(EOS(STATIC_693), i46, i72, i46, i72, i46) -> f698_0_mod_LT(EOS(STATIC_698), i46, i72, i46, i72, i46) :|: i72 >= i46
f697_0_mod_LT(EOS(STATIC_697), i46, i72, i46, i72, i46) -> f706_0_mod_Load(EOS(STATIC_706), i46, i72) :|: i72 < i46
f706_0_mod_Load(EOS(STATIC_706), i46, i72) -> f709_0_mod_Return(EOS(STATIC_709), i46, i72) :|: TRUE
f709_0_mod_Return(EOS(STATIC_709), i46, i72) -> f711_0_gcd_Store(EOS(STATIC_711), i46, i72) :|: TRUE
f711_0_gcd_Store(EOS(STATIC_711), i46, i72) -> f714_0_gcd_Load(EOS(STATIC_714), i72, i46) :|: TRUE
f714_0_gcd_Load(EOS(STATIC_714), i72, i46) -> f716_0_gcd_Store(EOS(STATIC_716), i72, i46) :|: TRUE
f716_0_gcd_Store(EOS(STATIC_716), i72, i46) -> f719_0_gcd_JMP(EOS(STATIC_719), i46, i72) :|: TRUE
f719_0_gcd_JMP(EOS(STATIC_719), i46, i72) -> f725_0_gcd_Load(EOS(STATIC_725), i46, i72) :|: TRUE
f725_0_gcd_Load(EOS(STATIC_725), i46, i72) -> f337_0_gcd_Load(EOS(STATIC_337), i46, i72) :|: TRUE
f337_0_gcd_Load(EOS(STATIC_337), i19, i44) -> f342_0_gcd_LE(EOS(STATIC_342), i19, i44, i44) :|: TRUE
f698_0_mod_LT(EOS(STATIC_698), i46, i72, i46, i72, i46) -> f708_0_mod_Load(EOS(STATIC_708), i46, i72, i46) :|: i72 >= i46
f708_0_mod_Load(EOS(STATIC_708), i46, i72, i46) -> f710_0_mod_LE(EOS(STATIC_710), i46, i72, i46, i46) :|: TRUE
f710_0_mod_LE(EOS(STATIC_710), i46, i72, i46, i46) -> f712_0_mod_Load(EOS(STATIC_712), i46, i72, i46) :|: i46 > 0
f712_0_mod_Load(EOS(STATIC_712), i46, i72, i46) -> f715_0_mod_Load(EOS(STATIC_715), i46, i46, i72) :|: TRUE
f715_0_mod_Load(EOS(STATIC_715), i46, i46, i72) -> f717_0_mod_IntArithmetic(EOS(STATIC_717), i46, i46, i72, i46) :|: TRUE
f717_0_mod_IntArithmetic(EOS(STATIC_717), i46, i46, i72, i46) -> f720_0_mod_Store(EOS(STATIC_720), i46, i46, i72 - i46) :|: i72 > 0 && i46 > 0
f720_0_mod_Store(EOS(STATIC_720), i46, i46, i74) -> f726_0_mod_JMP(EOS(STATIC_726), i46, i74, i46) :|: TRUE
f726_0_mod_JMP(EOS(STATIC_726), i46, i74, i46) -> f727_0_mod_Load(EOS(STATIC_727), i46, i74, i46) :|: TRUE
f727_0_mod_Load(EOS(STATIC_727), i46, i74, i46) -> f691_0_mod_Load(EOS(STATIC_691), i46, i74, i46) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f693_0_mod_LT(EOS(STATIC_693), i46:0, i72:0, i46:0, i72:0, i46:0) -> f693_0_mod_LT(EOS(STATIC_693), i46:0, i72:0 - i46:0, i46:0, i72:0 - i46:0, i46:0) :|: i72:0 >= i46:0 && i46:0 > 0 && i72:0 > 0
f693_0_mod_LT(EOS(STATIC_693), i46:0, i72:0, i46:0, i72:0, i46:0) -> f693_0_mod_LT(EOS(STATIC_693), i72:0, i46:0, i72:0, i46:0, i72:0) :|: i72:0 > 0 && i46:0 > 0 && i72:0 < i46:0
Filtered constant ground arguments:
   f693_0_mod_LT(x1, x2, x3, x4, x5, x6) -> f693_0_mod_LT(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f693_0_mod_LT(x1, x2, x3, x4, x5) -> f693_0_mod_LT(x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(i72:0 - i46:0, i46:0) :|: i46:0 > 0 && i72:0 > 0 && i72:0 >= i46:0
f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(i46:0, i72:0) :|: i46:0 > 0 && i72:0 < i46:0 && i72:0 > 0

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

(8)
Obligation:
Rules:
f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(i72:0 - i46:0, i46:0) :|: i46:0 > 0 && i72:0 > 0 && i72:0 >= i46:0
f693_0_mod_LT(x, x1) -> f693_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:
f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(arith, i46:0) :|: i46:0 > 0 && i72:0 > 0 && i72:0 >= i46:0 && arith = i72:0 - i46:0
f693_0_mod_LT(x, x1) -> f693_0_mod_LT(x1, x) :|: x1 > 0 && x < x1 && x > 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(arith, i46:0) :|: i46:0 > 0 && i72:0 > 0 && i72:0 >= i46:0 && arith = i72:0 - i46:0
(2) f693_0_mod_LT(x, x1) -> f693_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) f693_0_mod_LT(i72:0, i46:0) -> f693_0_mod_LT(arith, i46:0) :|: i46:0 > 0 && i72:0 > 0 && i72:0 >= i46:0 && arith = i72:0 - i46:0
(2) f693_0_mod_LT(x, x1) -> f693_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:
f693_0_mod_LT(x:0, x1:0) -> f693_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(i72:0:0 - i46:0:0, i46:0:0) :|: i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f693_0_mod_LT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f693_0_mod_LT(x:0, x1:0) -> f693_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(c, i46:0:0) :|: c = i72:0:0 - i46:0:0 && (i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0)

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f693_0_mod_LT(x, x1)] = x1

The following rules are decreasing:
f693_0_mod_LT(x:0, x1:0) -> f693_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
The following rules are bounded:
f693_0_mod_LT(x:0, x1:0) -> f693_0_mod_LT(x1:0, x:0) :|: x1:0 > 0 && x:0 < x1:0 && x:0 > 0
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(c, i46:0:0) :|: c = i72:0:0 - i46:0:0 && (i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0)

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

(18)
Obligation:
Rules:
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(c, i46:0:0) :|: c = i72:0:0 - i46:0:0 && (i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0)

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

(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f693_0_mod_LT(x, x1)] = x

The following rules are decreasing:
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(c, i46:0:0) :|: c = i72:0:0 - i46:0:0 && (i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0)
The following rules are bounded:
f693_0_mod_LT(i72:0:0, i46:0:0) -> f693_0_mod_LT(c, i46:0:0) :|: c = i72:0:0 - i46:0:0 && (i46:0:0 > 0 && i72:0:0 > 0 && i72:0:0 >= i46:0:0)

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

(20)
YES