/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 119 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 312 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 5 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 111 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 33 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 48 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
(18) IntTRS
(19) PolynomialOrderProcessor [EQUIVALENT, 0 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 211 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:
f429_0_gcd_LE(EOS(STATIC_429), i52, i58, i58) -> f431_0_gcd_LE(EOS(STATIC_431), i52, i58, i58) :|: TRUE
f431_0_gcd_LE(EOS(STATIC_431), i52, i58, i58) -> f433_0_gcd_Load(EOS(STATIC_433), i52, i58) :|: i58 > 0
f433_0_gcd_Load(EOS(STATIC_433), i52, i58) -> f436_0_gcd_LE(EOS(STATIC_436), i52, i58, i52) :|: TRUE
f436_0_gcd_LE(EOS(STATIC_436), i60, i58, i60) -> f460_0_gcd_LE(EOS(STATIC_460), i60, i58, i60) :|: TRUE
f460_0_gcd_LE(EOS(STATIC_460), i60, i58, i60) -> f463_0_gcd_Load(EOS(STATIC_463), i60, i58) :|: i60 > 0
f463_0_gcd_Load(EOS(STATIC_463), i60, i58) -> f466_0_gcd_Store(EOS(STATIC_466), i60, i58, i58) :|: TRUE
f466_0_gcd_Store(EOS(STATIC_466), i60, i58, i58) -> f469_0_gcd_Load(EOS(STATIC_469), i60, i58, i58) :|: TRUE
f469_0_gcd_Load(EOS(STATIC_469), i60, i58, i58) -> f474_0_gcd_Load(EOS(STATIC_474), i58, i58, i60) :|: TRUE
f474_0_gcd_Load(EOS(STATIC_474), i58, i58, i60) -> f475_0_gcd_InvokeMethod(EOS(STATIC_475), i58, i60, i58) :|: TRUE
f475_0_gcd_InvokeMethod(EOS(STATIC_475), i58, i60, i58) -> f476_0_mod_Load(EOS(STATIC_476), i58, i60, i58) :|: TRUE
f476_0_mod_Load(EOS(STATIC_476), i58, i60, i58) -> f547_0_mod_Load(EOS(STATIC_547), i58, i60, i58) :|: TRUE
f547_0_mod_Load(EOS(STATIC_547), i58, i70, i58) -> f548_0_mod_Load(EOS(STATIC_548), i58, i70, i58, i70) :|: TRUE
f548_0_mod_Load(EOS(STATIC_548), i58, i70, i58, i70) -> f549_0_mod_LT(EOS(STATIC_549), i58, i70, i58, i70, i58) :|: TRUE
f549_0_mod_LT(EOS(STATIC_549), i58, i70, i58, i70, i58) -> f551_0_mod_LT(EOS(STATIC_551), i58, i70, i58, i70, i58) :|: i70 < i58
f549_0_mod_LT(EOS(STATIC_549), i58, i70, i58, i70, i58) -> f552_0_mod_LT(EOS(STATIC_552), i58, i70, i58, i70, i58) :|: i70 >= i58
f551_0_mod_LT(EOS(STATIC_551), i58, i70, i58, i70, i58) -> f558_0_mod_Load(EOS(STATIC_558), i58, i70) :|: i70 < i58
f558_0_mod_Load(EOS(STATIC_558), i58, i70) -> f563_0_mod_Return(EOS(STATIC_563), i58, i70) :|: TRUE
f563_0_mod_Return(EOS(STATIC_563), i58, i70) -> f565_0_gcd_Store(EOS(STATIC_565), i58, i70) :|: TRUE
f565_0_gcd_Store(EOS(STATIC_565), i58, i70) -> f567_0_gcd_Load(EOS(STATIC_567), i70, i58) :|: TRUE
f567_0_gcd_Load(EOS(STATIC_567), i70, i58) -> f569_0_gcd_Store(EOS(STATIC_569), i70, i58) :|: TRUE
f569_0_gcd_Store(EOS(STATIC_569), i70, i58) -> f571_0_gcd_JMP(EOS(STATIC_571), i58, i70) :|: TRUE
f571_0_gcd_JMP(EOS(STATIC_571), i58, i70) -> f592_0_gcd_Load(EOS(STATIC_592), i58, i70) :|: TRUE
f592_0_gcd_Load(EOS(STATIC_592), i58, i70) -> f427_0_gcd_Load(EOS(STATIC_427), i58, i70) :|: TRUE
f427_0_gcd_Load(EOS(STATIC_427), i52, i53) -> f429_0_gcd_LE(EOS(STATIC_429), i52, i53, i53) :|: TRUE
f552_0_mod_LT(EOS(STATIC_552), i58, i70, i58, i70, i58) -> f562_0_mod_Load(EOS(STATIC_562), i58, i70, i58) :|: i70 >= i58
f562_0_mod_Load(EOS(STATIC_562), i58, i70, i58) -> f564_0_mod_LE(EOS(STATIC_564), i58, i70, i58, i58) :|: TRUE
f564_0_mod_LE(EOS(STATIC_564), i58, i70, i58, i58) -> f566_0_mod_Load(EOS(STATIC_566), i58, i70, i58) :|: i58 > 0
f566_0_mod_Load(EOS(STATIC_566), i58, i70, i58) -> f568_0_mod_Load(EOS(STATIC_568), i58, i58, i70) :|: TRUE
f568_0_mod_Load(EOS(STATIC_568), i58, i58, i70) -> f570_0_mod_IntArithmetic(EOS(STATIC_570), i58, i58, i70, i58) :|: TRUE
f570_0_mod_IntArithmetic(EOS(STATIC_570), i58, i58, i70, i58) -> f578_0_mod_Store(EOS(STATIC_578), i58, i58, i70 - i58) :|: i70 > 0 && i58 > 0
f578_0_mod_Store(EOS(STATIC_578), i58, i58, i72) -> f595_0_mod_JMP(EOS(STATIC_595), i58, i72, i58) :|: TRUE
f595_0_mod_JMP(EOS(STATIC_595), i58, i72, i58) -> f601_0_mod_Load(EOS(STATIC_601), i58, i72, i58) :|: TRUE
f601_0_mod_Load(EOS(STATIC_601), i58, i72, i58) -> f547_0_mod_Load(EOS(STATIC_547), i58, i72, i58) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f549_0_mod_LT(EOS(STATIC_549), i58:0, i70:0, i58:0, i70:0, i58:0) -> f549_0_mod_LT(EOS(STATIC_549), i70:0, i58:0, i70:0, i58:0, i70:0) :|: i70:0 > 0 && i58:0 > 0 && i70:0 < i58:0
f549_0_mod_LT(EOS(STATIC_549), i58:0, i70:0, i58:0, i70:0, i58:0) -> f549_0_mod_LT(EOS(STATIC_549), i58:0, i70:0 - i58:0, i58:0, i70:0 - i58:0, i58:0) :|: i70:0 >= i58:0 && i58:0 > 0 && i70:0 > 0
Filtered constant ground arguments:
   f549_0_mod_LT(x1, x2, x3, x4, x5, x6) -> f549_0_mod_LT(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f549_0_mod_LT(x1, x2, x3, x4, x5) -> f549_0_mod_LT(x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i58:0, i70:0) :|: i58:0 > 0 && i70:0 < i58:0 && i70:0 > 0
f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i70:0 - i58:0, i58:0) :|: i58:0 > 0 && i70:0 > 0 && i70:0 >= i58:0

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

(8)
Obligation:
Rules:
f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i58:0, i70:0) :|: i58:0 > 0 && i70:0 < i58:0 && i70:0 > 0
f549_0_mod_LT(x, x1) -> f549_0_mod_LT(x - x1, x1) :|: x1 > 0 && x > 0 && x >= x1

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

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

(10)
Obligation:
Rules:
f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i58:0, i70:0) :|: i58:0 > 0 && i70:0 < i58:0 && i70:0 > 0
f549_0_mod_LT(x, x1) -> f549_0_mod_LT(arith, x1) :|: x1 > 0 && x > 0 && x >= x1 && arith = x - x1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i58:0, i70:0) :|: i58:0 > 0 && i70:0 < i58:0 && i70:0 > 0
(2) f549_0_mod_LT(x, x1) -> f549_0_mod_LT(arith, x1) :|: x1 > 0 && x > 0 && x >= x1 && arith = x - x1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f549_0_mod_LT(i70:0, i58:0) -> f549_0_mod_LT(i58:0, i70:0) :|: i58:0 > 0 && i70:0 < i58:0 && i70:0 > 0
(2) f549_0_mod_LT(x, x1) -> f549_0_mod_LT(arith, x1) :|: x1 > 0 && x > 0 && x >= x1 && arith = x - x1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(x:0 - x1:0, x1:0) :|: x1:0 > 0 && x:0 > 0 && x:0 >= x1:0
f549_0_mod_LT(i70:0:0, i58:0:0) -> f549_0_mod_LT(i58:0:0, i70:0:0) :|: i58:0:0 > 0 && i70:0:0 < i58:0:0 && i70:0:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f549_0_mod_LT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(c, x1:0) :|: c = x:0 - x1:0 && (x1:0 > 0 && x:0 > 0 && x:0 >= x1:0)
f549_0_mod_LT(i70:0:0, i58:0:0) -> f549_0_mod_LT(i58:0:0, i70:0:0) :|: i58:0:0 > 0 && i70:0:0 < i58:0:0 && i70:0:0 > 0

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f549_0_mod_LT(x, x1)] = x1

The following rules are decreasing:
f549_0_mod_LT(i70:0:0, i58:0:0) -> f549_0_mod_LT(i58:0:0, i70:0:0) :|: i58:0:0 > 0 && i70:0:0 < i58:0:0 && i70:0:0 > 0
The following rules are bounded:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(c, x1:0) :|: c = x:0 - x1:0 && (x1:0 > 0 && x:0 > 0 && x:0 >= x1:0)
f549_0_mod_LT(i70:0:0, i58:0:0) -> f549_0_mod_LT(i58:0:0, i70:0:0) :|: i58:0:0 > 0 && i70:0:0 < i58:0:0 && i70:0:0 > 0

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

(18)
Obligation:
Rules:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(c, x1:0) :|: c = x:0 - x1:0 && (x1:0 > 0 && x:0 > 0 && x:0 >= x1:0)

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f549_0_mod_LT(x, x1)] = x

The following rules are decreasing:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(c, x1:0) :|: c = x:0 - x1:0 && (x1:0 > 0 && x:0 > 0 && x:0 >= x1:0)
The following rules are bounded:
f549_0_mod_LT(x:0, x1:0) -> f549_0_mod_LT(c, x1:0) :|: c = x:0 - x1:0 && (x1:0 > 0 && x:0 > 0 && x:0 >= x1:0)

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(20)
YES