/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


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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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 314 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 60 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 13 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 43 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 22 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
public class DivMinus {
  public static int div(int x, int y) {
    int res = 0;
    while (x >= y && y > 0) {
      x = x-y;
      res = res + 1;
    }
    return res;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    div(x, y);
  }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



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(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
public class DivMinus {
  public static int div(int x, int y) {
    int res = 0;
    while (x >= y && y > 0) {
      x = x-y;
      res = res + 1;
    }
    return res;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    div(x, y);
  }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



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(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
DivMinus.main([Ljava/lang/String;)V: Graph of 197 nodes with 1 SCC.





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(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: DivMinus.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:

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(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 17 IRulesP rules:
f597_0_div_Load(EOS(STATIC_597), i86, i87, i86) -> f598_0_div_LT(EOS(STATIC_598), i86, i87, i86, i87) :|: TRUE
f598_0_div_LT(EOS(STATIC_598), i86, i87, i86, i87) -> f602_0_div_LT(EOS(STATIC_602), i86, i87, i86, i87) :|: i86 >= i87
f602_0_div_LT(EOS(STATIC_602), i86, i87, i86, i87) -> f605_0_div_Load(EOS(STATIC_605), i86, i87) :|: i86 >= i87
f605_0_div_Load(EOS(STATIC_605), i86, i87) -> f609_0_div_LE(EOS(STATIC_609), i86, i87, i87) :|: TRUE
f609_0_div_LE(EOS(STATIC_609), i96, i95, i95) -> f616_0_div_LE(EOS(STATIC_616), i96, i95, i95) :|: TRUE
f616_0_div_LE(EOS(STATIC_616), i96, i95, i95) -> f626_0_div_Load(EOS(STATIC_626), i96, i95) :|: i95 > 0
f626_0_div_Load(EOS(STATIC_626), i96, i95) -> f631_0_div_Load(EOS(STATIC_631), i95, i96) :|: TRUE
f631_0_div_Load(EOS(STATIC_631), i95, i96) -> f633_0_div_IntArithmetic(EOS(STATIC_633), i95, i96, i95) :|: TRUE
f633_0_div_IntArithmetic(EOS(STATIC_633), i95, i96, i95) -> f635_0_div_Store(EOS(STATIC_635), i95, i96 - i95) :|: i96 > 0 && i95 > 0
f635_0_div_Store(EOS(STATIC_635), i95, i98) -> f636_0_div_Load(EOS(STATIC_636), i98, i95) :|: TRUE
f636_0_div_Load(EOS(STATIC_636), i98, i95) -> f637_0_div_ConstantStackPush(EOS(STATIC_637), i98, i95) :|: TRUE
f637_0_div_ConstantStackPush(EOS(STATIC_637), i98, i95) -> f638_0_div_IntArithmetic(EOS(STATIC_638), i98, i95) :|: TRUE
f638_0_div_IntArithmetic(EOS(STATIC_638), i98, i95) -> f639_0_div_Store(EOS(STATIC_639), i98, i95) :|: TRUE
f639_0_div_Store(EOS(STATIC_639), i98, i95) -> f640_0_div_JMP(EOS(STATIC_640), i98, i95) :|: TRUE
f640_0_div_JMP(EOS(STATIC_640), i98, i95) -> f662_0_div_Load(EOS(STATIC_662), i98, i95) :|: TRUE
f662_0_div_Load(EOS(STATIC_662), i98, i95) -> f592_0_div_Load(EOS(STATIC_592), i98, i95) :|: TRUE
f592_0_div_Load(EOS(STATIC_592), i86, i87) -> f597_0_div_Load(EOS(STATIC_597), i86, i87, i86) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f597_0_div_Load(EOS(STATIC_597), i86:0, i87:0, i86:0) -> f597_0_div_Load(EOS(STATIC_597), i86:0 - i87:0, i87:0, i86:0 - i87:0) :|: i87:0 <= i86:0 && i87:0 > 0 && i86:0 > 0
Filtered constant ground arguments:
   f597_0_div_Load(x1, x2, x3, x4) -> f597_0_div_Load(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f597_0_div_Load(x1, x2, x3) -> f597_0_div_Load(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f597_0_div_Load(i87:0, i86:0) -> f597_0_div_Load(i87:0, i86:0 - i87:0) :|: i87:0 > 0 && i86:0 > 0 && i87:0 <= i86:0

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(8)
Obligation:
Rules:
f597_0_div_Load(i87:0, i86:0) -> f597_0_div_Load(i87:0, i86:0 - i87:0) :|: i87:0 > 0 && i86:0 > 0 && i87:0 <= i86:0

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

(10)
Obligation:
Rules:
f597_0_div_Load(i87:0, i86:0) -> f597_0_div_Load(i87:0, arith) :|: i87:0 > 0 && i86:0 > 0 && i87:0 <= i86:0 && arith = i86:0 - i87:0

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f597_0_div_Load(i87:0, i86:0) -> f597_0_div_Load(i87:0, arith) :|: i87:0 > 0 && i86:0 > 0 && i87:0 <= i86:0 && arith = i86:0 - i87:0

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f597_0_div_Load(i87:0, i86:0) -> f597_0_div_Load(i87:0, arith) :|: i87:0 > 0 && i86:0 > 0 && i87:0 <= i86:0 && arith = i86:0 - i87:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f597_0_div_Load(i87:0:0, i86:0:0) -> f597_0_div_Load(i87:0:0, i86:0:0 - i87:0:0) :|: i87:0:0 > 0 && i86:0:0 > 0 && i87:0:0 <= i86:0:0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f597_0_div_Load(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f597_0_div_Load(i87:0:0, i86:0:0) -> f597_0_div_Load(i87:0:0, c) :|: c = i86:0:0 - i87:0:0 && (i87:0:0 > 0 && i86:0:0 > 0 && i87:0:0 <= i86:0:0)

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f597_0_div_Load ] = f597_0_div_Load_2

The following rules are decreasing:
f597_0_div_Load(i87:0:0, i86:0:0) -> f597_0_div_Load(i87:0:0, c) :|: c = i86:0:0 - i87:0:0 && (i87:0:0 > 0 && i86:0:0 > 0 && i87:0:0 <= i86:0:0)

The following rules are bounded:
f597_0_div_Load(i87:0:0, i86:0:0) -> f597_0_div_Load(i87:0:0, c) :|: c = i86:0:0 - i87:0:0 && (i87:0:0 > 0 && i86:0:0 > 0 && i87:0:0 <= i86:0:0)


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(18)
YES