/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 97 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 329 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 82 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 24 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 44 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 24 ms]
(18) YES


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

(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();
  }
}



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

(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();
  }
}



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

(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.





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

(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:

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

(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 17 IRulesP rules:
f616_0_div_Load(EOS(STATIC_616), i87, i88, i87) -> f617_0_div_LT(EOS(STATIC_617), i87, i88, i87, i88) :|: TRUE
f617_0_div_LT(EOS(STATIC_617), i87, i88, i87, i88) -> f627_0_div_LT(EOS(STATIC_627), i87, i88, i87, i88) :|: i87 >= i88
f627_0_div_LT(EOS(STATIC_627), i87, i88, i87, i88) -> f639_0_div_Load(EOS(STATIC_639), i87, i88) :|: i87 >= i88
f639_0_div_Load(EOS(STATIC_639), i87, i88) -> f642_0_div_LE(EOS(STATIC_642), i87, i88, i88) :|: TRUE
f642_0_div_LE(EOS(STATIC_642), i98, i97, i97) -> f645_0_div_LE(EOS(STATIC_645), i98, i97, i97) :|: TRUE
f645_0_div_LE(EOS(STATIC_645), i98, i97, i97) -> f650_0_div_Load(EOS(STATIC_650), i98, i97) :|: i97 > 0
f650_0_div_Load(EOS(STATIC_650), i98, i97) -> f652_0_div_Load(EOS(STATIC_652), i97, i98) :|: TRUE
f652_0_div_Load(EOS(STATIC_652), i97, i98) -> f653_0_div_IntArithmetic(EOS(STATIC_653), i97, i98, i97) :|: TRUE
f653_0_div_IntArithmetic(EOS(STATIC_653), i97, i98, i97) -> f656_0_div_Store(EOS(STATIC_656), i97, i98 - i97) :|: i98 > 0 && i97 > 0
f656_0_div_Store(EOS(STATIC_656), i97, i99) -> f658_0_div_Load(EOS(STATIC_658), i99, i97) :|: TRUE
f658_0_div_Load(EOS(STATIC_658), i99, i97) -> f661_0_div_ConstantStackPush(EOS(STATIC_661), i99, i97) :|: TRUE
f661_0_div_ConstantStackPush(EOS(STATIC_661), i99, i97) -> f664_0_div_IntArithmetic(EOS(STATIC_664), i99, i97) :|: TRUE
f664_0_div_IntArithmetic(EOS(STATIC_664), i99, i97) -> f667_0_div_Store(EOS(STATIC_667), i99, i97) :|: TRUE
f667_0_div_Store(EOS(STATIC_667), i99, i97) -> f669_0_div_JMP(EOS(STATIC_669), i99, i97) :|: TRUE
f669_0_div_JMP(EOS(STATIC_669), i99, i97) -> f702_0_div_Load(EOS(STATIC_702), i99, i97) :|: TRUE
f702_0_div_Load(EOS(STATIC_702), i99, i97) -> f613_0_div_Load(EOS(STATIC_613), i99, i97) :|: TRUE
f613_0_div_Load(EOS(STATIC_613), i87, i88) -> f616_0_div_Load(EOS(STATIC_616), i87, i88, i87) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f616_0_div_Load(EOS(STATIC_616), i87:0, i88:0, i87:0) -> f616_0_div_Load(EOS(STATIC_616), i87:0 - i88:0, i88:0, i87:0 - i88:0) :|: i88:0 <= i87:0 && i88:0 > 0 && i87:0 > 0
Filtered constant ground arguments:
   f616_0_div_Load(x1, x2, x3, x4) -> f616_0_div_Load(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f616_0_div_Load(x1, x2, x3) -> f616_0_div_Load(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f616_0_div_Load(i88:0, i87:0) -> f616_0_div_Load(i88:0, i87:0 - i88:0) :|: i88:0 > 0 && i87:0 > 0 && i88:0 <= i87:0

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

(8)
Obligation:
Rules:
f616_0_div_Load(i88:0, i87:0) -> f616_0_div_Load(i88:0, i87:0 - i88:0) :|: i88:0 > 0 && i87:0 > 0 && i88:0 <= i87:0

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

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

(10)
Obligation:
Rules:
f616_0_div_Load(i88:0, i87:0) -> f616_0_div_Load(i88:0, arith) :|: i88:0 > 0 && i87:0 > 0 && i88:0 <= i87:0 && arith = i87:0 - i88:0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f616_0_div_Load(i88:0, i87:0) -> f616_0_div_Load(i88:0, arith) :|: i88:0 > 0 && i87:0 > 0 && i88:0 <= i87:0 && arith = i87:0 - i88:0

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f616_0_div_Load(i88:0, i87:0) -> f616_0_div_Load(i88:0, arith) :|: i88:0 > 0 && i87:0 > 0 && i88:0 <= i87:0 && arith = i87:0 - i88:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f616_0_div_Load(i88:0:0, i87:0:0) -> f616_0_div_Load(i88:0:0, i87:0:0 - i88:0:0) :|: i88:0:0 > 0 && i87:0:0 > 0 && i88:0:0 <= i87:0:0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f616_0_div_Load(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f616_0_div_Load(i88:0:0, i87:0:0) -> f616_0_div_Load(i88:0:0, c) :|: c = i87:0:0 - i88:0:0 && (i88:0:0 > 0 && i87:0:0 > 0 && i88:0:0 <= i87:0:0)

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

(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f616_0_div_Load ] = f616_0_div_Load_2

The following rules are decreasing:
f616_0_div_Load(i88:0:0, i87:0:0) -> f616_0_div_Load(i88:0:0, c) :|: c = i87:0:0 - i88:0:0 && (i88:0:0 > 0 && i87:0:0 > 0 && i88:0:0 <= i87:0:0)

The following rules are bounded:
f616_0_div_Load(i88:0:0, i87:0:0) -> f616_0_div_Load(i88:0:0, c) :|: c = i87:0:0 - i88:0:0 && (i88:0:0 > 0 && i87:0:0 > 0 && i88:0:0 <= i87:0:0)


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

(18)
YES