/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 394 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, 23 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 50 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(20) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class DivWithoutMinus{
  // adaption of the algorithm from [Kolbe 95]
  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    int y = Random.random();
    int z = y;
    int res = 0;

    while (z > 0 && (y == 0 || y > 0 && x > 0))	{

      if (y == 0) {
        res++;
        y = z;
      }
      else {
        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 DivWithoutMinus{
  // adaption of the algorithm from [Kolbe 95]
  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    int y = Random.random();
    int z = y;
    int res = 0;

    while (z > 0 && (y == 0 || y > 0 && x > 0))	{

      if (y == 0) {
        res++;
        y = z;
      }
      else {
        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:
DivWithoutMinus.main([Ljava/lang/String;)V: Graph of 202 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: DivWithoutMinus.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 26 IRulesP rules:
f2062_0_main_LE(EOS(STATIC_2062), i82, i321, i343, i343) -> f2066_0_main_LE(EOS(STATIC_2066), i82, i321, i343, i343) :|: TRUE
f2066_0_main_LE(EOS(STATIC_2066), i82, i321, i343, i343) -> f2071_0_main_Load(EOS(STATIC_2071), i82, i321, i343) :|: i343 > 0
f2071_0_main_Load(EOS(STATIC_2071), i82, i321, i343) -> f2075_0_main_EQ(EOS(STATIC_2075), i82, i321, i343, i321) :|: TRUE
f2075_0_main_EQ(EOS(STATIC_2075), i82, i348, i343, i348) -> f2077_0_main_EQ(EOS(STATIC_2077), i82, i348, i343, i348) :|: TRUE
f2075_0_main_EQ(EOS(STATIC_2075), i82, matching1, i343, matching2) -> f2078_0_main_EQ(EOS(STATIC_2078), i82, 0, i343, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f2077_0_main_EQ(EOS(STATIC_2077), i82, i348, i343, i348) -> f2081_0_main_Load(EOS(STATIC_2081), i82, i348, i343) :|: i348 > 0
f2081_0_main_Load(EOS(STATIC_2081), i82, i348, i343) -> f2086_0_main_LE(EOS(STATIC_2086), i82, i348, i343, i348) :|: TRUE
f2086_0_main_LE(EOS(STATIC_2086), i82, i348, i343, i348) -> f2090_0_main_Load(EOS(STATIC_2090), i82, i348, i343) :|: i348 > 0
f2090_0_main_Load(EOS(STATIC_2090), i82, i348, i343) -> f2095_0_main_LE(EOS(STATIC_2095), i82, i348, i343, i82) :|: TRUE
f2095_0_main_LE(EOS(STATIC_2095), i353, i348, i343, i353) -> f2103_0_main_LE(EOS(STATIC_2103), i353, i348, i343, i353) :|: TRUE
f2103_0_main_LE(EOS(STATIC_2103), i353, i348, i343, i353) -> f2120_0_main_Load(EOS(STATIC_2120), i353, i348, i343) :|: i353 > 0
f2120_0_main_Load(EOS(STATIC_2120), i353, i348, i343) -> f2126_0_main_NE(EOS(STATIC_2126), i353, i348, i343, i348) :|: TRUE
f2126_0_main_NE(EOS(STATIC_2126), i353, i348, i343, i348) -> f2188_0_main_Inc(EOS(STATIC_2188), i353, i348, i343) :|: i348 > 0
f2188_0_main_Inc(EOS(STATIC_2188), i353, i348, i343) -> f2191_0_main_Inc(EOS(STATIC_2191), i353 + -1, i348, i343) :|: TRUE
f2191_0_main_Inc(EOS(STATIC_2191), i374, i348, i343) -> f2194_0_main_JMP(EOS(STATIC_2194), i374, i348 + -1, i343) :|: TRUE
f2194_0_main_JMP(EOS(STATIC_2194), i374, i375, i343) -> f2267_0_main_Load(EOS(STATIC_2267), i374, i375, i343) :|: TRUE
f2267_0_main_Load(EOS(STATIC_2267), i374, i375, i343) -> f2055_0_main_Load(EOS(STATIC_2055), i374, i375, i343) :|: TRUE
f2055_0_main_Load(EOS(STATIC_2055), i82, i321, i322) -> f2062_0_main_LE(EOS(STATIC_2062), i82, i321, i322, i322) :|: TRUE
f2078_0_main_EQ(EOS(STATIC_2078), i82, matching1, i343, matching2) -> f2084_0_main_Load(EOS(STATIC_2084), i82, 0, i343) :|: TRUE && matching1 = 0 && matching2 = 0
f2084_0_main_Load(EOS(STATIC_2084), i82, matching1, i343) -> f2088_0_main_NE(EOS(STATIC_2088), i82, 0, i343, 0) :|: TRUE && matching1 = 0
f2088_0_main_NE(EOS(STATIC_2088), i82, matching1, i343, matching2) -> f2093_0_main_Inc(EOS(STATIC_2093), i82, i343) :|: TRUE && matching1 = 0 && matching2 = 0
f2093_0_main_Inc(EOS(STATIC_2093), i82, i343) -> f2098_0_main_Load(EOS(STATIC_2098), i82, i343) :|: TRUE
f2098_0_main_Load(EOS(STATIC_2098), i82, i343) -> f2105_0_main_Store(EOS(STATIC_2105), i82, i343, i343) :|: TRUE
f2105_0_main_Store(EOS(STATIC_2105), i82, i343, i343) -> f2123_0_main_JMP(EOS(STATIC_2123), i82, i343, i343) :|: TRUE
f2123_0_main_JMP(EOS(STATIC_2123), i82, i343, i343) -> f2186_0_main_Load(EOS(STATIC_2186), i82, i343, i343) :|: TRUE
f2186_0_main_Load(EOS(STATIC_2186), i82, i343, i343) -> f2055_0_main_Load(EOS(STATIC_2055), i82, i343, i343) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f2062_0_main_LE(EOS(STATIC_2062), i82:0, i321:0, i343:0, i343:0) -> f2062_0_main_LE(EOS(STATIC_2062), i82:0 - 1, i321:0 - 1, i343:0, i343:0) :|: i343:0 > 0 && i321:0 > 0 && i82:0 > 0
f2062_0_main_LE(EOS(STATIC_2062), i82:0, 0, i343:0, i343:0) -> f2062_0_main_LE(EOS(STATIC_2062), i82:0, i343:0, i343:0, i343:0) :|: i343:0 > 0
Filtered constant ground arguments:
   f2062_0_main_LE(x1, x2, x3, x4, x5) -> f2062_0_main_LE(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f2062_0_main_LE(x1, x2, x3, x4) -> f2062_0_main_LE(x1, x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f2062_0_main_LE(i82:0, i321:0, i343:0) -> f2062_0_main_LE(i82:0 - 1, i321:0 - 1, i343:0) :|: i321:0 > 0 && i82:0 > 0 && i343:0 > 0
f2062_0_main_LE(i82:0, cons_0, i343:0) -> f2062_0_main_LE(i82:0, i343:0, i343:0) :|: i343:0 > 0 && cons_0 = 0

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

(8)
Obligation:
Rules:
f2062_0_main_LE(i82:0, i321:0, i343:0) -> f2062_0_main_LE(i82:0 - 1, i321:0 - 1, i343:0) :|: i321:0 > 0 && i82:0 > 0 && i343:0 > 0
f2062_0_main_LE(x, x1, x2) -> f2062_0_main_LE(x, x2, x2) :|: x2 > 0 && x1 = 0

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

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

(10)
Obligation:
Rules:
f2062_0_main_LE(i82:0, i321:0, i343:0) -> f2062_0_main_LE(arith, arith1, i343:0) :|: i321:0 > 0 && i82:0 > 0 && i343:0 > 0 && arith = i82:0 - 1 && arith1 = i321:0 - 1
f2062_0_main_LE(x, x1, x2) -> f2062_0_main_LE(x, x2, x2) :|: x2 > 0 && x1 = 0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2062_0_main_LE(i82:0, i321:0, i343:0) -> f2062_0_main_LE(arith, arith1, i343:0) :|: i321:0 > 0 && i82:0 > 0 && i343:0 > 0 && arith = i82:0 - 1 && arith1 = i321:0 - 1
(2) f2062_0_main_LE(x, x1, x2) -> f2062_0_main_LE(x, x2, x2) :|: x2 > 0 && x1 = 0

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f2062_0_main_LE(i82:0, i321:0, i343:0) -> f2062_0_main_LE(arith, arith1, i343:0) :|: i321:0 > 0 && i82:0 > 0 && i343:0 > 0 && arith = i82:0 - 1 && arith1 = i321:0 - 1
(2) f2062_0_main_LE(x, x1, x2) -> f2062_0_main_LE(x, x2, x2) :|: x2 > 0 && x1 = 0

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f2062_0_main_LE(x:0, cons_0, x2:0) -> f2062_0_main_LE(x:0, x2:0, x2:0) :|: x2:0 > 0 && cons_0 = 0
f2062_0_main_LE(i82:0:0, i321:0:0, i343:0:0) -> f2062_0_main_LE(i82:0:0 - 1, i321:0:0 - 1, i343:0:0) :|: i321:0:0 > 0 && i82:0:0 > 0 && i343:0:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2062_0_main_LE(VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f2062_0_main_LE(x:0, c, x2:0) -> f2062_0_main_LE(x:0, x2:0, x2:0) :|: c = 0 && (x2:0 > 0 && cons_0 = 0)
f2062_0_main_LE(i82:0:0, i321:0:0, i343:0:0) -> f2062_0_main_LE(c1, c2, i343:0:0) :|: c2 = i321:0:0 - 1 && c1 = i82:0:0 - 1 && (i321:0:0 > 0 && i82:0:0 > 0 && i343:0:0 > 0)

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2062_0_main_LE(x, x1, x2)] = -1 + x

The following rules are decreasing:
f2062_0_main_LE(i82:0:0, i321:0:0, i343:0:0) -> f2062_0_main_LE(c1, c2, i343:0:0) :|: c2 = i321:0:0 - 1 && c1 = i82:0:0 - 1 && (i321:0:0 > 0 && i82:0:0 > 0 && i343:0:0 > 0)
The following rules are bounded:
f2062_0_main_LE(i82:0:0, i321:0:0, i343:0:0) -> f2062_0_main_LE(c1, c2, i343:0:0) :|: c2 = i321:0:0 - 1 && c1 = i82:0:0 - 1 && (i321:0:0 > 0 && i82:0:0 > 0 && i343:0:0 > 0)

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

(18)
Obligation:
Rules:
f2062_0_main_LE(x:0, c, x2:0) -> f2062_0_main_LE(x:0, x2:0, x2:0) :|: c = 0 && (x2:0 > 0 && cons_0 = 0)

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2062_0_main_LE(x, x1, x2)] = -x1

The following rules are decreasing:
f2062_0_main_LE(x:0, c, x2:0) -> f2062_0_main_LE(x:0, x2:0, x2:0) :|: c = 0 && (x2:0 > 0 && cons_0 = 0)
The following rules are bounded:
f2062_0_main_LE(x:0, c, x2:0) -> f2062_0_main_LE(x:0, x2:0, x2:0) :|: c = 0 && (x2:0 > 0 && cons_0 = 0)

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(20)
YES