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


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


MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could not be shown:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 474 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 51 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 67 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) IRSwTChainingProof [EQUIVALENT, 0 ms]
(16) IRSwT
(17) IRSwTTerminationDigraphProof [EQUIVALENT, 16 ms]
(18) IRSwT
(19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(20) IRSwT
(21) TempFilterProof [SOUND, 1379 ms]
(22) IRSwT
(23) IRSwTTerminationDigraphProof [EQUIVALENT, 3 ms]
(24) IRSwT
(25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(26) IRSwT


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

(0)
Obligation:
need to prove termination of the following program:
public class MinusUserDefined{
  public static boolean gt(int x, int y) {

    while (x > 0 && y > 0) {
      x--;
      y--;
    }

    return x > 0;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;

    while (gt(x,y)) {

      y++;
      res++;

    }
  }
}


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 MinusUserDefined{
  public static boolean gt(int x, int y) {

    while (x > 0 && y > 0) {
      x--;
      y--;
    }

    return x > 0;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;

    while (gt(x,y)) {

      y++;
      res++;

    }
  }
}


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:
MinusUserDefined.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: MinusUserDefined.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:
f3555_0_main_Load(EOS(STATIC_3555), i715, i716, i715) -> f3556_0_main_InvokeMethod(EOS(STATIC_3556), i715, i716, i715, i716) :|: TRUE
f3556_0_main_InvokeMethod(EOS(STATIC_3556), i715, i716, i715, i716) -> f3557_0_gt_Load(EOS(STATIC_3557), i715, i716, i715, i716) :|: TRUE
f3557_0_gt_Load(EOS(STATIC_3557), i715, i716, i715, i716) -> f3752_0_gt_Load(EOS(STATIC_3752), i715, i716, i715, i716) :|: TRUE
f3752_0_gt_Load(EOS(STATIC_3752), i733, i734, i731, i732) -> f3754_0_gt_LE(EOS(STATIC_3754), i733, i734, i731, i732, i731) :|: TRUE
f3754_0_gt_LE(EOS(STATIC_3754), i784, i734, i783, i732, i783) -> f3757_0_gt_LE(EOS(STATIC_3757), i784, i734, i783, i732, i783) :|: TRUE
f3757_0_gt_LE(EOS(STATIC_3757), i784, i734, i783, i732, i783) -> f3763_0_gt_Load(EOS(STATIC_3763), i784, i734, i783, i732) :|: i783 > 0
f3763_0_gt_Load(EOS(STATIC_3763), i784, i734, i783, i732) -> f3767_0_gt_LE(EOS(STATIC_3767), i784, i734, i783, i732, i732) :|: TRUE
f3767_0_gt_LE(EOS(STATIC_3767), i784, i734, i783, matching1, matching2) -> f3774_0_gt_LE(EOS(STATIC_3774), i784, i734, i783, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f3767_0_gt_LE(EOS(STATIC_3767), i784, i788, i783, i787, i787) -> f3775_0_gt_LE(EOS(STATIC_3775), i784, i788, i783, i787, i787) :|: TRUE
f3774_0_gt_LE(EOS(STATIC_3774), i784, i734, i783, matching1, matching2) -> f3784_0_gt_Load(EOS(STATIC_3784), i784, i734, i783) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
f3784_0_gt_Load(EOS(STATIC_3784), i784, i734, i783) -> f3792_0_gt_LE(EOS(STATIC_3792), i784, i734, i783) :|: TRUE
f3792_0_gt_LE(EOS(STATIC_3792), i784, i734, i783) -> f3800_0_gt_ConstantStackPush(EOS(STATIC_3800), i784, i734) :|: i783 > 0
f3800_0_gt_ConstantStackPush(EOS(STATIC_3800), i784, i734) -> f3808_0_gt_JMP(EOS(STATIC_3808), i784, i734, 1) :|: TRUE
f3808_0_gt_JMP(EOS(STATIC_3808), i784, i734, matching1) -> f3849_0_gt_Return(EOS(STATIC_3849), i784, i734, 1) :|: TRUE && matching1 = 1
f3849_0_gt_Return(EOS(STATIC_3849), i784, i734, matching1) -> f3850_0_main_EQ(EOS(STATIC_3850), i784, i734, 1) :|: TRUE && matching1 = 1
f3850_0_main_EQ(EOS(STATIC_3850), i784, i734, matching1) -> f3851_0_main_Inc(EOS(STATIC_3851), i784, i734) :|: 1 > 0 && matching1 = 1
f3851_0_main_Inc(EOS(STATIC_3851), i784, i734) -> f3852_0_main_Inc(EOS(STATIC_3852), i784, i734 + 1) :|: TRUE
f3852_0_main_Inc(EOS(STATIC_3852), i784, i810) -> f3853_0_main_JMP(EOS(STATIC_3853), i784, i810) :|: TRUE
f3853_0_main_JMP(EOS(STATIC_3853), i784, i810) -> f3854_0_main_Load(EOS(STATIC_3854), i784, i810) :|: TRUE
f3854_0_main_Load(EOS(STATIC_3854), i784, i810) -> f3554_0_main_Load(EOS(STATIC_3554), i784, i810) :|: TRUE
f3554_0_main_Load(EOS(STATIC_3554), i715, i716) -> f3555_0_main_Load(EOS(STATIC_3555), i715, i716, i715) :|: TRUE
f3775_0_gt_LE(EOS(STATIC_3775), i784, i788, i783, i787, i787) -> f3787_0_gt_Inc(EOS(STATIC_3787), i784, i788, i783, i787) :|: i787 > 0
f3787_0_gt_Inc(EOS(STATIC_3787), i784, i788, i783, i787) -> f3795_0_gt_Inc(EOS(STATIC_3795), i784, i788, i783 + -1, i787) :|: TRUE
f3795_0_gt_Inc(EOS(STATIC_3795), i784, i788, i795, i787) -> f3803_0_gt_JMP(EOS(STATIC_3803), i784, i788, i795, i787 + -1) :|: TRUE
f3803_0_gt_JMP(EOS(STATIC_3803), i784, i788, i795, i796) -> f3848_0_gt_Load(EOS(STATIC_3848), i784, i788, i795, i796) :|: TRUE
f3848_0_gt_Load(EOS(STATIC_3848), i784, i788, i795, i796) -> f3752_0_gt_Load(EOS(STATIC_3752), i784, i788, i795, i796) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f3767_0_gt_LE(EOS(STATIC_3767), i784:0, i734:0, i783:0, 0, 0) -> f3767_0_gt_LE(EOS(STATIC_3767), i784:0, i734:0 + 1, i784:0, i734:0 + 1, i734:0 + 1) :|: i784:0 > 0 && i783:0 > 0
f3767_0_gt_LE(EOS(STATIC_3767), i784:0, i788:0, i783:0, i787:0, i787:0) -> f3767_0_gt_LE(EOS(STATIC_3767), i784:0, i788:0, i783:0 - 1, i787:0 - 1, i787:0 - 1) :|: i783:0 > 1 && i787:0 > 0
Filtered constant ground arguments:
   f3767_0_gt_LE(x1, x2, x3, x4, x5, x6) -> f3767_0_gt_LE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f3767_0_gt_LE(x1, x2, x3, x4, x5) -> f3767_0_gt_LE(x1, x2, x3, x5)
Finished conversion. Obtained 2 rules.P rules:
f3767_0_gt_LE(i784:0, i734:0, i783:0, cons_0) -> f3767_0_gt_LE(i784:0, i734:0 + 1, i784:0, i734:0 + 1) :|: i784:0 > 0 && i783:0 > 0 && cons_0 = 0
f3767_0_gt_LE(i784:0, i788:0, i783:0, i787:0) -> f3767_0_gt_LE(i784:0, i788:0, i783:0 - 1, i787:0 - 1) :|: i783:0 > 1 && i787:0 > 0

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

(8)
Obligation:
Rules:
f3767_0_gt_LE(i784:0, i734:0, i783:0, cons_0) -> f3767_0_gt_LE(i784:0, i734:0 + 1, i784:0, i734:0 + 1) :|: i784:0 > 0 && i783:0 > 0 && cons_0 = 0
f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1, x2 - 1, x3 - 1) :|: x2 > 1 && x3 > 0

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

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

(10)
Obligation:
Rules:
f3767_0_gt_LE(i784:0, i734:0, i783:0, cons_0) -> f3767_0_gt_LE(i784:0, arith, i784:0, arith) :|: i784:0 > 0 && i783:0 > 0 && cons_0 = 0 && arith = i734:0 + 1 && arith = i734:0 + 1
f3767_0_gt_LE(x4, x5, x6, x7) -> f3767_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3767_0_gt_LE(i784:0, i734:0, i783:0, cons_0) -> f3767_0_gt_LE(i784:0, arith, i784:0, arith) :|: i784:0 > 0 && i783:0 > 0 && cons_0 = 0 && arith = i734:0 + 1 && arith = i734:0 + 1
(2) f3767_0_gt_LE(x4, x5, x6, x7) -> f3767_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f3767_0_gt_LE(i784:0, i734:0, i783:0, cons_0) -> f3767_0_gt_LE(i784:0, arith, i784:0, arith) :|: i784:0 > 0 && i783:0 > 0 && cons_0 = 0 && arith = i734:0 + 1 && arith = i734:0 + 1
(2) f3767_0_gt_LE(x4, x5, x6, x7) -> f3767_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f3767_0_gt_LE(i784:0:0, i734:0:0, i783:0:0, cons_0) -> f3767_0_gt_LE(i784:0:0, i734:0:0 + 1, i784:0:0, i734:0:0 + 1) :|: i784:0:0 > 0 && i783:0:0 > 0 && cons_0 = 0
f3767_0_gt_LE(x4:0, x5:0, x6:0, x7:0) -> f3767_0_gt_LE(x4:0, x5:0, x6:0 - 1, x7:0 - 1) :|: x6:0 > 1 && x7:0 > 0

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

(15) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(16)
Obligation:
Rules:
f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 2, x, x1 + 2) :|: TRUE && x >= 1 && x2 >= 1 && x1 = -1 && x3 = 0
f3767_0_gt_LE(x4:0, x5:0, x6:0, x7:0) -> f3767_0_gt_LE(x4:0, x5:0, x6:0 - 1, x7:0 - 1) :|: x6:0 > 1 && x7:0 > 0
f3767_0_gt_LE(x8, x9, x10, x11) -> f3767_0_gt_LE(x8, x9 + 1, x8 + -1, x9) :|: TRUE && x10 >= 1 && x8 >= 2 && x9 >= 0 && x11 = 0

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

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 2, x, x1 + 2) :|: TRUE && x >= 1 && x2 >= 1 && x1 = -1 && x3 = 0
(2) f3767_0_gt_LE(x4:0, x5:0, x6:0, x7:0) -> f3767_0_gt_LE(x4:0, x5:0, x6:0 - 1, x7:0 - 1) :|: x6:0 > 1 && x7:0 > 0
(3) f3767_0_gt_LE(x8, x9, x10, x11) -> f3767_0_gt_LE(x8, x9 + 1, x8 + -1, x9) :|: TRUE && x10 >= 1 && x8 >= 2 && x9 >= 0 && x11 = 0

Arcs:
(1) -> (2)
(2) -> (1), (2), (3)
(3) -> (2), (3)

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 2, x, x1 + 2) :|: TRUE && x >= 1 && x2 >= 1 && x1 = -1 && x3 = 0
(2) f3767_0_gt_LE(x4:0, x5:0, x6:0, x7:0) -> f3767_0_gt_LE(x4:0, x5:0, x6:0 - 1, x7:0 - 1) :|: x6:0 > 1 && x7:0 > 0
(3) f3767_0_gt_LE(x8, x9, x10, x11) -> f3767_0_gt_LE(x8, x9 + 1, x8 + -1, x9) :|: TRUE && x10 >= 1 && x8 >= 2 && x9 >= 0 && x11 = 0

Arcs:
(1) -> (2)
(2) -> (1), (2), (3)
(3) -> (2), (3)

This digraph is fully evaluated!

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

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

(20)
Obligation:
Rules:
f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0 - 1, x7:0:0 - 1) :|: x6:0:0 > 1 && x7:0:0 > 0
f3767_0_gt_LE(x:0, cons_-1, x2:0, cons_0) -> f3767_0_gt_LE(x:0, 1, x:0, 1) :|: x2:0 > 0 && x:0 > 0 && cons_-1 = -1 && cons_0 = 0
f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 1, x - 1, x1) :|: x > 1 && x2 > 0 && x1 > -1 && x3 = 0

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f3767_0_gt_LE(VARIABLE, VARIABLE, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.The following proof was generated: 
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IntTRS could not be shown:



- IntTRS
  - PolynomialOrderProcessor

Rules:
f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, c, c1) :|: c1 = x7:0:0 - 1 && c = x6:0:0 - 1 && (x6:0:0 > 1 && x7:0:0 > 0)
f3767_0_gt_LE(x:0, c2, x2:0, c3) -> f3767_0_gt_LE(x:0, c4, x:0, c5) :|: c5 = 1 && (c4 = 1 && (c3 = 0 && c2 = -1)) && (x2:0 > 0 && x:0 > 0 && cons_-1 = -1 && cons_0 = 0)
f3767_0_gt_LE(x, x1, x2, c6) -> f3767_0_gt_LE(x, c7, c8, x1) :|: c8 = x - 1 && (c7 = x1 + 1 && c6 = 0) && (x > 1 && x2 > 0 && x1 > -1 && x3 = 0)

Found the following polynomial interpretation:
[f3767_0_gt_LE(x, x1, x2, x3)] = -3 + x - 2*x1

The following rules are decreasing:
f3767_0_gt_LE(x:0, c2, x2:0, c3) -> f3767_0_gt_LE(x:0, c4, x:0, c5) :|: c5 = 1 && (c4 = 1 && (c3 = 0 && c2 = -1)) && (x2:0 > 0 && x:0 > 0 && cons_-1 = -1 && cons_0 = 0)
f3767_0_gt_LE(x, x1, x2, c6) -> f3767_0_gt_LE(x, c7, c8, x1) :|: c8 = x - 1 && (c7 = x1 + 1 && c6 = 0) && (x > 1 && x2 > 0 && x1 > -1 && x3 = 0)
The following rules are bounded:
f3767_0_gt_LE(x:0, c2, x2:0, c3) -> f3767_0_gt_LE(x:0, c4, x:0, c5) :|: c5 = 1 && (c4 = 1 && (c3 = 0 && c2 = -1)) && (x2:0 > 0 && x:0 > 0 && cons_-1 = -1 && cons_0 = 0)


- IntTRS
  - PolynomialOrderProcessor
    - IntTRS

Rules:
f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, c, c1) :|: c1 = x7:0:0 - 1 && c = x6:0:0 - 1 && (x6:0:0 > 1 && x7:0:0 > 0)
f3767_0_gt_LE(x, x1, x2, c6) -> f3767_0_gt_LE(x, c7, c8, x1) :|: c8 = x - 1 && (c7 = x1 + 1 && c6 = 0) && (x > 1 && x2 > 0 && x1 > -1 && x3 = 0)



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

(22)
Obligation:
Rules:
f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0 - 1, x7:0:0 - 1) :|: x6:0:0 > 1 && x7:0:0 > 0
f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 1, x - 1, x1) :|: x > 1 && x2 > 0 && x1 > -1 && x3 = 0

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

(23) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0 - 1, x7:0:0 - 1) :|: x6:0:0 > 1 && x7:0:0 > 0
(2) f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 1, x - 1, x1) :|: x > 1 && x2 > 0 && x1 > -1 && x3 = 0

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

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

(24)
Obligation:

Termination digraph:
Nodes:
(1) f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0, x7:0:0) -> f3767_0_gt_LE(x4:0:0, x5:0:0, x6:0:0 - 1, x7:0:0 - 1) :|: x6:0:0 > 1 && x7:0:0 > 0
(2) f3767_0_gt_LE(x, x1, x2, x3) -> f3767_0_gt_LE(x, x1 + 1, x - 1, x1) :|: x > 1 && x2 > 0 && x1 > -1 && x3 = 0

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

This digraph is fully evaluated!

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

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

(26)
Obligation:
Rules:
f3767_0_gt_LE(x4:0:0:0, x5:0:0:0, x6:0:0:0, x7:0:0:0) -> f3767_0_gt_LE(x4:0:0:0, x5:0:0:0, x6:0:0:0 - 1, x7:0:0:0 - 1) :|: x6:0:0:0 > 1 && x7:0:0:0 > 0
f3767_0_gt_LE(x:0, x1:0, x2:0, cons_0) -> f3767_0_gt_LE(x:0, x1:0 + 1, x:0 - 1, x1:0) :|: x:0 > 1 && x2:0 > 0 && x1:0 > -1 && cons_0 = 0