/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 95 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 337 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 145 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 116 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 15 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
public class CountUpRound{
  public static int round (int x) {

    if (x % 2 == 0) return x;
    else return x+1;
  }


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



    while (x > y) {

      y = round(y+1);

    }


  }

}


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 CountUpRound{
  public static int round (int x) {

    if (x % 2 == 0) return x;
    else return x+1;
  }


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



    while (x > y) {

      y = round(y+1);

    }


  }

}


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:
CountUpRound.main([Ljava/lang/String;)V: Graph of 193 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: CountUpRound.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 27 IRulesP rules:
f282_0_main_Load(EOS(STATIC_282), i19, i42, i19) -> f285_0_main_LE(EOS(STATIC_285), i19, i42, i19, i42) :|: TRUE
f285_0_main_LE(EOS(STATIC_285), i19, i42, i19, i42) -> f290_0_main_LE(EOS(STATIC_290), i19, i42, i19, i42) :|: i19 > i42
f290_0_main_LE(EOS(STATIC_290), i19, i42, i19, i42) -> f298_0_main_Load(EOS(STATIC_298), i19, i42) :|: i19 > i42
f298_0_main_Load(EOS(STATIC_298), i19, i42) -> f308_0_main_ConstantStackPush(EOS(STATIC_308), i19, i42) :|: TRUE
f308_0_main_ConstantStackPush(EOS(STATIC_308), i19, i42) -> f315_0_main_IntArithmetic(EOS(STATIC_315), i19, i42, 1) :|: TRUE
f315_0_main_IntArithmetic(EOS(STATIC_315), i19, i42, matching1) -> f323_0_main_InvokeMethod(EOS(STATIC_323), i19, i42 + 1) :|: i42 >= 0 && matching1 = 1
f323_0_main_InvokeMethod(EOS(STATIC_323), i19, i45) -> f336_0_round_Load(EOS(STATIC_336), i19, i45) :|: TRUE
f336_0_round_Load(EOS(STATIC_336), i19, i45) -> f357_0_round_ConstantStackPush(EOS(STATIC_357), i19, i45, i45) :|: TRUE
f357_0_round_ConstantStackPush(EOS(STATIC_357), i19, i45, i45) -> f366_0_round_IntArithmetic(EOS(STATIC_366), i19, i45, i45, 2) :|: TRUE
f366_0_round_IntArithmetic(EOS(STATIC_366), i19, i45, i45, matching1) -> f369_0_round_NE(EOS(STATIC_369), i19, i45, i45 % 2) :|: TRUE && matching1 = 2
f369_0_round_NE(EOS(STATIC_369), i19, i45, matching1) -> f372_0_round_NE(EOS(STATIC_372), i19, i45, 1) :|: TRUE && matching1 = 1
f369_0_round_NE(EOS(STATIC_369), i19, i45, matching1) -> f373_0_round_NE(EOS(STATIC_373), i19, i45, 0) :|: TRUE && matching1 = 0
f372_0_round_NE(EOS(STATIC_372), i19, i45, matching1) -> f375_0_round_Load(EOS(STATIC_375), i19, i45) :|: 1 > 0 && matching1 = 1
f375_0_round_Load(EOS(STATIC_375), i19, i45) -> f378_0_round_ConstantStackPush(EOS(STATIC_378), i19, i45) :|: TRUE
f378_0_round_ConstantStackPush(EOS(STATIC_378), i19, i45) -> f381_0_round_IntArithmetic(EOS(STATIC_381), i19, i45, 1) :|: TRUE
f381_0_round_IntArithmetic(EOS(STATIC_381), i19, i45, matching1) -> f384_0_round_Return(EOS(STATIC_384), i19, i45 + 1) :|: i45 > 0 && matching1 = 1
f384_0_round_Return(EOS(STATIC_384), i19, i49) -> f386_0_main_Store(EOS(STATIC_386), i19, i49) :|: TRUE
f386_0_main_Store(EOS(STATIC_386), i19, i49) -> f414_0_main_JMP(EOS(STATIC_414), i19, i49) :|: TRUE
f414_0_main_JMP(EOS(STATIC_414), i19, i49) -> f797_0_main_Load(EOS(STATIC_797), i19, i49) :|: TRUE
f797_0_main_Load(EOS(STATIC_797), i19, i49) -> f279_0_main_Load(EOS(STATIC_279), i19, i49) :|: TRUE
f279_0_main_Load(EOS(STATIC_279), i19, i42) -> f282_0_main_Load(EOS(STATIC_282), i19, i42, i19) :|: TRUE
f373_0_round_NE(EOS(STATIC_373), i19, i45, matching1) -> f376_0_round_Load(EOS(STATIC_376), i19, i45) :|: TRUE && matching1 = 0
f376_0_round_Load(EOS(STATIC_376), i19, i45) -> f379_0_round_Return(EOS(STATIC_379), i19, i45) :|: TRUE
f379_0_round_Return(EOS(STATIC_379), i19, i45) -> f382_0_main_Store(EOS(STATIC_382), i19, i45) :|: TRUE
f382_0_main_Store(EOS(STATIC_382), i19, i45) -> f385_0_main_JMP(EOS(STATIC_385), i19, i45) :|: TRUE
f385_0_main_JMP(EOS(STATIC_385), i19, i45) -> f410_0_main_Load(EOS(STATIC_410), i19, i45) :|: TRUE
f410_0_main_Load(EOS(STATIC_410), i19, i45) -> f279_0_main_Load(EOS(STATIC_279), i19, i45) :|: TRUE
Combined rules. Obtained 4 IRulesP rules:
f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load'(EOS(STATIC_282), i19:0, i42:0, i19:0) :|: i42:0 < i19:0 && i42:0 > -1 && i42:0 + 1 - 2 * div = 1
f282_0_main_Load'(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0 + 2, i19:0) :|: i42:0 < i19:0 && i42:0 > -1 && i42:0 + 1 - 2 * div = 1 && i42:0 + 1 - 2 * div < 2 && i42:0 + 1 - 2 * div > -2
f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load'(EOS(STATIC_282), i19:0, i42:0, i19:0) :|: i42:0 < i19:0 && i42:0 + 1 - 2 * div = 0 && i42:0 > -1
f282_0_main_Load'(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0 + 1, i19:0) :|: i42:0 < i19:0 && i42:0 > -1 && i42:0 + 1 - 2 * div = 0 && i42:0 + 1 - 2 * div < 2 && i42:0 + 1 - 2 * div > -2
Filtered constant ground arguments:
   f282_0_main_Load(x1, x2, x3, x4) -> f282_0_main_Load(x2, x3, x4)
   f282_0_main_Load'(x1, x2, x3, x4) -> f282_0_main_Load'(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f282_0_main_Load(x1, x2, x3) -> f282_0_main_Load(x2, x3)
   f282_0_main_Load'(x1, x2, x3) -> f282_0_main_Load'(x2, x3)
Finished conversion. Obtained 4 rules.P rules:
f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load'(i42:0, i19:0) :|: i42:0 > -1 && i42:0 + 1 - 2 * div = 1 && i42:0 < i19:0
f282_0_main_Load'(i42:0, i19:0) -> f282_0_main_Load(i42:0 + 2, i19:0) :|: i42:0 > -1 && i42:0 < i19:0 && i42:0 + 1 - 2 * div = 1 && i42:0 + 1 - 2 * div > -2 && i42:0 + 1 - 2 * div < 2
f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load'(i42:0, i19:0) :|: i42:0 + 1 - 2 * div = 0 && i42:0 > -1 && i42:0 < i19:0
f282_0_main_Load'(i42:0, i19:0) -> f282_0_main_Load(i42:0 + 1, i19:0) :|: i42:0 > -1 && i42:0 < i19:0 && i42:0 + 1 - 2 * div = 0 && i42:0 + 1 - 2 * div > -2 && i42:0 + 1 - 2 * div < 2

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(8)
Obligation:
Rules:
f282_0_main_Load(x, x1) -> f282_0_main_Load'(x, x1) :|: x > -1 && x + 1 - 2 * x2 = 1 && x < x1
f282_0_main_Load'(x3, x4) -> f282_0_main_Load(x3 + 2, x4) :|: x3 > -1 && x3 < x4 && x3 + 1 - 2 * x5 = 1 && x3 + 1 - 2 * x5 > -2 && x3 + 1 - 2 * x5 < 2
f282_0_main_Load(x6, x7) -> f282_0_main_Load'(x6, x7) :|: x6 + 1 - 2 * x8 = 0 && x6 > -1 && x6 < x7
f282_0_main_Load'(x9, x10) -> f282_0_main_Load(x9 + 1, x10) :|: x9 > -1 && x9 < x10 && x9 + 1 - 2 * x11 = 0 && x9 + 1 - 2 * x11 > -2 && x9 + 1 - 2 * x11 < 2

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

(10)
Obligation:
Rules:
f282_0_main_Load(x, x1) -> f282_0_main_Load'(x, x1) :|: x > -1 && x + 1 - 2 * x2 = 1 && x < x1
f282_0_main_Load'(x3, x4) -> f282_0_main_Load(arith, x4) :|: x3 > -1 && x3 < x4 && x3 + 1 - 2 * x5 = 1 && x3 + 1 - 2 * x5 > -2 && x3 + 1 - 2 * x5 < 2 && arith = x3 + 2
f282_0_main_Load(x6, x7) -> f282_0_main_Load'(x6, x7) :|: x6 + 1 - 2 * x8 = 0 && x6 > -1 && x6 < x7
f282_0_main_Load'(x12, x13) -> f282_0_main_Load(x14, x13) :|: x12 > -1 && x12 < x13 && x12 + 1 - 2 * x15 = 0 && x12 + 1 - 2 * x15 > -2 && x12 + 1 - 2 * x15 < 2 && x14 = x12 + 1

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f282_0_main_Load(x, x1) -> f282_0_main_Load'(x, x1) :|: x > -1 && x + 1 - 2 * x2 = 1 && x < x1
(2) f282_0_main_Load'(x3, x4) -> f282_0_main_Load(arith, x4) :|: x3 > -1 && x3 < x4 && x3 + 1 - 2 * x5 = 1 && x3 + 1 - 2 * x5 > -2 && x3 + 1 - 2 * x5 < 2 && arith = x3 + 2
(3) f282_0_main_Load(x6, x7) -> f282_0_main_Load'(x6, x7) :|: x6 + 1 - 2 * x8 = 0 && x6 > -1 && x6 < x7
(4) f282_0_main_Load'(x12, x13) -> f282_0_main_Load(x14, x13) :|: x12 > -1 && x12 < x13 && x12 + 1 - 2 * x15 = 0 && x12 + 1 - 2 * x15 > -2 && x12 + 1 - 2 * x15 < 2 && x14 = x12 + 1

Arcs:
(1) -> (2)
(2) -> (1)
(3) -> (4)
(4) -> (1)

This digraph is fully evaluated!
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(12)
Obligation:

Termination digraph:
Nodes:
(1) f282_0_main_Load(x, x1) -> f282_0_main_Load'(x, x1) :|: x > -1 && x + 1 - 2 * x2 = 1 && x < x1
(2) f282_0_main_Load'(x3, x4) -> f282_0_main_Load(arith, x4) :|: x3 > -1 && x3 < x4 && x3 + 1 - 2 * x5 = 1 && x3 + 1 - 2 * x5 > -2 && x3 + 1 - 2 * x5 < 2 && arith = x3 + 2

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

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f282_0_main_Load(x:0, x1:0) -> f282_0_main_Load(x:0 + 2, x1:0) :|: x:0 + 1 - 2 * x2:0 = 1 && x:0 + 1 - 2 * x5:0 < 2 && x:0 + 1 - 2 * x5:0 > -2 && x:0 + 1 - 2 * x5:0 = 1 && x:0 < x1:0 && x:0 > -1

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f282_0_main_Load(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f282_0_main_Load(x:0, x1:0) -> f282_0_main_Load(c, x1:0) :|: c = x:0 + 2 && (x:0 + 1 - 2 * x2:0 = 1 && x:0 + 1 - 2 * x5:0 < 2 && x:0 + 1 - 2 * x5:0 > -2 && x:0 + 1 - 2 * x5:0 = 1 && x:0 < x1:0 && x:0 > -1)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f282_0_main_Load(x, x1)] = -x + x1

The following rules are decreasing:
f282_0_main_Load(x:0, x1:0) -> f282_0_main_Load(c, x1:0) :|: c = x:0 + 2 && (x:0 + 1 - 2 * x2:0 = 1 && x:0 + 1 - 2 * x5:0 < 2 && x:0 + 1 - 2 * x5:0 > -2 && x:0 + 1 - 2 * x5:0 = 1 && x:0 < x1:0 && x:0 > -1)
The following rules are bounded:
f282_0_main_Load(x:0, x1:0) -> f282_0_main_Load(c, x1:0) :|: c = x:0 + 2 && (x:0 + 1 - 2 * x2:0 = 1 && x:0 + 1 - 2 * x5:0 < 2 && x:0 + 1 - 2 * x5:0 > -2 && x:0 + 1 - 2 * x5:0 = 1 && x:0 < x1:0 && x:0 > -1)

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(18)
YES