/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 292 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 33 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 61 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 53 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) IntTRS
(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
(20) YES


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(0)
Obligation:
need to prove termination of the following program:
public class McCarthyIterative {
  public static int main(int x) {
    int c = 1;
    while (c > 0) {
      if (x > 100) {
        x -= 10;
        c--;
      } else {
        x += 11;
        c++;
      }
    }
    return x;
  }

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


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 McCarthyIterative {
  public static int main(int x) {
    int c = 1;
    while (c > 0) {
      if (x > 100) {
        x -= 10;
        c--;
      } else {
        x += 11;
        c++;
      }
    }
    return x;
  }

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


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:
McCarthyIterative.main([Ljava/lang/String;)V: Graph of 125 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: McCarthyIterative.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:
f603_0_main_LE(EOS(STATIC_603), i89, i122, i122) -> f608_0_main_LE(EOS(STATIC_608), i89, i122, i122) :|: TRUE
f608_0_main_LE(EOS(STATIC_608), i89, i122, i122) -> f614_0_main_Load(EOS(STATIC_614), i89, i122) :|: i122 > 0
f614_0_main_Load(EOS(STATIC_614), i89, i122) -> f618_0_main_ConstantStackPush(EOS(STATIC_618), i89, i122, i89) :|: TRUE
f618_0_main_ConstantStackPush(EOS(STATIC_618), i89, i122, i89) -> f624_0_main_LE(EOS(STATIC_624), i89, i122, i89, 100) :|: TRUE
f624_0_main_LE(EOS(STATIC_624), i123, i122, i123, matching1) -> f635_0_main_LE(EOS(STATIC_635), i123, i122, i123, 100) :|: TRUE && matching1 = 100
f624_0_main_LE(EOS(STATIC_624), i124, i122, i124, matching1) -> f636_0_main_LE(EOS(STATIC_636), i124, i122, i124, 100) :|: TRUE && matching1 = 100
f635_0_main_LE(EOS(STATIC_635), i123, i122, i123, matching1) -> f647_0_main_Inc(EOS(STATIC_647), i123, i122) :|: i123 <= 100 && matching1 = 100
f647_0_main_Inc(EOS(STATIC_647), i123, i122) -> f654_0_main_Inc(EOS(STATIC_654), i123 + 11, i122) :|: TRUE
f654_0_main_Inc(EOS(STATIC_654), i125, i122) -> f660_0_main_JMP(EOS(STATIC_660), i125, i122 + 1) :|: TRUE
f660_0_main_JMP(EOS(STATIC_660), i125, i127) -> f667_0_main_Load(EOS(STATIC_667), i125, i127) :|: TRUE
f667_0_main_Load(EOS(STATIC_667), i125, i127) -> f393_0_main_Load(EOS(STATIC_393), i125, i127) :|: TRUE
f393_0_main_Load(EOS(STATIC_393), i89, i90) -> f603_0_main_LE(EOS(STATIC_603), i89, i90, i90) :|: TRUE
f636_0_main_LE(EOS(STATIC_636), i124, i122, i124, matching1) -> f651_0_main_Inc(EOS(STATIC_651), i124, i122) :|: i124 > 100 && matching1 = 100
f651_0_main_Inc(EOS(STATIC_651), i124, i122) -> f657_0_main_Inc(EOS(STATIC_657), i124 + -10, i122) :|: TRUE
f657_0_main_Inc(EOS(STATIC_657), i126, i122) -> f662_0_main_JMP(EOS(STATIC_662), i126, i122 + -1) :|: TRUE
f662_0_main_JMP(EOS(STATIC_662), i126, i128) -> f673_0_main_Load(EOS(STATIC_673), i126, i128) :|: TRUE
f673_0_main_Load(EOS(STATIC_673), i126, i128) -> f393_0_main_Load(EOS(STATIC_393), i126, i128) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f603_0_main_LE(EOS(STATIC_603), i89:0, i122:0, i122:0) -> f603_0_main_LE(EOS(STATIC_603), i89:0 + 11, i122:0 + 1, i122:0 + 1) :|: i89:0 < 101 && i122:0 > 0
f603_0_main_LE(EOS(STATIC_603), i89:0, i122:0, i122:0) -> f603_0_main_LE(EOS(STATIC_603), i89:0 - 10, i122:0 - 1, i122:0 - 1) :|: i89:0 > 100 && i122:0 > 0
Filtered constant ground arguments:
   f603_0_main_LE(x1, x2, x3, x4) -> f603_0_main_LE(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f603_0_main_LE(x1, x2, x3) -> f603_0_main_LE(x1, x3)
Finished conversion. Obtained 2 rules.P rules:
f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(i89:0 + 11, i122:0 + 1) :|: i89:0 < 101 && i122:0 > 0
f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(i89:0 - 10, i122:0 - 1) :|: i89:0 > 100 && i122:0 > 0

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(8)
Obligation:
Rules:
f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(i89:0 + 11, i122:0 + 1) :|: i89:0 < 101 && i122:0 > 0
f603_0_main_LE(x, x1) -> f603_0_main_LE(x - 10, x1 - 1) :|: x > 100 && x1 > 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:
f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(arith, arith1) :|: i89:0 < 101 && i122:0 > 0 && arith = i89:0 + 11 && arith1 = i122:0 + 1
f603_0_main_LE(x2, x3) -> f603_0_main_LE(x4, x5) :|: x2 > 100 && x3 > 0 && x4 = x2 - 10 && x5 = x3 - 1

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(arith, arith1) :|: i89:0 < 101 && i122:0 > 0 && arith = i89:0 + 11 && arith1 = i122:0 + 1
(2) f603_0_main_LE(x2, x3) -> f603_0_main_LE(x4, x5) :|: x2 > 100 && x3 > 0 && x4 = x2 - 10 && x5 = x3 - 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f603_0_main_LE(i89:0, i122:0) -> f603_0_main_LE(arith, arith1) :|: i89:0 < 101 && i122:0 > 0 && arith = i89:0 + 11 && arith1 = i122:0 + 1
(2) f603_0_main_LE(x2, x3) -> f603_0_main_LE(x4, x5) :|: x2 > 100 && x3 > 0 && x4 = x2 - 10 && x5 = x3 - 1

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

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f603_0_main_LE(i89:0:0, i122:0:0) -> f603_0_main_LE(i89:0:0 + 11, i122:0:0 + 1) :|: i89:0:0 < 101 && i122:0:0 > 0
f603_0_main_LE(x2:0, x3:0) -> f603_0_main_LE(x2:0 - 10, x3:0 - 1) :|: x2:0 > 100 && x3:0 > 0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f603_0_main_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f603_0_main_LE(i89:0:0, i122:0:0) -> f603_0_main_LE(c, c1) :|: c1 = i122:0:0 + 1 && c = i89:0:0 + 11 && (i89:0:0 < 101 && i122:0:0 > 0)
f603_0_main_LE(x2:0, x3:0) -> f603_0_main_LE(c2, c3) :|: c3 = x3:0 - 1 && c2 = x2:0 - 10 && (x2:0 > 100 && x3:0 > 0)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f603_0_main_LE(x, x1)] = 90 - x + 10*x1

The following rules are decreasing:
f603_0_main_LE(i89:0:0, i122:0:0) -> f603_0_main_LE(c, c1) :|: c1 = i122:0:0 + 1 && c = i89:0:0 + 11 && (i89:0:0 < 101 && i122:0:0 > 0)
The following rules are bounded:
f603_0_main_LE(i89:0:0, i122:0:0) -> f603_0_main_LE(c, c1) :|: c1 = i122:0:0 + 1 && c = i89:0:0 + 11 && (i89:0:0 < 101 && i122:0:0 > 0)

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

(18)
Obligation:
Rules:
f603_0_main_LE(x2:0, x3:0) -> f603_0_main_LE(c2, c3) :|: c3 = x3:0 - 1 && c2 = x2:0 - 10 && (x2:0 > 100 && x3:0 > 0)

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f603_0_main_LE ] = f603_0_main_LE_2

The following rules are decreasing:
f603_0_main_LE(x2:0, x3:0) -> f603_0_main_LE(c2, c3) :|: c3 = x3:0 - 1 && c2 = x2:0 - 10 && (x2:0 > 100 && x3:0 > 0)

The following rules are bounded:
f603_0_main_LE(x2:0, x3:0) -> f603_0_main_LE(c2, c3) :|: c3 = x3:0 - 1 && c2 = x2:0 - 10 && (x2:0 > 100 && x3:0 > 0)


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(20)
YES