Termination proof of /tmp/tmpkTTUmg/FlattenTreeListRec.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 AND

    ↳5 IDP

        ↳6 IDPNonInfProof (⇒)

        ↳7 IDP

        ↳8 IDependencyGraphProof (⇔)

        ↳9 TRUE

    ↳10 IDP

        ↳11 IDPtoQDPProof (⇒)

        ↳12 QDP

        ↳13 UsableRulesProof (⇔)

        ↳14 QDP

        ↳15 QReductionProof (⇔)

        ↳16 QDP

        ↳17 UsableRulesReductionPairsProof (⇔)

        ↳18 QDP

        ↳19 PisEmptyProof (⇔)

        ↳20 YES

    ↳21 IDP

        ↳22 IDPNonInfProof (⇒)

        ↳23 AND

            ↳24 IDP

                ↳25 IDependencyGraphProof (⇔)

                ↳26 TRUE

            ↳27 IDP

                ↳28 IDependencyGraphProof (⇔)

                ↳29 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_22 (Sun Microsystems Inc.) Main-Class: FlattenTreeListRec/FlattenTreeListRec

package FlattenTreeListRec;

public class FlattenTreeListRec {
  public static void main(String[] args) {
    Random.args = args;
    int listLength = Random.random();
    TreeList list = null;
    for (int i = listLength; i > 0; i--) {
      Tree tree = Tree.createTree();
      list = new TreeList(tree, list);
    }

    flatten(list);
  }

  public static ObjectList flatten(TreeList start) {
      if (start == null) {
        return null;
      } else {
        Tree tree = start.value;
      if (tree != null) {
        Object value = tree.value;
        start = start.next;
        start = new TreeList(tree.left, start);
        start = new TreeList(tree.right, start);
        return new ObjectList(value, flatten(start));
      } else {
        return flatten(start.next);
      }
    }
  }
}


package FlattenTreeListRec;

public class ObjectList {
  Object value;
  ObjectList next;

  public ObjectList(Object value, ObjectList next) {
    this.value = value;
    this.next = next;
  }

  public static ObjectList createList() {
    ObjectList result = null;
    int length = Random.random();
    while (length > 0) {
      result = new ObjectList(new Object(), result);
      length--;
    }
    return result;
  }
}


package FlattenTreeListRec;

public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}


package FlattenTreeListRec;

public class Tree {
  Tree left;
  Tree right;
  Object value;

  public Tree(Tree l, Tree r) {
    this.left = l;
    this.right = r;
  }

  public Tree() {
  }

  public static Tree createNode() {
    Tree result = new Tree();
    result.value = new Object();
    return result;
  }

  public static Tree createTree() {
    int counter = Random.random();
    if (counter == 0) {
      return null;
    }
    Tree result = createNode();
    Tree t = result;

    while (counter > 0) {
      int branch = Random.random();
      if (branch > 0) {
        if (t.left == null) {
          t.left = createNode();
          t = result;
        } else {
          t = t.left;
        }
      } else {
        if (t.right == null) {
          t.right = createNode();
          t = result;
        } else {
          t = t.right;
        }
      }
      counter--;
    }

    return result;
  }
}


package FlattenTreeListRec;

public class TreeList {
  Tree value;
  TreeList next;

  public TreeList(Tree value, TreeList next) {
    this.value = value;
    this.next = next;
  }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
FlattenTreeListRec.FlattenTreeListRec.main([Ljava/lang/String;)V: Graph of 162 nodes with 1 SCC.

FlattenTreeListRec.FlattenTreeListRec.flatten(LFlattenTreeListRec/TreeList;)LFlattenTreeListRec/ObjectList;: Graph of 119 nodes with 0 SCCs.

FlattenTreeListRec.Tree.createTree()LFlattenTreeListRec/Tree;: Graph of 444 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 257 rules for P and 74 rules for R.

Combined rules. Obtained 15 rules for P and 0 rules for R.

Filtered ground terms:

FlattenTreeListRec.Tree(x1, x2, x3) → FlattenTreeListRec.Tree(x2, x3)
16311_0_random_ArrayAccess(x1, x2, x3) → 16311_0_random_ArrayAccess(x2, x3)
16497_0_random_IntArithmetic(x1, x2, x3, x4) → 16497_0_random_IntArithmetic(x2, x3)
Cond_16497_1_createTree_InvokeMethod9(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod9(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod2(x1, x2, x3)

Filtered all non-integer terms:

16311_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16311_1_createTree_InvokeMethod(x1, x2)
Cond_16311_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16311_1_createTree_InvokeMethod(x1, x2, x3)
16497_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16497_1_createTree_InvokeMethod(x1, x2)
16497_0_random_IntArithmetic(x1, x2) → 16497_0_random_IntArithmetic(x2)
FlattenTreeListRec.Tree(x1, x2) → FlattenTreeListRec.Tree
Cond_16497_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod3(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod3(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod4(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod4(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod5(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod5(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod6(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod6(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod7(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod7(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod8(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod8(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod10(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod10(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod11(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod11(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod12(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod12(x1, x2, x3)
Cond_16497_1_createTree_InvokeMethod13(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod13(x1, x2, x3)

Filtered all free variables:

16497_1_createTree_InvokeMethod(x1, x2) → 16497_1_createTree_InvokeMethod(x2)
Cond_16497_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod(x1, x3)
16311_1_createTree_InvokeMethod(x1, x2) → 16311_1_createTree_InvokeMethod(x2)
Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod1(x1, x3)
Cond_16497_1_createTree_InvokeMethod2(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod2(x1, x3)
Cond_16497_1_createTree_InvokeMethod3(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod3(x1, x3)
Cond_16497_1_createTree_InvokeMethod4(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod4(x1, x3)
Cond_16497_1_createTree_InvokeMethod5(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod5(x1, x3)
Cond_16497_1_createTree_InvokeMethod6(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod6(x1, x3)
Cond_16497_1_createTree_InvokeMethod7(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod7(x1, x3)
Cond_16497_1_createTree_InvokeMethod8(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod8(x1, x3)
Cond_16497_1_createTree_InvokeMethod9(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod9(x1, x3)
Cond_16497_1_createTree_InvokeMethod10(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod10(x1, x3)
Cond_16497_1_createTree_InvokeMethod11(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod11(x1, x3)
Cond_16497_1_createTree_InvokeMethod12(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod12(x1, x3)
Cond_16497_1_createTree_InvokeMethod13(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod13(x1, x3)
Cond_16311_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16311_1_createTree_InvokeMethod(x1, x3)

Combined rules. Obtained 1 rules for P and 0 rules for R.

Finished conversion. Obtained 1 rules for P and 0 rules for R. System has predefined symbols.

Log for SCC 1:

Generated 66 rules for P and 52 rules for R.

Combined rules. Obtained 2 rules for P and 11 rules for R.

Filtered ground terms:

1297_0_flatten_NONNULL(x1, x2, x3) → 1297_0_flatten_NONNULL(x2, x3)
FlattenTreeListRec.TreeList(x1, x2, x3) → FlattenTreeListRec.TreeList(x2, x3)
2020_1_flatten_InvokeMethod(x1, x2, x3, x4, x5, x6) → 2020_1_flatten_InvokeMethod(x1, x2, x5, x6)
FlattenTreeListRec.ObjectList(x1) → FlattenTreeListRec.ObjectList
FlattenTreeListRec.Tree(x1, x2, x3, x4) → FlattenTreeListRec.Tree(x2, x3, x4)
3007_0_flatten_Return(x1, x2) → 3007_0_flatten_Return
3181_0_flatten_Return(x1, x2, x3) → 3181_0_flatten_Return(x2)
2373_0_flatten_Return(x1, x2) → 2373_0_flatten_Return(x2)
2697_0_flatten_Return(x1, x2, x3) → 2697_0_flatten_Return(x2)
1421_0_flatten_Return(x1, x2) → 1421_0_flatten_Return
1311_0_flatten_Return(x1, x2, x3) → 1311_0_flatten_Return

Filtered duplicate args:

1297_0_flatten_NONNULL(x1, x2) → 1297_0_flatten_NONNULL(x2)
2020_1_flatten_InvokeMethod(x1, x2, x3, x4) → 2020_1_flatten_InvokeMethod(x1, x3, x4)

Filtered unneeded arguments:

2020_1_flatten_InvokeMethod(x1, x2, x3) → 2020_1_flatten_InvokeMethod(x1, x3)

Finished conversion. Obtained 2 rules for P and 11 rules for R. System has no predefined symbols.

Log for SCC 2:

Generated 47 rules for P and 608 rules for R.

Combined rules. Obtained 2 rules for P and 49 rules for R.

Filtered ground terms:

FlattenTreeListRec.TreeList(x1) → FlattenTreeListRec.TreeList
8117_0_createTree_InvokeMethod(x1) → 8117_0_createTree_InvokeMethod
Cond_8117_1_main_InvokeMethod1(x1, x2, x3, x4) → Cond_8117_1_main_InvokeMethod1(x1, x3, x4)
FlattenTreeListRec.Tree(x1) → FlattenTreeListRec.Tree
16185_0_createTree_Return(x1, x2) → 16185_0_createTree_Return
Cond_8117_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_8117_1_main_InvokeMethod(x1, x3, x4)
1621_0_createTree_Return(x1, x2, x3) → 1621_0_createTree_Return
16160_0_createTree_LE(x1, x2, x3, x4, x5) → 16160_0_createTree_LE(x2, x4, x5)
Cond_19952_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → Cond_19952_0_createTree_FieldAccess(x1, x3)
19952_0_createTree_FieldAccess(x1, x2, x3, x4) → 19952_0_createTree_FieldAccess(x2)
Cond_20003_0_createTree_Store(x1, x2, x3, x4, x5) → Cond_20003_0_createTree_Store(x1, x3, x5)
20003_0_createTree_Store(x1, x2, x3, x4) → 20003_0_createTree_Store(x2, x4)
Cond_23896_0_createTree_FieldAccess(x1, x2, x3, x4, x5, x6) → Cond_23896_0_createTree_FieldAccess(x1, x3)
23896_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → 23896_0_createTree_FieldAccess(x2)
Cond_23704_0_createTree_Load(x1, x2, x3, x4) → Cond_23704_0_createTree_Load(x1, x3)
23704_0_createTree_Load(x1, x2, x3) → 23704_0_createTree_Load(x2)
Cond_23905_0_createTree_Load(x1, x2, x3, x4) → Cond_23905_0_createTree_Load(x1, x3)
23905_0_createTree_Load(x1, x2, x3) → 23905_0_createTree_Load(x2)
Cond_20056_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → Cond_20056_0_createTree_FieldAccess(x1, x3)
20056_0_createTree_FieldAccess(x1, x2, x3, x4) → 20056_0_createTree_FieldAccess(x2)
Cond_20122_0_createTree_Store(x1, x2, x3, x4, x5) → Cond_20122_0_createTree_Store(x1, x3, x5)
20122_0_createTree_Store(x1, x2, x3, x4) → 20122_0_createTree_Store(x2, x4)
Cond_23964_0_createTree_FieldAccess(x1, x2, x3, x4, x5, x6) → Cond_23964_0_createTree_FieldAccess(x1, x3)
23964_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → 23964_0_createTree_FieldAccess(x2)
Cond_23836_0_createTree_Load(x1, x2, x3, x4) → Cond_23836_0_createTree_Load(x1, x3)
23836_0_createTree_Load(x1, x2, x3) → 23836_0_createTree_Load(x2)
Cond_23974_0_createTree_Load(x1, x2, x3, x4) → Cond_23974_0_createTree_Load(x1, x3)
23974_0_createTree_Load(x1, x2, x3) → 23974_0_createTree_Load(x2)
1678_0_createTree_InvokeMethod(x1, x2) → 1678_0_createTree_InvokeMethod
java.lang.ArrayIndexOutOfBoundsException(x1) → java.lang.ArrayIndexOutOfBoundsException
java.lang.IndexOutOfBoundsException(x1) → java.lang.IndexOutOfBoundsException
1307_0_random_ArrayAccess(x1, x2, x3) → 1307_0_random_ArrayAccess(x2, x3)
18752_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 18752_0_createTree_InvokeMethod(x3, x5)
Cond_16269_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16269_1_createTree_InvokeMethod(x1, x2, x3, x5)
16269_0_random_ArrayAccess(x1, x2, x3) → 16269_0_random_ArrayAccess(x2, x3)
16269_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16269_1_createTree_InvokeMethod(x1, x2, x4)
17784_0_createTree_LE(x1, x2, x3, x4, x5) → 17784_0_createTree_LE(x2, x4, x5)
Cond_17784_0_createTree_LE8(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE8(x1, x3)
Cond_17784_0_createTree_LE7(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE7(x1, x3)
Cond_17784_0_createTree_LE6(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE6(x1, x3, x6)
Cond_17784_0_createTree_LE5(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE5(x1, x3, x6)
Cond_17784_0_createTree_LE4(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE4(x1, x3, x6)
Cond_17784_0_createTree_LE3(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE3(x1, x3, x6)
Cond_17784_0_createTree_LE2(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE2(x1, x3, x6)
Cond_17784_0_createTree_LE1(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE1(x1, x3, x6)
Cond_17784_0_createTree_LE(x1, x2, x3, x4, x5, x6) → Cond_17784_0_createTree_LE(x1, x3, x6)
Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3, x5)
16497_0_random_IntArithmetic(x1, x2, x3, x4) → 16497_0_random_IntArithmetic(x2, x3)
16497_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16497_1_createTree_InvokeMethod(x1, x2, x4)
20690_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 20690_0_createTree_InvokeMethod(x3, x5)
java.lang.NullPointerException(x1) → java.lang.NullPointerException
Cond_16497_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16497_1_createTree_InvokeMethod(x1, x2, x3, x5)
Cond_16311_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16311_1_createTree_InvokeMethod(x1, x2, x3, x5)
16311_0_random_ArrayAccess(x1, x2, x3) → 16311_0_random_ArrayAccess(x2, x3)
16311_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16311_1_createTree_InvokeMethod(x1, x2, x4)
19112_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 19112_0_createTree_InvokeMethod(x3, x5)
Cond_16324_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16324_1_createTree_InvokeMethod(x1, x2, x3, x5)
16324_0_random_ArrayAccess(x1, x2, x3) → 16324_0_random_ArrayAccess(x2, x3)
16324_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16324_1_createTree_InvokeMethod(x1, x2, x4)
Cond_16160_0_createTree_LE2(x1, x2, x3, x4, x5, x6) → Cond_16160_0_createTree_LE2(x1, x3, x5, x6)
Cond_16160_0_createTree_LE1(x1, x2, x3, x4, x5, x6) → Cond_16160_0_createTree_LE1(x1, x3, x5, x6)
Cond_16160_0_createTree_LE(x1, x2, x3, x4, x5, x6) → Cond_16160_0_createTree_LE(x1, x3, x5, x6)
Cond_1569_0_createTree_NE(x1, x2, x3, x4) → Cond_1569_0_createTree_NE(x1, x3, x4)
1569_0_createTree_NE(x1, x2, x3) → 1569_0_createTree_NE(x2, x3)
1356_0_random_IntArithmetic(x1, x2, x3, x4) → 1356_0_random_IntArithmetic(x2, x3)
1812_0_createTree_InvokeMethod(x1, x2) → 1812_0_createTree_InvokeMethod
1315_0_random_ArrayAccess(x1, x2, x3) → 1315_0_random_ArrayAccess(x2, x3)
1728_0_createTree_InvokeMethod(x1, x2) → 1728_0_createTree_InvokeMethod
1317_0_random_ArrayAccess(x1, x2, x3) → 1317_0_random_ArrayAccess(x2, x3)
8340_0_main_InvokeMethod(x1, x2, x3, x4) → 8340_0_main_InvokeMethod(x2, x3, x4)

Filtered duplicate args:

16160_0_createTree_LE(x1, x2, x3) → 16160_0_createTree_LE(x2, x3)
Cond_16160_0_createTree_LE2(x1, x2, x3, x4) → Cond_16160_0_createTree_LE2(x1, x3, x4)
Cond_16160_0_createTree_LE1(x1, x2, x3, x4) → Cond_16160_0_createTree_LE1(x1, x3, x4)
Cond_16160_0_createTree_LE(x1, x2, x3, x4) → Cond_16160_0_createTree_LE(x1, x3, x4)
Cond_1569_0_createTree_NE(x1, x2, x3) → Cond_1569_0_createTree_NE(x1, x3)
1569_0_createTree_NE(x1, x2) → 1569_0_createTree_NE(x2)

Filtered unneeded arguments:

8117_1_main_InvokeMethod(x1, x2, x3) → 8117_1_main_InvokeMethod(x1, x3)
Cond_8117_1_main_InvokeMethod(x1, x2, x3) → Cond_8117_1_main_InvokeMethod(x1, x3)
Cond_8117_1_main_InvokeMethod1(x1, x2, x3) → Cond_8117_1_main_InvokeMethod1(x1, x3)
Cond_16160_0_createTree_LE(x1, x2, x3) → Cond_16160_0_createTree_LE(x1, x2)
Cond_16160_0_createTree_LE2(x1, x2, x3) → Cond_16160_0_createTree_LE2(x1, x2)
16324_1_createTree_InvokeMethod(x1, x2, x3) → 16324_1_createTree_InvokeMethod(x1, x3)
Cond_16324_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_16324_1_createTree_InvokeMethod(x1, x2, x4)
Cond_16497_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_16497_1_createTree_InvokeMethod(x1, x2, x4)
Cond_17784_0_createTree_LE(x1, x2, x3) → Cond_17784_0_createTree_LE(x1, x2)
Cond_17784_0_createTree_LE1(x1, x2, x3) → Cond_17784_0_createTree_LE1(x1, x2)
Cond_17784_0_createTree_LE2(x1, x2, x3) → Cond_17784_0_createTree_LE2(x1, x2)
Cond_17784_0_createTree_LE3(x1, x2, x3) → Cond_17784_0_createTree_LE3(x1, x2)
Cond_17784_0_createTree_LE4(x1, x2, x3) → Cond_17784_0_createTree_LE4(x1, x2)
Cond_17784_0_createTree_LE5(x1, x2, x3) → Cond_17784_0_createTree_LE5(x1, x2)
Cond_17784_0_createTree_LE6(x1, x2, x3) → Cond_17784_0_createTree_LE6(x1, x2)
16269_1_createTree_InvokeMethod(x1, x2, x3) → 16269_1_createTree_InvokeMethod(x1, x3)
Cond_16269_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_16269_1_createTree_InvokeMethod(x1, x2, x4)

Filtered all non-integer terms:

8340_0_main_InvokeMethod(x1, x2, x3) → 8340_0_main_InvokeMethod(x2, x3)
18752_0_createTree_InvokeMethod(x1, x2) → 18752_0_createTree_InvokeMethod(x1)
19112_0_createTree_InvokeMethod(x1, x2) → 19112_0_createTree_InvokeMethod(x1)
20690_0_createTree_InvokeMethod(x1, x2) → 20690_0_createTree_InvokeMethod(x1)
1356_0_random_IntArithmetic(x1, x2) → 1356_0_random_IntArithmetic(x2)
16160_0_createTree_LE(x1, x2) → 16160_0_createTree_LE(x2)
Cond_16160_0_createTree_LE(x1, x2) → Cond_16160_0_createTree_LE(x1)
16269_1_createTree_InvokeMethod(x1, x2) → 16269_1_createTree_InvokeMethod(x1)
Cond_16160_0_createTree_LE1(x1, x2, x3) → Cond_16160_0_createTree_LE1(x1, x3)
16311_1_createTree_InvokeMethod(x1, x2, x3) → 16311_1_createTree_InvokeMethod(x1, x2)
Cond_16160_0_createTree_LE2(x1, x2) → Cond_16160_0_createTree_LE2(x1)
16324_1_createTree_InvokeMethod(x1, x2) → 16324_1_createTree_InvokeMethod(x1)
Cond_16324_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16324_1_createTree_InvokeMethod(x1, x2)
Cond_16311_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_16311_1_createTree_InvokeMethod(x1, x2, x3)
16497_1_createTree_InvokeMethod(x1, x2, x3) → 16497_1_createTree_InvokeMethod(x1, x2)
Cond_16497_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16497_1_createTree_InvokeMethod(x1, x2)
16497_0_random_IntArithmetic(x1, x2) → 16497_0_random_IntArithmetic(x2)
Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_16497_1_createTree_InvokeMethod1(x1, x2, x3)
17784_0_createTree_LE(x1, x2, x3) → 17784_0_createTree_LE(x1, x3)
20122_0_createTree_Store(x1, x2) → 20122_0_createTree_Store(x1)
20003_0_createTree_Store(x1, x2) → 20003_0_createTree_Store(x1)
Cond_16269_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16269_1_createTree_InvokeMethod(x1, x2)
Cond_20122_0_createTree_Store(x1, x2, x3) → Cond_20122_0_createTree_Store(x1, x2)
Cond_20003_0_createTree_Store(x1, x2, x3) → Cond_20003_0_createTree_Store(x1, x2)

Combined rules. Obtained 2 rules for P and 47 rules for R.

Finished conversion. Obtained 2 rules for P and 47 rules for R. System has predefined symbols.

(4) Complex Obligation (AND)

(5) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 16311_1_CREATETREE_INVOKEMETHOD(x0[0]) → COND_16311_1_CREATETREE_INVOKEMETHOD(x0[0] > 0 && 0 < x0[0] + -1, x0[0])
(1): COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1]) → 16311_1_CREATETREE_INVOKEMETHOD(x0[1] + -1)

(0) -> (1), if ((x0[0] > 0 && 0 < x0[0] + -1 →^* TRUE)∧(x0[0] →^* x0[1]))

(1) -> (0), if ((x0[1] + -1 →^* x0[0]))

The set Q is empty.

(6) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.

For Pair 16311_1_CREATETREE_INVOKEMETHOD(x0) → COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0, 0), <(0, +(x0, -1))), x0) the following chains were created:

We consider the chain 16311_1_CREATETREE_INVOKEMETHOD(x0[0]) → COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0]), COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1]) → 16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1)) which results in the following constraint:
(1)    (&&(>(x0[0], 0), <(0, +(x0[0], -1)))=TRUE∧x0[0]=x0[1] ⇒ 16311_1_CREATETREE_INVOKEMETHOD(x0[0])≥NonInfC∧16311_1_CREATETREE_INVOKEMETHOD(x0[0])≥COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])∧(U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE∧<(0, +(x0[0], -1))=TRUE ⇒ 16311_1_CREATETREE_INVOKEMETHOD(x0[0])≥NonInfC∧16311_1_CREATETREE_INVOKEMETHOD(x0[0])≥COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])∧(U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0∧x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0∧x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0∧x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧[-1] + x0[0] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10 + (2)bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    ([1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10 + (4)bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)

For Pair COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0) → 16311_1_CREATETREE_INVOKEMETHOD(+(x0, -1)) the following chains were created:

We consider the chain COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1]) → 16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1)) which results in the following constraint:
(8)    (COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1])≥NonInfC∧COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1])≥16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))∧(U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    ((U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    ((U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    ((U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    ((U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_13] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

16311_1_CREATETREE_INVOKEMETHOD(x0) → COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0, 0), <(0, +(x0, -1))), x0)
- ([1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])), ≥)∧[(-1)Bound*bni_10 + (4)bni_10] + [(2)bni_10]x0[0] ≥ 0∧[1 + (-1)bso_11] ≥ 0)
COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0) → 16311_1_CREATETREE_INVOKEMETHOD(+(x0, -1))
- ((U^Increasing(16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_13] ≥ 0)

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0
POL(FALSE) = 0
POL(16311_1_CREATETREE_INVOKEMETHOD(x₁)) = [2]x₁
POL(COND_16311_1_CREATETREE_INVOKEMETHOD(x₁, x₂)) = [-1] + [2]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]

The following pairs are in P_>:

16311_1_CREATETREE_INVOKEMETHOD(x0[0]) → COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])
COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1]) → 16311_1_CREATETREE_INVOKEMETHOD(+(x0[1], -1))

The following pairs are in P_bound:

16311_1_CREATETREE_INVOKEMETHOD(x0[0]) → COND_16311_1_CREATETREE_INVOKEMETHOD(&&(>(x0[0], 0), <(0, +(x0[0], -1))), x0[0])

The following pairs are in P_≥:
none

There are no usable rules.

(7) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_16311_1_CREATETREE_INVOKEMETHOD(TRUE, x0[1]) → 16311_1_CREATETREE_INVOKEMETHOD(x0[1] + -1)

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(9) TRUE

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:
none

The ITRS R consists of the following rules:
1297_0_flatten_NONNULL(NULL) → 1311_0_flatten_Return
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1))))) → 2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))) → 3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3))))) → 2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))) → 3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL) → 1421_0_flatten_Return
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL))) → 2373_0_flatten_Return(NULL)
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1))))) → 2373_0_flatten_Return(x0)
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1))) → 3007_0_flatten_Return
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3))))) → 2373_0_flatten_Return(java.lang.Object(FlattenTreeListRec.ObjectList))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4))) → 3007_0_flatten_Return

The integer pair graph contains the following rules and edges:
(0): 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))) → 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))))
(1): 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))) → 1297_0_FLATTEN_NONNULL(x0[1])

(0) -> (0), if ((java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))) →^* java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0]', x1[0]', x2[0]')), x3[0]'))))

(0) -> (1), if ((java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))) →^* java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))))

(1) -> (0), if ((x0[1] →^* java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))))

(1) -> (1), if ((x0[1] →^* java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]'))))

The set Q consists of the following terms:
1297_0_flatten_NONNULL(NULL)
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL)
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL)))
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1)))
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4)))

(11) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(12) Obligation:

Q DP problem:
The TRS P consists of the following rules:

1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))) → 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))))
1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))) → 1297_0_FLATTEN_NONNULL(x0[1])

The TRS R consists of the following rules:

1297_0_flatten_NONNULL(NULL) → 1311_0_flatten_Return
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1))))) → 2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))) → 3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3))))) → 2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))) → 3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL) → 1421_0_flatten_Return
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL))) → 2373_0_flatten_Return(NULL)
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1))))) → 2373_0_flatten_Return(x0)
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1))) → 3007_0_flatten_Return
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3))))) → 2373_0_flatten_Return(java.lang.Object(FlattenTreeListRec.ObjectList))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4))) → 3007_0_flatten_Return

The set Q consists of the following terms:

1297_0_flatten_NONNULL(NULL)
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL)
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL)))
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1)))
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4)))

We have to consider all minimal (P,Q,R)-chains.

(13) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(14) Obligation:

Q DP problem:
The TRS P consists of the following rules:

1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))) → 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))))
1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))) → 1297_0_FLATTEN_NONNULL(x0[1])

R is empty.
The set Q consists of the following terms:

1297_0_flatten_NONNULL(NULL)
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL)
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL)))
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1)))
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4)))

We have to consider all minimal (P,Q,R)-chains.

(15) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

1297_0_flatten_NONNULL(NULL)
2020_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
2020_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, java.lang.Object(FlattenTreeListRec.TreeList(x1, x2))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x3, x0, NULL)), java.lang.Object(FlattenTreeListRec.TreeList(x1, x2)))))
2020_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
2020_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, java.lang.Object(FlattenTreeListRec.TreeList(x4, x5))))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x6, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), java.lang.Object(FlattenTreeListRec.TreeList(x4, x5)))))
1404_1_flatten_InvokeMethod(1311_0_flatten_Return, NULL)
1404_1_flatten_InvokeMethod(1421_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, NULL)))
1404_1_flatten_InvokeMethod(2373_0_flatten_Return(x0), java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(NULL, x1)))))
1404_1_flatten_InvokeMethod(2697_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(x0, x1))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x2, x0, NULL)), x1)))
1404_1_flatten_InvokeMethod(3007_0_flatten_Return, java.lang.Object(FlattenTreeListRec.TreeList(NULL, java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), x3)))))
1404_1_flatten_InvokeMethod(3181_0_flatten_Return(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)), java.lang.Object(FlattenTreeListRec.TreeList(x3, x4))))), java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x5, x3, java.lang.Object(FlattenTreeListRec.Tree(x0, x1, x2)))), x4)))

(16) Obligation:

Q DP problem:
The TRS P consists of the following rules:

1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))) → 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))))
1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))) → 1297_0_FLATTEN_NONNULL(x0[1])

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(17) UsableRulesReductionPairsProof (EQUIVALENT transformation)

By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(java.lang.Object(FlattenTreeListRec.Tree(x0[0], x1[0], x2[0])), x3[0]))) → 1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(x2[0], java.lang.Object(FlattenTreeListRec.TreeList(x1[0], x3[0])))))
1297_0_FLATTEN_NONNULL(java.lang.Object(FlattenTreeListRec.TreeList(NULL, x0[1]))) → 1297_0_FLATTEN_NONNULL(x0[1])

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(1297_0_FLATTEN_NONNULL(x₁)) = 2·x₁
POL(FlattenTreeListRec.Tree(x₁, x₂, x₃)) = 2 + x₁ + 2·x₂ + x₃
POL(FlattenTreeListRec.TreeList(x₁, x₂)) = 1 + 2·x₁ + x₂
POL(NULL) = 0
POL(java.lang.Object(x₁)) = x₁

(18) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(19) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(20) YES

(21) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
8117_0_createTree_InvokeMethod → 1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1317_1_createTree_InvokeMethod(x2 >= x0, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1728_0_createTree_InvokeMethod
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1315_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x4))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0)) → Cond_1356_1_createTree_InvokeMethod(x0 >= 0, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0)) → 1812_0_createTree_InvokeMethod
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x1)) → Cond_1356_1_createTree_InvokeMethod1(x1 >= 0, 1356_0_random_IntArithmetic(x1))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x1)) → 1569_0_createTree_NE(x3)
1569_0_createTree_NE(0) → 1621_0_createTree_Return
1569_0_createTree_NE(x0) → Cond_1569_0_createTree_NE(!(x0 = 0), x0)
Cond_1569_0_createTree_NE(TRUE, x0) → 16160_0_createTree_LE(x0)
16160_0_createTree_LE(0) → 16185_0_createTree_Return
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE(x0 > 0, x0)
Cond_16160_0_createTree_LE(TRUE, x0) → 16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE1(x0 > 0, x0)
Cond_16160_0_createTree_LE1(TRUE, x0) → 16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4), x0)
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE2(x0 > 0, x0)
Cond_16160_0_createTree_LE2(TRUE, x0) → 16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16324_1_createTree_InvokeMethod(x2 >= x0, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 19112_0_createTree_InvokeMethod(x3)
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → Cond_16311_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x6), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x2) → Cond_16497_1_createTree_InvokeMethod(x0 >= 0, 16497_0_random_IntArithmetic(x0), x2)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x2) → 20690_0_createTree_InvokeMethod(x2)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x1), x3) → Cond_16497_1_createTree_InvokeMethod1(x1 >= 0, 16497_0_random_IntArithmetic(x1), x3)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x1), x3) → 17784_0_createTree_LE(x3, x5)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE(x1 > 0 && x0 > 0, x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE1(x1 > 0, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1) → 23974_0_createTree_Load(x0)
17784_0_createTree_LE(x0, 0) → Cond_17784_0_createTree_LE6(x0 > 0, x0, 0)
Cond_17784_0_createTree_LE6(TRUE, x0, 0) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, 0) → 23974_0_createTree_Load(x0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16269_1_createTree_InvokeMethod(x2 <= -1, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 18752_0_createTree_InvokeMethod(x3)
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1307_1_createTree_InvokeMethod(x2 <= -1, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1678_0_createTree_InvokeMethod
23974_0_createTree_Load(x0) → Cond_23974_0_createTree_Load(x0 > 0, x0)
Cond_23974_0_createTree_Load(TRUE, x0) → 16160_0_createTree_LE(x0 + -1)

The integer pair graph contains the following rules and edges:
(0): 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0]) → COND_8117_1_MAIN_INVOKEMETHOD(x2[0] > 0 && 0 < x2[0] + -1, 1621_0_createTree_Return, x2[0])
(1): COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, x2[1] + -1)
(2): 8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2]) → COND_8117_1_MAIN_INVOKEMETHOD1(x1[2] > 0 && 0 < x1[2] + -1, 16185_0_createTree_Return, x1[2])
(3): COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, x1[3] + -1)

(0) -> (1), if ((x2[0] > 0 && 0 < x2[0] + -1 →^* TRUE)∧(x2[0] →^* x2[1]))

(1) -> (0), if ((8117_0_createTree_InvokeMethod →^* 1621_0_createTree_Return)∧(x2[1] + -1 →^* x2[0]))

(1) -> (2), if ((8117_0_createTree_InvokeMethod →^* 16185_0_createTree_Return)∧(x2[1] + -1 →^* x1[2]))

(2) -> (3), if ((x1[2] > 0 && 0 < x1[2] + -1 →^* TRUE)∧(x1[2] →^* x1[3]))

(3) -> (0), if ((8117_0_createTree_InvokeMethod →^* 1621_0_createTree_Return)∧(x1[3] + -1 →^* x2[0]))

(3) -> (2), if ((8117_0_createTree_InvokeMethod →^* 16185_0_createTree_Return)∧(x1[3] + -1 →^* x1[2]))

The set Q consists of the following terms:
8117_0_createTree_InvokeMethod
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x1)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x0))
1569_0_createTree_NE(x0)
Cond_1569_0_createTree_NE(TRUE, x0)
16160_0_createTree_LE(x0)
Cond_16160_0_createTree_LE(TRUE, x0)
Cond_16160_0_createTree_LE1(TRUE, x0)
Cond_16160_0_createTree_LE2(TRUE, x0)
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x0), x1)
17784_0_createTree_LE(x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1)
Cond_17784_0_createTree_LE6(TRUE, x0, 0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
23974_0_createTree_Load(x0)
Cond_23974_0_createTree_Load(TRUE, x0)

(22) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.

For Pair 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2) → COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), <(0, +(x2, -1))), 1621_0_createTree_Return, x2) the following chains were created:

We consider the chain 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0]) → COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0]), COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1)) which results in the following constraint:
(1)    (&&(>(x2[0], 0), <(0, +(x2[0], -1)))=TRUE∧x2[0]=x2[1] ⇒ 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0])≥NonInfC∧8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0])≥COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])∧(U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x2[0], 0)=TRUE∧<(0, +(x2[0], -1))=TRUE ⇒ 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0])≥NonInfC∧8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0])≥COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])∧(U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] + [-1] ≥ 0∧x2[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] + [-1] ≥ 0∧x2[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] + [-1] ≥ 0∧x2[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x2[0] ≥ 0∧[-1] + x2[0] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103 + (2)bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    ([1] + x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103 + (4)bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)

For Pair COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2, -1)) the following chains were created:

We consider the chain COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1)) which results in the following constraint:
(8)    (COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1])≥NonInfC∧COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1])≥8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))∧(U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥)∧[2 + (-1)bso_106] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥)∧[2 + (-1)bso_106] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥)∧[2 + (-1)bso_106] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥)∧0 = 0∧[2 + (-1)bso_106] ≥ 0)

For Pair 8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1) → COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <(0, +(x1, -1))), 16185_0_createTree_Return, x1) the following chains were created:

We consider the chain 8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2]) → COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2]), COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1)) which results in the following constraint:
(13)    (&&(>(x1[2], 0), <(0, +(x1[2], -1)))=TRUE∧x1[2]=x1[3] ⇒ 8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2])≥NonInfC∧8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2])≥COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])∧(U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥))

We simplified constraint (13) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(14)    (>(x1[2], 0)=TRUE∧<(0, +(x1[2], -1))=TRUE ⇒ 8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2])≥NonInfC∧8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2])≥COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])∧(U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (x1[2] + [-1] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (x1[2] + [-1] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (x1[2] + [-1] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (x1[2] ≥ 0∧[-1] + x1[2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107 + (2)bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(19)    ([1] + x1[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107 + (4)bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)

For Pair COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1, -1)) the following chains were created:

We consider the chain COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1)) which results in the following constraint:
(20)    (COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3])≥NonInfC∧COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3])≥8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))∧(U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥)∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥)∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥)∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_110] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2) → COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), <(0, +(x2, -1))), 1621_0_createTree_Return, x2)
- ([1] + x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])), ≥)∧[(-1)Bound*bni_103 + (4)bni_103] + [(2)bni_103]x2[0] ≥ 0∧[(-1)bso_104] ≥ 0)
COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2, -1))
- ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))), ≥)∧0 = 0∧[2 + (-1)bso_106] ≥ 0)
8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1) → COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <(0, +(x1, -1))), 16185_0_createTree_Return, x1)
- ([1] + x1[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])), ≥)∧[(-1)Bound*bni_107 + (4)bni_107] + [(2)bni_107]x1[2] ≥ 0∧[1 + (-1)bso_108] ≥ 0)
COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1, -1))
- ((U^Increasing(8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_110] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(8117_0_createTree_InvokeMethod) = [-1]
POL(1307_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(1307_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(1315_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(1315_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(1317_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(1317_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(8117_1_main_InvokeMethod(x₁, x₂)) = [-1]
POL(1678_0_createTree_InvokeMethod) = [-1]
POL(8340_0_main_InvokeMethod(x₁, x₂)) = [-1]
POL(1728_0_createTree_InvokeMethod) = [-1]
POL(1812_0_createTree_InvokeMethod) = [-1]
POL(18752_0_createTree_InvokeMethod(x₁)) = [-1]
POL(19112_0_createTree_InvokeMethod(x₁)) = [-1]
POL(20690_0_createTree_InvokeMethod(x₁)) = x₁
POL(Cond_1317_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(>=(x₁, x₂)) = [-1]
POL(Cond_1315_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(1356_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(1356_0_random_IntArithmetic(x₁)) = x₁
POL(Cond_1356_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(Cond_1356_1_createTree_InvokeMethod1(x₁, x₂)) = [-1] + [-1]x₂
POL(1569_0_createTree_NE(x₁)) = [-1] + [-1]x₁
POL(1621_0_createTree_Return) = [-1]
POL(Cond_1569_0_createTree_NE(x₁, x₂)) = [-1] + [-1]x₂
POL(!(x₁)) = [-1]
POL(=(x₁, x₂)) = [-1]
POL(16160_0_createTree_LE(x₁)) = [-1] + [-1]x₁
POL(16185_0_createTree_Return) = [-1]
POL(Cond_16160_0_createTree_LE(x₁, x₂)) = [-1] + [-1]x₂
POL(>(x₁, x₂)) = [-1]
POL(16269_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(16269_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(Cond_16160_0_createTree_LE1(x₁, x₂)) = [-1] + [-1]x₂
POL(16311_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(16311_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(Cond_16160_0_createTree_LE2(x₁, x₂)) = [-1] + [-1]x₂
POL(16324_1_createTree_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(16324_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(Cond_16324_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(Cond_16311_1_createTree_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(16497_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(16497_0_random_IntArithmetic(x₁)) = x₁
POL(Cond_16497_1_createTree_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(Cond_16497_1_createTree_InvokeMethod1(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(17784_0_createTree_LE(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(Cond_17784_0_createTree_LE(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(Cond_17784_0_createTree_LE1(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(23974_0_createTree_Load(x₁)) = [-1] + [-1]x₁
POL(Cond_17784_0_createTree_LE6(x₁, x₂, x₃)) = [-1] + [-1]x₂
POL(Cond_16269_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(Cond_1307_1_createTree_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂
POL(Cond_23974_0_createTree_Load(x₁, x₂)) = [-1] + [-1]x₂
POL(8117_1_MAIN_INVOKEMETHOD(x₁, x₂)) = [2]x₂
POL(COND_8117_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [2]x₃
POL(COND_8117_1_MAIN_INVOKEMETHOD1(x₁, x₂, x₃)) = [-1] + [2]x₃

The following pairs are in P_>:

COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x2[1], -1))
8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2]) → COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])
COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, +(x1[3], -1))

The following pairs are in P_bound:

8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0]) → COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])
8117_1_MAIN_INVOKEMETHOD(16185_0_createTree_Return, x1[2]) → COND_8117_1_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <(0, +(x1[2], -1))), 16185_0_createTree_Return, x1[2])

The following pairs are in P_≥:

8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0]) → COND_8117_1_MAIN_INVOKEMETHOD(&&(>(x2[0], 0), <(0, +(x2[0], -1))), 1621_0_createTree_Return, x2[0])

There are no usable rules.

(23) Complex Obligation (AND)

(24) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
8117_0_createTree_InvokeMethod → 1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1317_1_createTree_InvokeMethod(x2 >= x0, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1728_0_createTree_InvokeMethod
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1315_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x4))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0)) → Cond_1356_1_createTree_InvokeMethod(x0 >= 0, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0)) → 1812_0_createTree_InvokeMethod
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x1)) → Cond_1356_1_createTree_InvokeMethod1(x1 >= 0, 1356_0_random_IntArithmetic(x1))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x1)) → 1569_0_createTree_NE(x3)
1569_0_createTree_NE(0) → 1621_0_createTree_Return
1569_0_createTree_NE(x0) → Cond_1569_0_createTree_NE(!(x0 = 0), x0)
Cond_1569_0_createTree_NE(TRUE, x0) → 16160_0_createTree_LE(x0)
16160_0_createTree_LE(0) → 16185_0_createTree_Return
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE(x0 > 0, x0)
Cond_16160_0_createTree_LE(TRUE, x0) → 16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE1(x0 > 0, x0)
Cond_16160_0_createTree_LE1(TRUE, x0) → 16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4), x0)
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE2(x0 > 0, x0)
Cond_16160_0_createTree_LE2(TRUE, x0) → 16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16324_1_createTree_InvokeMethod(x2 >= x0, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 19112_0_createTree_InvokeMethod(x3)
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → Cond_16311_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x6), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x2) → Cond_16497_1_createTree_InvokeMethod(x0 >= 0, 16497_0_random_IntArithmetic(x0), x2)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x2) → 20690_0_createTree_InvokeMethod(x2)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x1), x3) → Cond_16497_1_createTree_InvokeMethod1(x1 >= 0, 16497_0_random_IntArithmetic(x1), x3)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x1), x3) → 17784_0_createTree_LE(x3, x5)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE(x1 > 0 && x0 > 0, x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE1(x1 > 0, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1) → 23974_0_createTree_Load(x0)
17784_0_createTree_LE(x0, 0) → Cond_17784_0_createTree_LE6(x0 > 0, x0, 0)
Cond_17784_0_createTree_LE6(TRUE, x0, 0) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, 0) → 23974_0_createTree_Load(x0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16269_1_createTree_InvokeMethod(x2 <= -1, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 18752_0_createTree_InvokeMethod(x3)
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1307_1_createTree_InvokeMethod(x2 <= -1, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1678_0_createTree_InvokeMethod
23974_0_createTree_Load(x0) → Cond_23974_0_createTree_Load(x0 > 0, x0)
Cond_23974_0_createTree_Load(TRUE, x0) → 16160_0_createTree_LE(x0 + -1)

The integer pair graph contains the following rules and edges:
(0): 8117_1_MAIN_INVOKEMETHOD(1621_0_createTree_Return, x2[0]) → COND_8117_1_MAIN_INVOKEMETHOD(x2[0] > 0 && 0 < x2[0] + -1, 1621_0_createTree_Return, x2[0])

The set Q consists of the following terms:
8117_0_createTree_InvokeMethod
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x1)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x0))
1569_0_createTree_NE(x0)
Cond_1569_0_createTree_NE(TRUE, x0)
16160_0_createTree_LE(x0)
Cond_16160_0_createTree_LE(TRUE, x0)
Cond_16160_0_createTree_LE1(TRUE, x0)
Cond_16160_0_createTree_LE2(TRUE, x0)
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x0), x1)
17784_0_createTree_LE(x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1)
Cond_17784_0_createTree_LE6(TRUE, x0, 0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
23974_0_createTree_Load(x0)
Cond_23974_0_createTree_Load(TRUE, x0)

(25) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(26) TRUE

(27) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
8117_0_createTree_InvokeMethod → 1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_0_createTree_InvokeMethod → 1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x1) → 8340_0_main_InvokeMethod(x0, x1)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x3) → 8340_0_main_InvokeMethod(x2, x3)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1317_1_createTree_InvokeMethod(x2 >= x0, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1728_0_createTree_InvokeMethod
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1315_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x4))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0)) → Cond_1356_1_createTree_InvokeMethod(x0 >= 0, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0)) → 1812_0_createTree_InvokeMethod
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x1)) → Cond_1356_1_createTree_InvokeMethod1(x1 >= 0, 1356_0_random_IntArithmetic(x1))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x1)) → 1569_0_createTree_NE(x3)
1569_0_createTree_NE(0) → 1621_0_createTree_Return
1569_0_createTree_NE(x0) → Cond_1569_0_createTree_NE(!(x0 = 0), x0)
Cond_1569_0_createTree_NE(TRUE, x0) → 16160_0_createTree_LE(x0)
16160_0_createTree_LE(0) → 16185_0_createTree_Return
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE(x0 > 0, x0)
Cond_16160_0_createTree_LE(TRUE, x0) → 16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE1(x0 > 0, x0)
Cond_16160_0_createTree_LE1(TRUE, x0) → 16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4), x0)
16160_0_createTree_LE(x0) → Cond_16160_0_createTree_LE2(x0 > 0, x0)
Cond_16160_0_createTree_LE2(TRUE, x0) → 16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x2, x3)), x4))
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16324_1_createTree_InvokeMethod(x2 >= x0, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 19112_0_createTree_InvokeMethod(x3)
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → Cond_16311_1_createTree_InvokeMethod(x2 >= 0 && x2 < x0, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x6), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x2) → Cond_16497_1_createTree_InvokeMethod(x0 >= 0, 16497_0_random_IntArithmetic(x0), x2)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x2) → 20690_0_createTree_InvokeMethod(x2)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x1), x3) → Cond_16497_1_createTree_InvokeMethod1(x1 >= 0, 16497_0_random_IntArithmetic(x1), x3)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x1), x3) → 17784_0_createTree_LE(x3, x5)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE(x1 > 0 && x0 > 0, x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, x1) → Cond_17784_0_createTree_LE1(x1 > 0, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1) → 23974_0_createTree_Load(x0)
17784_0_createTree_LE(x0, 0) → Cond_17784_0_createTree_LE6(x0 > 0, x0, 0)
Cond_17784_0_createTree_LE6(TRUE, x0, 0) → 16160_0_createTree_LE(x0 + -1)
17784_0_createTree_LE(x0, 0) → 23974_0_createTree_Load(x0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_16269_1_createTree_InvokeMethod(x2 <= -1, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 18752_0_createTree_InvokeMethod(x3)
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → Cond_1307_1_createTree_InvokeMethod(x2 <= -1, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2)) → 1678_0_createTree_InvokeMethod
23974_0_createTree_Load(x0) → Cond_23974_0_createTree_Load(x0 > 0, x0)
Cond_23974_0_createTree_Load(TRUE, x0) → 16160_0_createTree_LE(x0 + -1)

The integer pair graph contains the following rules and edges:
(1): COND_8117_1_MAIN_INVOKEMETHOD(TRUE, 1621_0_createTree_Return, x2[1]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, x2[1] + -1)
(3): COND_8117_1_MAIN_INVOKEMETHOD1(TRUE, 16185_0_createTree_Return, x1[3]) → 8117_1_MAIN_INVOKEMETHOD(8117_0_createTree_InvokeMethod, x1[3] + -1)

The set Q consists of the following terms:
8117_0_createTree_InvokeMethod
8117_1_main_InvokeMethod(1678_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1728_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(1812_0_createTree_InvokeMethod, x0)
8117_1_main_InvokeMethod(18752_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(19112_0_createTree_InvokeMethod(x0), x1)
8117_1_main_InvokeMethod(20690_0_createTree_InvokeMethod(x0), x1)
1317_1_createTree_InvokeMethod(1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1317_1_createTree_InvokeMethod(TRUE, 1317_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1315_1_createTree_InvokeMethod(1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1315_1_createTree_InvokeMethod(TRUE, 1315_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1356_1_createTree_InvokeMethod(1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod(TRUE, 1356_0_random_IntArithmetic(x0))
Cond_1356_1_createTree_InvokeMethod1(TRUE, 1356_0_random_IntArithmetic(x0))
1569_0_createTree_NE(x0)
Cond_1569_0_createTree_NE(TRUE, x0)
16160_0_createTree_LE(x0)
Cond_16160_0_createTree_LE(TRUE, x0)
Cond_16160_0_createTree_LE1(TRUE, x0)
Cond_16160_0_createTree_LE2(TRUE, x0)
16324_1_createTree_InvokeMethod(16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16324_1_createTree_InvokeMethod(TRUE, 16324_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
16311_1_createTree_InvokeMethod(16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
Cond_16311_1_createTree_InvokeMethod(TRUE, 16311_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
16497_1_createTree_InvokeMethod(16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod(TRUE, 16497_0_random_IntArithmetic(x0), x1)
Cond_16497_1_createTree_InvokeMethod1(TRUE, 16497_0_random_IntArithmetic(x0), x1)
17784_0_createTree_LE(x0, x1)
Cond_17784_0_createTree_LE(TRUE, x0, x1)
Cond_17784_0_createTree_LE1(TRUE, x0, x1)
Cond_17784_0_createTree_LE6(TRUE, x0, 0)
16269_1_createTree_InvokeMethod(16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_16269_1_createTree_InvokeMethod(TRUE, 16269_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
1307_1_createTree_InvokeMethod(1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
Cond_1307_1_createTree_InvokeMethod(TRUE, 1307_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2))
23974_0_createTree_Load(x0)
Cond_23974_0_createTree_Load(TRUE, x0)

(28) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) IDPNonInfProof (SOUND transformation)

(7) Obligation:

(8) IDependencyGraphProof (EQUIVALENT transformation)

(9) TRUE

(10) Obligation:

(11) IDPtoQDPProof (SOUND transformation)

(12) Obligation:

(13) UsableRulesProof (EQUIVALENT transformation)

(14) Obligation:

(15) QReductionProof (EQUIVALENT transformation)

(16) Obligation:

(17) UsableRulesReductionPairsProof (EQUIVALENT transformation)

(18) Obligation:

(19) PisEmptyProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) IDPNonInfProof (SOUND transformation)

(23) Complex Obligation (AND)

(24) Obligation:

(25) IDependencyGraphProof (EQUIVALENT transformation)

(26) TRUE

(27) Obligation:

(28) IDependencyGraphProof (EQUIVALENT transformation)

(29) TRUE