Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Sun Microsystems Inc.) Main-Class: OrderedCollection/Main

package OrderedCollection;

/**
 *
 * @author cotto
 */
public abstract class Element {
    protected Value value;

    protected Element(final Value valueParam) {
        this.value = valueParam;
    }

    public Value getValue() {
        return this.value;
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public class IntValue implements Value {
    private final int intValue;

    public IntValue(final int val) {
        this.intValue = val;
    }

    @Override
    public boolean isSmaller(final Value other) {
        if (other instanceof IntValue) {
            return this.intValue < ((IntValue) other).intValue;
        }
        return false;
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public class ListElement extends Element {
    private ListElement next;

    public ListElement(final Value value, final ListElement nextParam) {
        super(value);
        this.next = nextParam;
    }

    public void setNext(final ListElement next) {
        this.next = next;
    }

    public ListElement getNext() {
        return this.next;
    }
}


package OrderedCollection;
/**
 *
 * @author cotto
 */
public class List extends OrderedCollection {
    @Override
    public Value minimum() {
        if (this.root == null) {
            return null;
        }
        return this.root.getValue();
    }

    @Override
    public void insert(final Value v) {
        this.root = insert((ListElement) this.root, v);
    }

    private static ListElement insert(final ListElement l, final Value v) {
        if (l == null) {
            return new ListElement(v, null);
        }
        if (v.isSmaller(l.getValue())) {
            return new ListElement(v, l);
        }
        l.setNext(insert(l.getNext(), v));
        return l;
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public class Main {
    public static void main(final String[] args) {
        Random.args = args;
        final OrderedCollection coll = createCollection();
        coll.minimum();
    }

    /**
     * @return
     */
    private static OrderedCollection createCollection() {
        OrderedCollection result;
        if (Random.random() > 0) {
            result = new List();
        } else {
            result = new Tree();
        }
        int num = Random.random();
        for (int i = 0; i < num; i++) {
            result.insert(new IntValue(Random.random()));
        }
        return result;
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public class Node extends Element {
    private Node left;
    private Node right;

    public Node(final Value value, final Node leftParam, final Node rightParam) {
        super(value);
        this.left = leftParam;
        this.right = rightParam;
    }

    public void setLeft(final Node leftParam) {
        this.left = leftParam;
    }

    public void setRight(final Node rightParam) {
        this.right = rightParam;
    }

    public Node getLeft() {
        return this.left;
    }

    public Node getRight() {
        return this.right;
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public abstract class OrderedCollection {
    protected Element root;

    public abstract Value minimum();

    public abstract void insert(Value v);
}


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

    public static int random() {
        if (args.length <= index) {
            return 0;
        }
        final String string = args[index];
        index++;
        if (string == null) {
            return 0;
        }
        return string.length();
    }
}


package OrderedCollection;

/**
 *
 * @author cotto
 */
public class Tree extends OrderedCollection {
    @Override
    public Value minimum() {
        if (this.root == null) {
            return null;
        }
        return minimum((Node) this.root);
    }

    private static Value minimum(final Node n) {
        if (n.getLeft() == null) {
            return n.getValue();
        }
        return minimum(n.getLeft());
    }

    @Override
    public void insert(final Value v) {
        this.root = insert((Node) this.root, v);
    }

    private static Node insert(final Node n, final Value v) {
        if (n == null) {
            return new Node(v, null, null);
        }
        if (v.isSmaller(n.getValue())) {
            n.setLeft(insert(n.getLeft(), v));
            return n;
        }
        n.setRight(insert(n.getRight(), v));
        return n;
    }
}


package OrderedCollection;

/**
 * @author cotto
 */
public interface Value {
    boolean isSmaller(Value other);
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
OrderedCollection.Main.main([Ljava/lang/String;)V: Graph of 98 nodes with 0 SCCs.

OrderedCollection.Main.createCollection()LOrderedCollection/OrderedCollection;: Graph of 485 nodes with 2 SCCs.

OrderedCollection.Tree.insert(LOrderedCollection/Node;LOrderedCollection/Value;)LOrderedCollection/Node;: Graph of 116 nodes with 0 SCCs.

OrderedCollection.List.insert(LOrderedCollection/ListElement;LOrderedCollection/Value;)LOrderedCollection/ListElement;: Graph of 112 nodes with 0 SCCs.

OrderedCollection.Tree.minimum(LOrderedCollection/Node;)LOrderedCollection/Value;: Graph of 32 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

---

Log for SCC 0:

Generated 17 rules for P and 14 rules for R.

Combined rules. Obtained 1 rules for P and 3 rules for R.

Filtered ground terms:

2900_0_minimum_InvokeMethod(x1, x2, x3) → 2900_0_minimum_InvokeMethod(x2, x3)
OrderedCollection.Node(x1, x2) → OrderedCollection.Node(x2)
3610_0_minimum_Return(x1) → 3610_0_minimum_Return
3436_0_minimum_Return(x1) → 3436_0_minimum_Return
3363_0_minimum_Return(x1, x2) → 3363_0_minimum_Return

Filtered duplicate args:

2900_0_minimum_InvokeMethod(x1, x2) → 2900_0_minimum_InvokeMethod(x2)

Finished conversion. Obtained 1 rules for P and 3 rules for R. System has no predefined symbols.

---

Log for SCC 1:

Generated 48 rules for P and 68 rules for R.

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

Filtered ground terms:

OrderedCollection.ListElement(x1, x2) → OrderedCollection.ListElement(x2)
9579_0_insert_NONNULL(x1, x2, x3, x4) → 9579_0_insert_NONNULL(x2, x3, x4)
11986_0_insert_Return(x1, x2) → 11986_0_insert_Return(x2)
11929_0_insert_Return(x1, x2) → 11929_0_insert_Return(x2)
10473_0_insert_Return(x1, x2) → 10473_0_insert_Return(x2)
10469_0_insert_Return(x1, x2) → 10469_0_insert_Return(x2)
10063_0_insert_Return(x1, x2, x3, x4) → 10063_0_insert_Return(x3, x4)

Filtered duplicate args:

10223_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10223_1_insert_InvokeMethod(x1, x3, x4, x5)
9579_0_insert_NONNULL(x1, x2, x3) → 9579_0_insert_NONNULL(x2, x3)
10207_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10207_1_insert_InvokeMethod(x1, x3, x4, x5)

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

---

Log for SCC 2:

Generated 48 rules for P and 72 rules for R.

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

Filtered ground terms:

OrderedCollection.Node(x1, x2) → OrderedCollection.Node(x2)
9773_0_insert_NONNULL(x1, x2, x3, x4) → 9773_0_insert_NONNULL(x2, x3, x4)
12734_0_insert_Return(x1, x2) → 12734_0_insert_Return(x2)
12671_0_insert_Return(x1, x2) → 12671_0_insert_Return(x2)
10796_0_insert_Return(x1, x2) → 10796_0_insert_Return(x2)
10790_0_insert_Return(x1, x2) → 10790_0_insert_Return(x2)
10370_0_insert_Return(x1, x2, x3, x4) → 10370_0_insert_Return(x3, x4)

Filtered duplicate args:

10447_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10447_1_insert_InvokeMethod(x1, x3, x4, x5)
9773_0_insert_NONNULL(x1, x2, x3) → 9773_0_insert_NONNULL(x2, x3)
10431_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10431_1_insert_InvokeMethod(x1, x3, x4, x5)

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

---

Log for SCC 3:

Generated 119 rules for P and 165 rules for R.

Combined rules. Obtained 20 rules for P and 27 rules for R.

Filtered ground terms:

15160_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15160_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
OrderedCollection.Tree(x1) → OrderedCollection.Tree
OrderedCollection.OrderedCollection(x1, x2) → OrderedCollection.OrderedCollection(x2)
OrderedCollection.IntValue(x1) → OrderedCollection.IntValue
15160_0_insert_CheckCast(x1, x2, x3, x4) → 15160_0_insert_CheckCast(x3, x4)
Cond_14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14687_0_random_GT(x1, x2, x3) → 14687_0_random_GT(x2, x3)
14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
14532_0_createCollection_Load(x1, x2, x3, x4, x5) → 14532_0_createCollection_Load(x2, x3, x4, x5)
OrderedCollection.Node(x1) → OrderedCollection.Node
OrderedCollection.Element(x1) → OrderedCollection.Element
15346_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15346_2_createCollection_InvokeMethod(x1, x3, x4)
10370_0_insert_Return(x1, x2, x3, x4) → 10370_0_insert_Return(x3)
15346_1_insert_InvokeMethod(x1, x2, x3, x4) → 15346_1_insert_InvokeMethod(x1)
15346_0_insert_Load(x1, x2, x3) → 15346_0_insert_Load
15260_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15260_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
10796_0_insert_Return(x1, x2) → 10796_0_insert_Return
15260_1_insert_InvokeMethod(x1, x2, x3, x4) → 15260_1_insert_InvokeMethod(x1, x2, x3)
10790_0_insert_Return(x1, x2) → 10790_0_insert_Return
12734_0_insert_Return(x1, x2) → 12734_0_insert_Return
12671_0_insert_Return(x1, x2) → 12671_0_insert_Return
15260_0_insert_Load(x1, x2, x3) → 15260_0_insert_Load(x2, x3)
Cond_14967_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14967_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6)
14967_0_random_IntArithmetic(x1, x2, x3, x4) → 14967_0_random_IntArithmetic(x2, x3)
14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
15940_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15940_2_createCollection_InvokeMethod(x1, x3, x4)
15940_1_insert_InvokeMethod(x1, x2, x3, x4) → 15940_1_insert_InvokeMethod(x1)
15940_0_insert_Load(x1, x2, x3) → 15940_0_insert_Load
Cond_14967_1_createCollection_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14967_1_createCollection_InvokeMethod1(x1, x2, x4, x5)
15848_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15848_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
15848_1_insert_InvokeMethod(x1, x2, x3, x4) → 15848_1_insert_InvokeMethod(x1, x2, x3)
15848_0_insert_Load(x1, x2, x3) → 15848_0_insert_Load(x2, x3)
Cond_14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
Cond_14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14771_0_random_ArrayAccess(x1, x2, x3) → 14771_0_random_ArrayAccess(x2, x3)
14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
Cond_14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14684_0_random_GT(x1, x2, x3) → 14684_0_random_GT(x2, x3)
14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
Cond_14532_0_createCollection_Load1(x1, x2, x3, x4, x5, x6) → Cond_14532_0_createCollection_Load1(x1, x3, x4, x5, x6)
Cond_14532_0_createCollection_Load(x1, x2, x3, x4, x5, x6) → Cond_14532_0_createCollection_Load(x1, x3, x4, x5, x6)
10431_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10431_1_insert_InvokeMethod(x1, x4, x5)
9773_0_insert_NONNULL(x1, x2, x3, x4) → 9773_0_insert_NONNULL(x2, x3, x4)
10447_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10447_1_insert_InvokeMethod(x1, x4, x5)
15371_0_insert_Return(x1, x2) → 15371_0_insert_Return
15365_0_insert_Return(x1) → 15365_0_insert_Return
15358_0_insert_Return(x1, x2) → 15358_0_insert_Return
15356_0_insert_Return(x1, x2) → 15356_0_insert_Return
15265_0_insert_Return(x1, x2, x3, x4) → 15265_0_insert_Return(x3)
15962_0_insert_Return(x1, x2) → 15962_0_insert_Return
15956_0_insert_Return(x1) → 15956_0_insert_Return
15950_0_insert_Return(x1, x2) → 15950_0_insert_Return
15948_0_insert_Return(x1, x2) → 15948_0_insert_Return
15853_0_insert_Return(x1, x2, x3, x4) → 15853_0_insert_Return(x3)

Filtered duplicate args:

15160_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 15160_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14687_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14687_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14532_0_createCollection_Load(x1, x2, x3, x4) → 14532_0_createCollection_Load(x1, x2, x4)
15260_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 15260_2_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14967_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_14967_1_createCollection_InvokeMethod2(x1, x2, x4, x5, x6)
14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14967_1_createCollection_InvokeMethod(x1, x3, x4, x5)
15848_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 15848_2_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14967_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
Cond_14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14771_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14771_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14684_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14684_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14532_0_createCollection_Load1(x1, x2, x3, x4, x5) → Cond_14532_0_createCollection_Load1(x1, x2, x3, x5)
Cond_14532_0_createCollection_Load(x1, x2, x3, x4, x5) → Cond_14532_0_createCollection_Load(x1, x2, x3, x5)
9773_0_insert_NONNULL(x1, x2, x3) → 9773_0_insert_NONNULL(x2, x3)

Filtered all free variables:

14684_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14684_1_createCollection_InvokeMethod(x2, x3, x4)
14687_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14687_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14684_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14684_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14771_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14771_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14771_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14771_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14967_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14967_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14967_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14967_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14967_1_createCollection_InvokeMethod1(x1, x2, x3, x4) → Cond_14967_1_createCollection_InvokeMethod1(x1, x3, x4)
Cond_14967_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_14967_1_createCollection_InvokeMethod2(x1, x3, x4, x5)
Cond_14687_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14687_1_createCollection_InvokeMethod(x1, x3, x4, x5)
10447_1_insert_InvokeMethod(x1, x2, x3) → 10447_1_insert_InvokeMethod(x1, x3)
9773_0_insert_NONNULL(x1, x2) → 9773_0_insert_NONNULL(x1)
10431_1_insert_InvokeMethod(x1, x2, x3) → 10431_1_insert_InvokeMethod(x1, x3)

Combined rules. Obtained 14 rules for P and 27 rules for R.

Finished conversion. Obtained 14 rules for P and 27 rules for R. System has predefined symbols.

---

Log for SCC 4:

Generated 119 rules for P and 161 rules for R.

Combined rules. Obtained 20 rules for P and 27 rules for R.

Filtered ground terms:

14767_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 14767_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
OrderedCollection.List(x1) → OrderedCollection.List
OrderedCollection.OrderedCollection(x1, x2) → OrderedCollection.OrderedCollection(x2)
OrderedCollection.IntValue(x1) → OrderedCollection.IntValue
14767_0_insert_CheckCast(x1, x2, x3, x4) → 14767_0_insert_CheckCast(x3, x4)
Cond_14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14537_0_random_GT(x1, x2, x3) → 14537_0_random_GT(x2, x3)
14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
14162_0_createCollection_Load(x1, x2, x3, x4, x5) → 14162_0_createCollection_Load(x2, x3, x4, x5)
OrderedCollection.ListElement(x1) → OrderedCollection.ListElement
OrderedCollection.Element(x1) → OrderedCollection.Element
14938_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 14938_2_createCollection_InvokeMethod(x1, x3, x4)
10063_0_insert_Return(x1, x2, x3, x4) → 10063_0_insert_Return(x3)
14938_1_insert_InvokeMethod(x1, x2, x3, x4) → 14938_1_insert_InvokeMethod(x1)
14938_0_insert_Load(x1, x2, x3) → 14938_0_insert_Load
14864_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 14864_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
10473_0_insert_Return(x1, x2) → 10473_0_insert_Return
14864_1_insert_InvokeMethod(x1, x2, x3, x4) → 14864_1_insert_InvokeMethod(x1, x2, x3)
10469_0_insert_Return(x1, x2) → 10469_0_insert_Return
11986_0_insert_Return(x1, x2) → 11986_0_insert_Return
11929_0_insert_Return(x1, x2) → 11929_0_insert_Return
14864_0_insert_Load(x1, x2, x3) → 14864_0_insert_Load(x2, x3)
Cond_14645_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14645_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6)
14645_0_random_IntArithmetic(x1, x2, x3, x4) → 14645_0_random_IntArithmetic(x2, x3)
14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
15646_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15646_2_createCollection_InvokeMethod(x1, x3, x4)
15646_1_insert_InvokeMethod(x1, x2, x3, x4) → 15646_1_insert_InvokeMethod(x1)
15646_0_insert_Load(x1, x2, x3) → 15646_0_insert_Load
Cond_14645_1_createCollection_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14645_1_createCollection_InvokeMethod1(x1, x2, x4, x5)
15556_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → 15556_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
15556_1_insert_InvokeMethod(x1, x2, x3, x4) → 15556_1_insert_InvokeMethod(x1, x2, x3)
15556_0_insert_Load(x1, x2, x3) → 15556_0_insert_Load(x2, x3)
Cond_14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
Cond_14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14591_0_random_ArrayAccess(x1, x2, x3) → 14591_0_random_ArrayAccess(x2, x3)
14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
Cond_14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6)
14535_0_random_GT(x1, x2, x3) → 14535_0_random_GT(x2, x3)
14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5)
Cond_14162_0_createCollection_Load1(x1, x2, x3, x4, x5, x6) → Cond_14162_0_createCollection_Load1(x1, x3, x4, x5, x6)
Cond_14162_0_createCollection_Load(x1, x2, x3, x4, x5, x6) → Cond_14162_0_createCollection_Load(x1, x3, x4, x5, x6)
10207_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10207_1_insert_InvokeMethod(x1, x4, x5)
9579_0_insert_NONNULL(x1, x2, x3, x4) → 9579_0_insert_NONNULL(x2, x3, x4)
10223_1_insert_InvokeMethod(x1, x2, x3, x4, x5) → 10223_1_insert_InvokeMethod(x1, x4, x5)
14959_0_insert_Return(x1, x2) → 14959_0_insert_Return
14954_0_insert_Return(x1) → 14954_0_insert_Return
14948_0_insert_Return(x1, x2) → 14948_0_insert_Return
14946_0_insert_Return(x1, x2) → 14946_0_insert_Return
14869_0_insert_Return(x1, x2, x3, x4) → 14869_0_insert_Return(x3)
15672_0_insert_Return(x1, x2) → 15672_0_insert_Return
15666_0_insert_Return(x1) → 15666_0_insert_Return
15660_0_insert_Return(x1, x2) → 15660_0_insert_Return
15658_0_insert_Return(x1, x2) → 15658_0_insert_Return
15561_0_insert_Return(x1, x2, x3, x4) → 15561_0_insert_Return(x3)

Filtered duplicate args:

14767_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14767_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14537_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14537_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14162_0_createCollection_Load(x1, x2, x3, x4) → 14162_0_createCollection_Load(x1, x2, x4)
14864_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14864_2_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14645_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_14645_1_createCollection_InvokeMethod2(x1, x2, x4, x5, x6)
14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14645_1_createCollection_InvokeMethod(x1, x3, x4, x5)
15556_2_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 15556_2_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14645_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
Cond_14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14591_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14591_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_14535_1_createCollection_InvokeMethod(x1, x2, x4, x5, x6)
14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → 14535_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14162_0_createCollection_Load1(x1, x2, x3, x4, x5) → Cond_14162_0_createCollection_Load1(x1, x2, x3, x5)
Cond_14162_0_createCollection_Load(x1, x2, x3, x4, x5) → Cond_14162_0_createCollection_Load(x1, x2, x3, x5)
9579_0_insert_NONNULL(x1, x2, x3) → 9579_0_insert_NONNULL(x2, x3)

Filtered all free variables:

14535_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14535_1_createCollection_InvokeMethod(x2, x3, x4)
14537_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14537_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14535_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14535_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14591_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14591_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14591_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14591_1_createCollection_InvokeMethod(x1, x3, x4, x5)
14645_1_createCollection_InvokeMethod(x1, x2, x3, x4) → 14645_1_createCollection_InvokeMethod(x2, x3, x4)
Cond_14645_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14645_1_createCollection_InvokeMethod(x1, x3, x4, x5)
Cond_14645_1_createCollection_InvokeMethod1(x1, x2, x3, x4) → Cond_14645_1_createCollection_InvokeMethod1(x1, x3, x4)
Cond_14645_1_createCollection_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_14645_1_createCollection_InvokeMethod2(x1, x3, x4, x5)
Cond_14537_1_createCollection_InvokeMethod(x1, x2, x3, x4, x5) → Cond_14537_1_createCollection_InvokeMethod(x1, x3, x4, x5)
10223_1_insert_InvokeMethod(x1, x2, x3) → 10223_1_insert_InvokeMethod(x1, x3)
9579_0_insert_NONNULL(x1, x2) → 9579_0_insert_NONNULL(x1)
10207_1_insert_InvokeMethod(x1, x2, x3) → 10207_1_insert_InvokeMethod(x1, x3)

Combined rules. Obtained 14 rules for P and 27 rules for R.

Finished conversion. Obtained 14 rules for P and 27 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:
none


The ITRS R consists of the following rules:
3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))) → 3436_0_minimum_Return
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))))) → 3610_0_minimum_Return
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0)))))))))) → 3610_0_minimum_Return

The integer pair graph contains the following rules and edges:
(0): 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]))))) → 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(x0[0]))

(0) -> (0), if ((java.lang.Object(x0[0]) →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]'))))))

The set Q consists of the following terms:
3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))))))
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0))))))))))

(6) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(7) Obligation:

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

2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]))))) → 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(x0[0]))

The TRS R consists of the following rules:

3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))) → 3436_0_minimum_Return
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))))) → 3610_0_minimum_Return
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0)))))))))) → 3610_0_minimum_Return

The set Q consists of the following terms:

3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))))))
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0))))))))))

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

(8) 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.

(9) Obligation:

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

2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]))))) → 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(x0[0]))

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

3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))))))
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0))))))))))

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

(10) 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].

3398_1_minimum_InvokeMethod(3363_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL))))
3398_1_minimum_InvokeMethod(3436_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL)))))))
3398_1_minimum_InvokeMethod(3610_0_minimum_Return, java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0))))))))))

(11) Obligation:

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

2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]))))) → 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(x0[0]))

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

(12) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(x0[0]))))) → 2900_0_MINIMUM_INVOKEMETHOD(java.lang.Object(x0[0]))
  The graph contains the following edges 1 > 1

(13) YES

(14) 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:
9579_0_insert_NONNULL(java.lang.Object(x0), NULL) → 10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0))))
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0)) → 10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1))))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(x3))))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(x2))))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(x5))))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(x4))))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0)) → 10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL)))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), NULL)))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), NULL)))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), NULL)))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), NULL)))

The integer pair graph contains the following rules and edges:
(0): 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))) → 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
(1): 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))) → 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

(0) -> (0), if ((java.lang.Object(x2[0]) →^* java.lang.Object(x2[0]'))∧(x0[0] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]'), java.lang.Object(x1[0]')))))

(0) -> (1), if ((java.lang.Object(x2[0]) →^* java.lang.Object(x1[1]))∧(x0[0] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))))

(1) -> (0), if ((java.lang.Object(x1[1]) →^* java.lang.Object(x2[0]))∧(x0[1] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))))

(1) -> (1), if ((java.lang.Object(x1[1]) →^* java.lang.Object(x1[1]'))∧(x0[1] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]'), NULL))))

The set Q consists of the following terms:
9579_0_insert_NONNULL(java.lang.Object(x0), NULL)
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4))

(15) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(16) Obligation:

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

9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))) → 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))) → 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

The TRS R consists of the following rules:

9579_0_insert_NONNULL(java.lang.Object(x0), NULL) → 10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0))))
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0)) → 10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1))))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(x3))))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(x2))))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(x5))))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5)) → 11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(x4))))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0)) → 10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL)))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), NULL)))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), NULL)))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), NULL)))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4)) → 11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), NULL)))

The set Q consists of the following terms:

9579_0_insert_NONNULL(java.lang.Object(x0), NULL)
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4))

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

(17) 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.

(18) Obligation:

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

9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))) → 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))) → 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

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

9579_0_insert_NONNULL(java.lang.Object(x0), NULL)
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4))

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

(19) 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].

9579_0_insert_NONNULL(java.lang.Object(x0), NULL)
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10207_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), NULL)), NULL, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x2), NULL)), x2, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x1), NULL)), x1, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x4), NULL)), x4, java.lang.Object(x5))
10223_1_insert_InvokeMethod(11986_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x3), NULL)), x3, java.lang.Object(x4))

(20) Obligation:

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

9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))) → 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))) → 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

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

(21) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[0]), java.lang.Object(x1[0])))) → 9579_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
  The graph contains the following edges 1 >= 1, 2 > 2

• 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.ListElement(x0[1]), NULL))) → 9579_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])
  The graph contains the following edges 1 >= 1, 2 > 2

(22) YES

(23) 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:
9773_0_insert_NONNULL(java.lang.Object(x0), NULL) → 10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0))))
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0)) → 10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1))))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(x3))))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(x2))))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(x5))))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(x4))))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0)) → 10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL)))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), NULL)))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), NULL)))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), NULL)))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), NULL)))

The integer pair graph contains the following rules and edges:
(0): 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))) → 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
(1): 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))) → 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

(0) -> (0), if ((java.lang.Object(x2[0]) →^* java.lang.Object(x2[0]'))∧(x0[0] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]'), java.lang.Object(x1[0]')))))

(0) -> (1), if ((java.lang.Object(x2[0]) →^* java.lang.Object(x1[1]))∧(x0[0] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))))

(1) -> (0), if ((java.lang.Object(x1[1]) →^* java.lang.Object(x2[0]))∧(x0[1] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))))

(1) -> (1), if ((java.lang.Object(x1[1]) →^* java.lang.Object(x1[1]'))∧(x0[1] →^* java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]'), NULL))))

The set Q consists of the following terms:
9773_0_insert_NONNULL(java.lang.Object(x0), NULL)
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4))

(24) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(25) Obligation:

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

9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))) → 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))) → 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

The TRS R consists of the following rules:

9773_0_insert_NONNULL(java.lang.Object(x0), NULL) → 10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0))))
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0)) → 10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1))))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(x3))))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(x2))))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(x5))))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5)) → 12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(x4))))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0)) → 10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL)))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), NULL)))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), NULL)))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), NULL)))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4)) → 12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), NULL)))

The set Q consists of the following terms:

9773_0_insert_NONNULL(java.lang.Object(x0), NULL)
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4))

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

(26) 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.

(27) Obligation:

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

9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))) → 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))) → 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

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

9773_0_insert_NONNULL(java.lang.Object(x0), NULL)
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4))

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

(28) 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].

9773_0_insert_NONNULL(java.lang.Object(x0), NULL)
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x1))), NULL, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), java.lang.Object(x3))), x2, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), java.lang.Object(x2))), x1, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), java.lang.Object(x5))), x4, java.lang.Object(x6))
10431_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), java.lang.Object(x4))), x3, java.lang.Object(x5))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), NULL)), NULL, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), java.lang.Object(x1)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x2), NULL)), x2, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(NULL), java.lang.Object(x0)))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x1), NULL)), x1, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), java.lang.Object(x3)))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x4), NULL)), x4, java.lang.Object(x5))
10447_1_insert_InvokeMethod(12734_0_insert_Return(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0), x1))), x2))), NULL))), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x3), NULL)), x3, java.lang.Object(x4))

(29) Obligation:

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

9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))) → 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))) → 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])

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

(30) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[0]), java.lang.Object(x1[0])))) → 9773_0_INSERT_NONNULL(java.lang.Object(x2[0]), x0[0])
  The graph contains the following edges 1 >= 1, 2 > 2

• 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), java.lang.Object(OrderedCollection.Element(OrderedCollection.Node(x0[1]), NULL))) → 9773_0_INSERT_NONNULL(java.lang.Object(x1[1]), x0[1])
  The graph contains the following edges 1 >= 1, 2 > 2

(31) YES

(32) 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

The ITRS R consists of the following rules:
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15853_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15948_0_insert_Return
15940_0_insert_Load → 15950_0_insert_Return
15940_0_insert_Load → 15956_0_insert_Return
15940_0_insert_Load → 15962_0_insert_Return
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15265_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15356_0_insert_Return
15940_0_insert_Load → 15358_0_insert_Return
15940_0_insert_Load → 15365_0_insert_Return
15940_0_insert_Load → 15371_0_insert_Return
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15940_0_insert_Load → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10370_0_insert_Return(java.lang.Object(x0))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10447_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10796_0_insert_Return
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10431_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10790_0_insert_Return

The integer pair graph contains the following rules and edges:
(0): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], x2[0] + 1)
(1): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], x2[1] + 1)
(2): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], x2[2] + 1)
(3): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], x2[3] + 1)
(4): 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], x1[4] + 1)
(5): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], x2[5] + 1)
(6): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], x2[6] + 1)
(7): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], x2[7] + 1)
(8): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], x2[8] + 1)
(9): 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], x1[9] + 1)
(10): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14532_0_CREATECOLLECTION_LOAD(x2[10] < x1[10], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
(11): COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(12): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14532_0_CREATECOLLECTION_LOAD1(x1[12] < x0[12], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
(13): COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])
(14): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14532_0_CREATECOLLECTION_LOAD2(x2[14] < x1[14], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
(15): COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(16): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14532_0_CREATECOLLECTION_LOAD3(x1[16] < x0[16], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
(17): COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])

(0) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[0] →^* x1[10])∧(x2[0] + 1 →^* x2[10]))

(0) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[0] →^* x0[12])∧(x2[0] + 1 →^* x1[12]))

(0) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[0] →^* x1[14])∧(x2[0] + 1 →^* x2[14]))

(0) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[0] →^* x0[16])∧(x2[0] + 1 →^* x1[16]))

(1) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[1] →^* x1[10])∧(x2[1] + 1 →^* x2[10]))

(1) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[1] →^* x0[12])∧(x2[1] + 1 →^* x1[12]))

(1) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[1] →^* x1[14])∧(x2[1] + 1 →^* x2[14]))

(1) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[1] →^* x0[16])∧(x2[1] + 1 →^* x1[16]))

(2) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[2] →^* x1[10])∧(x2[2] + 1 →^* x2[10]))

(2) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[2] →^* x0[12])∧(x2[2] + 1 →^* x1[12]))

(2) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[2] →^* x1[14])∧(x2[2] + 1 →^* x2[14]))

(2) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[2] →^* x0[16])∧(x2[2] + 1 →^* x1[16]))

(3) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[3] →^* x1[10])∧(x2[3] + 1 →^* x2[10]))

(3) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[3] →^* x0[12])∧(x2[3] + 1 →^* x1[12]))

(3) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[3] →^* x1[14])∧(x2[3] + 1 →^* x2[14]))

(3) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[3] →^* x0[16])∧(x2[3] + 1 →^* x1[16]))

(4) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x0[4] →^* x1[10])∧(x1[4] + 1 →^* x2[10]))

(4) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[4] →^* x0[12])∧(x1[4] + 1 →^* x1[12]))

(4) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x0[4] →^* x1[14])∧(x1[4] + 1 →^* x2[14]))

(4) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[4] →^* x0[16])∧(x1[4] + 1 →^* x1[16]))

(5) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[5] →^* x1[10])∧(x2[5] + 1 →^* x2[10]))

(5) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[5] →^* x0[12])∧(x2[5] + 1 →^* x1[12]))

(5) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[5] →^* x1[14])∧(x2[5] + 1 →^* x2[14]))

(5) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[5] →^* x0[16])∧(x2[5] + 1 →^* x1[16]))

(6) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[6] →^* x1[10])∧(x2[6] + 1 →^* x2[10]))

(6) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[6] →^* x0[12])∧(x2[6] + 1 →^* x1[12]))

(6) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[6] →^* x1[14])∧(x2[6] + 1 →^* x2[14]))

(6) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[6] →^* x0[16])∧(x2[6] + 1 →^* x1[16]))

(7) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[7] →^* x1[10])∧(x2[7] + 1 →^* x2[10]))

(7) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[7] →^* x0[12])∧(x2[7] + 1 →^* x1[12]))

(7) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[7] →^* x1[14])∧(x2[7] + 1 →^* x2[14]))

(7) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[7] →^* x0[16])∧(x2[7] + 1 →^* x1[16]))

(8) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[8] →^* x1[10])∧(x2[8] + 1 →^* x2[10]))

(8) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[8] →^* x0[12])∧(x2[8] + 1 →^* x1[12]))

(8) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[8] →^* x1[14])∧(x2[8] + 1 →^* x2[14]))

(8) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[8] →^* x0[16])∧(x2[8] + 1 →^* x1[16]))

(9) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x0[9] →^* x1[10])∧(x1[9] + 1 →^* x2[10]))

(9) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[9] →^* x0[12])∧(x1[9] + 1 →^* x1[12]))

(9) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x0[9] →^* x1[14])∧(x1[9] + 1 →^* x2[14]))

(9) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[9] →^* x0[16])∧(x1[9] + 1 →^* x1[16]))

(10) -> (11), if ((x2[10] < x1[10] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(x1[10] →^* x1[11])∧(x2[10] →^* x2[11]))

(11) -> (0), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])))∧(x1[11] →^* x1[0])∧(x2[11] →^* x2[0])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))))

(11) -> (1), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])))∧(x1[11] →^* x1[1])∧(x2[11] →^* x2[1])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))))

(11) -> (2), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])))∧(x1[11] →^* x1[2])∧(x2[11] →^* x2[2])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))))

(11) -> (3), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])))∧(x1[11] →^* x1[3])∧(x2[11] →^* x2[3])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))))

(12) -> (13), if ((x1[12] < x0[12] →^* TRUE)∧(x0[12] →^* x0[13])∧(x1[12] →^* x1[13]))

(13) -> (4), if ((15940_1_insert_InvokeMethod(15940_0_insert_Load) →^* 15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[13] →^* x0[4])∧(x1[13] →^* x1[4]))

(14) -> (15), if ((x2[14] < x1[14] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(x1[14] →^* x1[15])∧(x2[14] →^* x2[15]))

(15) -> (5), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])))∧(x1[15] →^* x1[5])∧(x2[15] →^* x2[5])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))))

(15) -> (6), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])))∧(x1[15] →^* x1[6])∧(x2[15] →^* x2[6])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))))

(15) -> (7), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])))∧(x1[15] →^* x1[7])∧(x2[15] →^* x2[7])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))))

(15) -> (8), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])))∧(x1[15] →^* x1[8])∧(x2[15] →^* x2[8])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))))

(16) -> (17), if ((x1[16] < x0[16] →^* TRUE)∧(x0[16] →^* x0[17])∧(x1[16] →^* x1[17]))

(17) -> (9), if ((15346_1_insert_InvokeMethod(15940_0_insert_Load) →^* 15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[17] →^* x0[9])∧(x1[17] →^* x1[9]))

The set Q consists of the following terms:
15848_0_insert_Load(NULL, java.lang.Object(x0))
15940_0_insert_Load
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(33) 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 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1)) which results in the following constraint:
  

  (1)    (15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))))≥NonInfC∧15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥))

  
  
  We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (2)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (3)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (4)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (5)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_49] ≥ 0)

  
  
  

For Pair 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1)) which results in the following constraint:
  

  (6)    (15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))))≥NonInfC∧15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥))

  
  
  We simplified constraint (6) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (7)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (7) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (8)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (8) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (9)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (9) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (10)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

  
  
  

For Pair 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1)) which results in the following constraint:
  

  (11)    (15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))))≥NonInfC∧15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥))

  
  
  We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (12)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (12) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (13)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (13) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (14)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (14) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (15)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 0)

  
  
  

For Pair 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1)) which results in the following constraint:
  

  (16)    (15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))))≥NonInfC∧15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥))

  
  
  We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (17)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (18)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (19)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (20)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)

  
  
  

For Pair 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1)) the following chains were created:

• We consider the chain 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1)) which results in the following constraint:
  

  (21)    (15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4])≥NonInfC∧15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4])≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥))

  
  
  We simplified constraint (21) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (22)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (23)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (24)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (25)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)

  
  
  

For Pair 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1)) which results in the following constraint:
  

  (26)    (15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))))≥NonInfC∧15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥))

  
  
  We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (27)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (28)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (29)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (30)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_59] ≥ 0)

  
  
  

For Pair 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1)) which results in the following constraint:
  

  (31)    (15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))))≥NonInfC∧15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥))

  
  
  We simplified constraint (31) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (32)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (32) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (33)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (33) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (34)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (34) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (35)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_61] ≥ 0)

  
  
  

For Pair 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1)) which results in the following constraint:
  

  (36)    (15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))))≥NonInfC∧15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥))

  
  
  We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (37)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (37) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (38)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (39)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (40)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_63] ≥ 0)

  
  
  

For Pair 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1)) which results in the following constraint:
  

  (41)    (15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))))≥NonInfC∧15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))))≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥))

  
  
  We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (42)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (43)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (44)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (45)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_65] ≥ 0)

  
  
  

For Pair 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1)) the following chains were created:

• We consider the chain 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1)) which results in the following constraint:
  

  (46)    (15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9])≥NonInfC∧15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9])≥14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))∧(U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥))

  
  
  We simplified constraint (46) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (47)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (47) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (48)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (48) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (49)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (49) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (50)    ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_67] ≥ 0)

  
  
  

For Pair 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14532_0_CREATECOLLECTION_LOAD(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) the following chains were created:

• We consider the chain 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]), COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))) which results in the following constraint:
  

  (51)    (<(x2[10], x1[10])=TRUE∧java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10])))=java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))∧x1[10]=x1[11]∧x2[10]=x2[11] ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥))

  
  
  We simplified constraint (51) using rules (I), (II), (IV) which results in the following new constraint:
  

  (52)    (<(x2[10], x1[10])=TRUE ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥))

  
  
  We simplified constraint (52) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (53)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (53) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (54)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (54) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (55)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (56)    (x1[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (57)    (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  

  (58)    (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  

For Pair COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) the following chains were created:

• We consider the chain COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))) which results in the following constraint:
  

  (59)    (COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11])≥NonInfC∧COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11])≥15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥))

  
  
  We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (60)    ((U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (61)    ((U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (62)    ((U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (62) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (63)    ((U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

  
  
  

For Pair 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14532_0_CREATECOLLECTION_LOAD1(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) the following chains were created:

• We consider the chain 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]), COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13]) which results in the following constraint:
  

  (64)    (<(x1[12], x0[12])=TRUE∧x0[12]=x0[13]∧x1[12]=x1[13] ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥))

  
  
  We simplified constraint (64) using rule (IV) which results in the following new constraint:
  

  (65)    (<(x1[12], x0[12])=TRUE ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥))

  
  
  We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (66)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (66) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (67)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (67) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (68)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (69)    (x0[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (70)    (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  

  (71)    (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  

For Pair COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0, x1) the following chains were created:

• We consider the chain COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13]) which results in the following constraint:
  

  (72)    (COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13])≥NonInfC∧COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13])≥15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])∧(U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥))

  
  
  We simplified constraint (72) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (73)    ((U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (73) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (74)    ((U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (74) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (75)    ((U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (75) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (76)    ((U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

  
  
  

For Pair 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14532_0_CREATECOLLECTION_LOAD2(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) the following chains were created:

• We consider the chain 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]), COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))) which results in the following constraint:
  

  (77)    (<(x2[14], x1[14])=TRUE∧java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14])))=java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))∧x1[14]=x1[15]∧x2[14]=x2[15] ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥))

  
  
  We simplified constraint (77) using rules (I), (II), (IV) which results in the following new constraint:
  

  (78)    (<(x2[14], x1[14])=TRUE ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥))

  
  
  We simplified constraint (78) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (79)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (79) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (80)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (80) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (81)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (82)    (x1[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (82) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (83)    (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  

  (84)    (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  

For Pair COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) the following chains were created:

• We consider the chain COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))) which results in the following constraint:
  

  (85)    (COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15])≥NonInfC∧COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15])≥15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥))

  
  
  We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (86)    ((U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (86) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (87)    ((U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (87) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (88)    ((U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (88) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (89)    ((U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_79] ≥ 0)

  
  
  

For Pair 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14532_0_CREATECOLLECTION_LOAD3(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) the following chains were created:

• We consider the chain 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]), COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17]) which results in the following constraint:
  

  (90)    (<(x1[16], x0[16])=TRUE∧x0[16]=x0[17]∧x1[16]=x1[17] ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥))

  
  
  We simplified constraint (90) using rule (IV) which results in the following new constraint:
  

  (91)    (<(x1[16], x0[16])=TRUE ⇒ 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥NonInfC∧14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])∧(U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥))

  
  
  We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (92)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (93)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (93) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (94)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (94) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (95)    (x0[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (95) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (96)    (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  

  (97)    (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  

For Pair COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0, x1) the following chains were created:

• We consider the chain COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17]) which results in the following constraint:
  

  (98)    (COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17])≥NonInfC∧COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17])≥15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])∧(U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥))

  
  
  We simplified constraint (98) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (99)    ((U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (99) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (100)    ((U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (100) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (101)    ((U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (102)    ((U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_83] ≥ 0)

  
  
  

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

• 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_49] ≥ 0)
    
  
  
• 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)
    
  
  
• 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 0)
    
  
  
• 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)
    
  
  
• 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)
    
  
  
• 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_59] ≥ 0)
    
  
  
• 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_61] ≥ 0)
    
  
  
• 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_63] ≥ 0)
    
  
  
• 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_65] ≥ 0)
    
  
  
• 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1))
  
  • ((U^Increasing(14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_67] ≥ 0)
    
  
  
• 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14532_0_CREATECOLLECTION_LOAD(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2)
  
  • (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)
    
  • (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)
    
  
  
• COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))))
  
  • ((U^Increasing(15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)
    
  
  
• 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14532_0_CREATECOLLECTION_LOAD1(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1)
  
  • (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)
    
  • (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)
    
  
  
• COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0, x1)
  
  • ((U^Increasing(15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)
    
  
  
• 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14532_0_CREATECOLLECTION_LOAD2(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2)
  
  • (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)
    
  • (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)
    
  
  
• COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))))
  
  • ((U^Increasing(15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_79] ≥ 0)
    
  
  
• 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14532_0_CREATECOLLECTION_LOAD3(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1)
  
  • (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)
    
  • (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)
    
  
  
• COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0, x1)
  
  • ((U^Increasing(15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_83] ≥ 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(15848_0_insert_Load(x₁, x₂)) = [-1]   
POL(NULL) = [-1]   
POL(java.lang.Object(x₁)) = [-1]   
POL(15853_0_insert_Return(x₁)) = [-1]   
POL(15940_0_insert_Load) = [-1]   
POL(15948_0_insert_Return) = [-1]   
POL(15950_0_insert_Return) = [-1]   
POL(15956_0_insert_Return) = [-1]   
POL(15962_0_insert_Return) = [-1]   
POL(15265_0_insert_Return(x₁)) = [-1]   
POL(15356_0_insert_Return) = [-1]   
POL(15358_0_insert_Return) = [-1]   
POL(15365_0_insert_Return) = [-1]   
POL(15371_0_insert_Return) = [-1]   
POL(OrderedCollection.IntValue) = [-1]   
POL(9773_0_insert_NONNULL(x₁)) = [-1]   
POL(10370_0_insert_Return(x₁)) = [-1]   
POL(10447_1_insert_InvokeMethod(x₁, x₂)) = [-1]   
POL(12671_0_insert_Return) = [-1]   
POL(12734_0_insert_Return) = [-1]   
POL(10790_0_insert_Return) = [-1]   
POL(10796_0_insert_Return) = [-1]   
POL(10431_1_insert_InvokeMethod(x₁, x₂)) = [-1]   
POL(15848_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₂ + [-1]x₃   
POL(15848_1_insert_InvokeMethod(x₁, x₂, x₃)) = [-1]   
POL(OrderedCollection.OrderedCollection(x₁)) = [-1]   
POL(14532_0_CREATECOLLECTION_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂   
POL(OrderedCollection.Element) = [-1]   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(15940_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃   
POL(15940_1_insert_InvokeMethod(x₁)) = [-1]   
POL(15260_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₂ + [-1]x₃   
POL(15260_1_insert_InvokeMethod(x₁, x₂, x₃)) = [-1]   
POL(15346_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃   
POL(15346_1_insert_InvokeMethod(x₁)) = [-1]   
POL(COND_14532_0_CREATECOLLECTION_LOAD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(<(x₁, x₂)) = [-1]   
POL(COND_14532_0_CREATECOLLECTION_LOAD1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(COND_14532_0_CREATECOLLECTION_LOAD2(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(COND_14532_0_CREATECOLLECTION_LOAD3(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   

The following pairs are in P_>:

15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))
15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))
15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))
15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))
15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))
15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))
15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))
15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))
15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))
15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))

The following pairs are in P_bound:

14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])

The following pairs are in P_≥:

14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14532_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14532_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14532_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14532_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])

There are no usable rules.

(34) Complex Obligation (AND)

(35) 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

The ITRS R consists of the following rules:
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15853_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15948_0_insert_Return
15940_0_insert_Load → 15950_0_insert_Return
15940_0_insert_Load → 15956_0_insert_Return
15940_0_insert_Load → 15962_0_insert_Return
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15265_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15356_0_insert_Return
15940_0_insert_Load → 15358_0_insert_Return
15940_0_insert_Load → 15365_0_insert_Return
15940_0_insert_Load → 15371_0_insert_Return
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15940_0_insert_Load → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10370_0_insert_Return(java.lang.Object(x0))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10447_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10796_0_insert_Return
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10431_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10790_0_insert_Return

The integer pair graph contains the following rules and edges:
(10): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14532_0_CREATECOLLECTION_LOAD(x2[10] < x1[10], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
(11): COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(12): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14532_0_CREATECOLLECTION_LOAD1(x1[12] < x0[12], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
(13): COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])
(14): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14532_0_CREATECOLLECTION_LOAD2(x2[14] < x1[14], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
(15): COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(16): 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14532_0_CREATECOLLECTION_LOAD3(x1[16] < x0[16], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
(17): COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])

(10) -> (11), if ((x2[10] < x1[10] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(x1[10] →^* x1[11])∧(x2[10] →^* x2[11]))

(12) -> (13), if ((x1[12] < x0[12] →^* TRUE)∧(x0[12] →^* x0[13])∧(x1[12] →^* x1[13]))

(14) -> (15), if ((x2[14] < x1[14] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(x1[14] →^* x1[15])∧(x2[14] →^* x2[15]))

(16) -> (17), if ((x1[16] < x0[16] →^* TRUE)∧(x0[16] →^* x0[17])∧(x1[16] →^* x1[17]))

The set Q consists of the following terms:
15848_0_insert_Load(NULL, java.lang.Object(x0))
15940_0_insert_Load
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(36) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 8 less nodes.

(37) TRUE

(38) 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

The ITRS R consists of the following rules:
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15853_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15948_0_insert_Return
15940_0_insert_Load → 15950_0_insert_Return
15940_0_insert_Load → 15956_0_insert_Return
15940_0_insert_Load → 15962_0_insert_Return
15848_0_insert_Load(NULL, java.lang.Object(o2829)) → 15265_0_insert_Return(java.lang.Object(o2829))
15940_0_insert_Load → 15356_0_insert_Return
15940_0_insert_Load → 15358_0_insert_Return
15940_0_insert_Load → 15365_0_insert_Return
15940_0_insert_Load → 15371_0_insert_Return
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15940_0_insert_Load → 9773_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10370_0_insert_Return(java.lang.Object(x0))
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10447_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12734_0_insert_Return
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10796_0_insert_Return
9773_0_insert_NONNULL(java.lang.Object(x0)) → 10431_1_insert_InvokeMethod(9773_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x1)) → 12671_0_insert_Return
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10790_0_insert_Return

The integer pair graph contains the following rules and edges:
(0): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], x2[0] + 1)
(1): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], x2[1] + 1)
(2): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], x2[2] + 1)
(3): 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], x2[3] + 1)
(4): 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], x1[4] + 1)
(5): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], x2[5] + 1)
(6): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], x2[6] + 1)
(7): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], x2[7] + 1)
(8): 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], x2[8] + 1)
(9): 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14532_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], x1[9] + 1)
(11): COND_14532_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15848_2_CREATECOLLECTION_INVOKEMETHOD(15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(13): COND_14532_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15940_2_CREATECOLLECTION_INVOKEMETHOD(15940_1_insert_InvokeMethod(15940_0_insert_Load), x0[13], x1[13])
(15): COND_14532_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 15260_2_CREATECOLLECTION_INVOKEMETHOD(15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(17): COND_14532_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 15346_2_CREATECOLLECTION_INVOKEMETHOD(15346_1_insert_InvokeMethod(15940_0_insert_Load), x0[17], x1[17])

(11) -> (0), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])))∧(x1[11] →^* x1[0])∧(x2[11] →^* x2[0])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))))

(11) -> (1), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])))∧(x1[11] →^* x1[1])∧(x2[11] →^* x2[1])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))))

(11) -> (2), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])))∧(x1[11] →^* x1[2])∧(x2[11] →^* x2[2])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))))

(11) -> (3), if ((15848_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15848_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])))∧(x1[11] →^* x1[3])∧(x2[11] →^* x2[3])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))))

(13) -> (4), if ((15940_1_insert_InvokeMethod(15940_0_insert_Load) →^* 15940_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[13] →^* x0[4])∧(x1[13] →^* x1[4]))

(15) -> (5), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])))∧(x1[15] →^* x1[5])∧(x2[15] →^* x2[5])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))))

(15) -> (6), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])))∧(x1[15] →^* x1[6])∧(x2[15] →^* x2[6])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))))

(15) -> (7), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])))∧(x1[15] →^* x1[7])∧(x2[15] →^* x2[7])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))))

(15) -> (8), if ((15260_1_insert_InvokeMethod(15848_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 15260_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])))∧(x1[15] →^* x1[8])∧(x2[15] →^* x2[8])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))))

(17) -> (9), if ((15346_1_insert_InvokeMethod(15940_0_insert_Load) →^* 15346_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[17] →^* x0[9])∧(x1[17] →^* x1[9]))

The set Q consists of the following terms:
15848_0_insert_Load(NULL, java.lang.Object(x0))
15940_0_insert_Load
15848_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9773_0_insert_NONNULL(java.lang.Object(x0))
10447_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10447_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10431_1_insert_InvokeMethod(12671_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(12734_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10790_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10796_0_insert_Return, java.lang.Object(x0))
10431_1_insert_InvokeMethod(10370_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(39) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 14 less nodes.

(40) TRUE

(41) 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

The ITRS R consists of the following rules:
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 15561_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 15658_0_insert_Return
15646_0_insert_Load → 15660_0_insert_Return
15646_0_insert_Load → 15666_0_insert_Return
15646_0_insert_Load → 15672_0_insert_Return
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 14869_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 14946_0_insert_Return
15646_0_insert_Load → 14948_0_insert_Return
15646_0_insert_Load → 14954_0_insert_Return
15646_0_insert_Load → 14959_0_insert_Return
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15646_0_insert_Load → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10063_0_insert_Return(java.lang.Object(x0))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10223_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10473_0_insert_Return
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10207_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10469_0_insert_Return

The integer pair graph contains the following rules and edges:
(0): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], x2[0] + 1)
(1): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], x2[1] + 1)
(2): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], x2[2] + 1)
(3): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], x2[3] + 1)
(4): 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], x1[4] + 1)
(5): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], x2[5] + 1)
(6): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], x2[6] + 1)
(7): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], x2[7] + 1)
(8): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], x2[8] + 1)
(9): 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], x1[9] + 1)
(10): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14162_0_CREATECOLLECTION_LOAD(x2[10] < x1[10], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
(11): COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(12): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14162_0_CREATECOLLECTION_LOAD1(x1[12] < x0[12], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
(13): COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])
(14): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14162_0_CREATECOLLECTION_LOAD2(x2[14] < x1[14], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
(15): COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(16): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14162_0_CREATECOLLECTION_LOAD3(x1[16] < x0[16], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
(17): COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])

(0) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[0] →^* x1[10])∧(x2[0] + 1 →^* x2[10]))

(0) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[0] →^* x0[12])∧(x2[0] + 1 →^* x1[12]))

(0) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[0] →^* x1[14])∧(x2[0] + 1 →^* x2[14]))

(0) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[0] →^* x0[16])∧(x2[0] + 1 →^* x1[16]))

(1) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[1] →^* x1[10])∧(x2[1] + 1 →^* x2[10]))

(1) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[1] →^* x0[12])∧(x2[1] + 1 →^* x1[12]))

(1) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[1] →^* x1[14])∧(x2[1] + 1 →^* x2[14]))

(1) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[1] →^* x0[16])∧(x2[1] + 1 →^* x1[16]))

(2) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[2] →^* x1[10])∧(x2[2] + 1 →^* x2[10]))

(2) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[2] →^* x0[12])∧(x2[2] + 1 →^* x1[12]))

(2) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[2] →^* x1[14])∧(x2[2] + 1 →^* x2[14]))

(2) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[2] →^* x0[16])∧(x2[2] + 1 →^* x1[16]))

(3) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[3] →^* x1[10])∧(x2[3] + 1 →^* x2[10]))

(3) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[3] →^* x0[12])∧(x2[3] + 1 →^* x1[12]))

(3) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[3] →^* x1[14])∧(x2[3] + 1 →^* x2[14]))

(3) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[3] →^* x0[16])∧(x2[3] + 1 →^* x1[16]))

(4) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x0[4] →^* x1[10])∧(x1[4] + 1 →^* x2[10]))

(4) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[4] →^* x0[12])∧(x1[4] + 1 →^* x1[12]))

(4) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x0[4] →^* x1[14])∧(x1[4] + 1 →^* x2[14]))

(4) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[4] →^* x0[16])∧(x1[4] + 1 →^* x1[16]))

(5) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[5] →^* x1[10])∧(x2[5] + 1 →^* x2[10]))

(5) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[5] →^* x0[12])∧(x2[5] + 1 →^* x1[12]))

(5) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[5] →^* x1[14])∧(x2[5] + 1 →^* x2[14]))

(5) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[5] →^* x0[16])∧(x2[5] + 1 →^* x1[16]))

(6) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[6] →^* x1[10])∧(x2[6] + 1 →^* x2[10]))

(6) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[6] →^* x0[12])∧(x2[6] + 1 →^* x1[12]))

(6) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[6] →^* x1[14])∧(x2[6] + 1 →^* x2[14]))

(6) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[6] →^* x0[16])∧(x2[6] + 1 →^* x1[16]))

(7) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[7] →^* x1[10])∧(x2[7] + 1 →^* x2[10]))

(7) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[7] →^* x0[12])∧(x2[7] + 1 →^* x1[12]))

(7) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[7] →^* x1[14])∧(x2[7] + 1 →^* x2[14]))

(7) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[7] →^* x0[16])∧(x2[7] + 1 →^* x1[16]))

(8) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x1[8] →^* x1[10])∧(x2[8] + 1 →^* x2[10]))

(8) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[8] →^* x0[12])∧(x2[8] + 1 →^* x1[12]))

(8) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x1[8] →^* x1[14])∧(x2[8] + 1 →^* x2[14]))

(8) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x1[8] →^* x0[16])∧(x2[8] + 1 →^* x1[16]))

(9) -> (10), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))))∧(x0[9] →^* x1[10])∧(x1[9] + 1 →^* x2[10]))

(9) -> (12), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[9] →^* x0[12])∧(x1[9] + 1 →^* x1[12]))

(9) -> (14), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))))∧(x0[9] →^* x1[14])∧(x1[9] + 1 →^* x2[14]))

(9) -> (16), if ((java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))) →^* java.lang.Object(OrderedCollection.OrderedCollection(NULL)))∧(x0[9] →^* x0[16])∧(x1[9] + 1 →^* x1[16]))

(10) -> (11), if ((x2[10] < x1[10] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(x1[10] →^* x1[11])∧(x2[10] →^* x2[11]))

(11) -> (0), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])))∧(x1[11] →^* x1[0])∧(x2[11] →^* x2[0])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))))

(11) -> (1), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])))∧(x1[11] →^* x1[1])∧(x2[11] →^* x2[1])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))))

(11) -> (2), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])))∧(x1[11] →^* x1[2])∧(x2[11] →^* x2[2])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))))

(11) -> (3), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])))∧(x1[11] →^* x1[3])∧(x2[11] →^* x2[3])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))))

(12) -> (13), if ((x1[12] < x0[12] →^* TRUE)∧(x0[12] →^* x0[13])∧(x1[12] →^* x1[13]))

(13) -> (4), if ((15646_1_insert_InvokeMethod(15646_0_insert_Load) →^* 15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[13] →^* x0[4])∧(x1[13] →^* x1[4]))

(14) -> (15), if ((x2[14] < x1[14] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(x1[14] →^* x1[15])∧(x2[14] →^* x2[15]))

(15) -> (5), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])))∧(x1[15] →^* x1[5])∧(x2[15] →^* x2[5])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))))

(15) -> (6), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])))∧(x1[15] →^* x1[6])∧(x2[15] →^* x2[6])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))))

(15) -> (7), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])))∧(x1[15] →^* x1[7])∧(x2[15] →^* x2[7])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))))

(15) -> (8), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])))∧(x1[15] →^* x1[8])∧(x2[15] →^* x2[8])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))))

(16) -> (17), if ((x1[16] < x0[16] →^* TRUE)∧(x0[16] →^* x0[17])∧(x1[16] →^* x1[17]))

(17) -> (9), if ((14938_1_insert_InvokeMethod(15646_0_insert_Load) →^* 14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[17] →^* x0[9])∧(x1[17] →^* x1[9]))

The set Q consists of the following terms:
15556_0_insert_Load(NULL, java.lang.Object(x0))
15646_0_insert_Load
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(42) 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 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1)) which results in the following constraint:
  

  (1)    (15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))))≥NonInfC∧15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥))

  
  
  We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (2)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (3)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (4)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧[1 + (-1)bso_49] ≥ 0)

  
  
  We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (5)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_49] ≥ 0)

  
  
  

For Pair 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1)) which results in the following constraint:
  

  (6)    (15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))))≥NonInfC∧15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥))

  
  
  We simplified constraint (6) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (7)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (7) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (8)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (8) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (9)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧[1 + (-1)bso_51] ≥ 0)

  
  
  We simplified constraint (9) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (10)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

  
  
  

For Pair 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1)) which results in the following constraint:
  

  (11)    (15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))))≥NonInfC∧15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥))

  
  
  We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (12)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (12) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (13)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (13) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (14)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

  
  
  We simplified constraint (14) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (15)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 0)

  
  
  

For Pair 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1)) which results in the following constraint:
  

  (16)    (15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))))≥NonInfC∧15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥))

  
  
  We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (17)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (18)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (19)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧[1 + (-1)bso_55] ≥ 0)

  
  
  We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (20)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)

  
  
  

For Pair 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1)) the following chains were created:

• We consider the chain 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1)) which results in the following constraint:
  

  (21)    (15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4])≥NonInfC∧15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4])≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥))

  
  
  We simplified constraint (21) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (22)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (23)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (24)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧[1 + (-1)bso_57] ≥ 0)

  
  
  We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (25)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)

  
  
  

For Pair 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1)) which results in the following constraint:
  

  (26)    (14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))))≥NonInfC∧14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥))

  
  
  We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (27)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (28)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (29)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧[1 + (-1)bso_59] ≥ 0)

  
  
  We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (30)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_59] ≥ 0)

  
  
  

For Pair 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1)) which results in the following constraint:
  

  (31)    (14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))))≥NonInfC∧14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥))

  
  
  We simplified constraint (31) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (32)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (32) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (33)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (33) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (34)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧[1 + (-1)bso_61] ≥ 0)

  
  
  We simplified constraint (34) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (35)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_61] ≥ 0)

  
  
  

For Pair 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1)) which results in the following constraint:
  

  (36)    (14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))))≥NonInfC∧14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥))

  
  
  We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (37)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (37) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (38)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (39)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧[1 + (-1)bso_63] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (40)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_63] ≥ 0)

  
  
  

For Pair 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1)) the following chains were created:

• We consider the chain 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1)) which results in the following constraint:
  

  (41)    (14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))))≥NonInfC∧14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))))≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥))

  
  
  We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (42)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (43)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (44)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧[1 + (-1)bso_65] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (45)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_65] ≥ 0)

  
  
  

For Pair 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1)) the following chains were created:

• We consider the chain 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1)) which results in the following constraint:
  

  (46)    (14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9])≥NonInfC∧14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9])≥14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))∧(U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥))

  
  
  We simplified constraint (46) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (47)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (47) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (48)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (48) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (49)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧[1 + (-1)bso_67] ≥ 0)

  
  
  We simplified constraint (49) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (50)    ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_67] ≥ 0)

  
  
  

For Pair 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14162_0_CREATECOLLECTION_LOAD(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) the following chains were created:

• We consider the chain 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]), COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))) which results in the following constraint:
  

  (51)    (<(x2[10], x1[10])=TRUE∧java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10])))=java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))∧x1[10]=x1[11]∧x2[10]=x2[11] ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥))

  
  
  We simplified constraint (51) using rules (I), (II), (IV) which results in the following new constraint:
  

  (52)    (<(x2[10], x1[10])=TRUE ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])≥COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥))

  
  
  We simplified constraint (52) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (53)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (53) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (54)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (54) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (55)    (x1[10] + [-1] + [-1]x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]x2[10] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (56)    (x1[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (57)    (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  

  (58)    (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)

  
  
  

For Pair COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) the following chains were created:

• We consider the chain COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11])))) which results in the following constraint:
  

  (59)    (COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11])≥NonInfC∧COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11])≥15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥))

  
  
  We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (60)    ((U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (61)    ((U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (62)    ((U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧[(-1)bso_71] ≥ 0)

  
  
  We simplified constraint (62) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (63)    ((U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

  
  
  

For Pair 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14162_0_CREATECOLLECTION_LOAD1(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) the following chains were created:

• We consider the chain 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]), COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13]) which results in the following constraint:
  

  (64)    (<(x1[12], x0[12])=TRUE∧x0[12]=x0[13]∧x1[12]=x1[13] ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥))

  
  
  We simplified constraint (64) using rule (IV) which results in the following new constraint:
  

  (65)    (<(x1[12], x0[12])=TRUE ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])≥COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥))

  
  
  We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (66)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (66) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (67)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (67) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (68)    (x0[12] + [-1] + [-1]x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]x1[12] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (69)    (x0[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (70)    (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  

  (71)    (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)

  
  
  

For Pair COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0, x1) the following chains were created:

• We consider the chain COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13]) which results in the following constraint:
  

  (72)    (COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13])≥NonInfC∧COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13])≥15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])∧(U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥))

  
  
  We simplified constraint (72) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (73)    ((U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (73) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (74)    ((U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (74) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (75)    ((U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥)∧[(-1)bso_75] ≥ 0)

  
  
  We simplified constraint (75) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (76)    ((U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

  
  
  

For Pair 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14162_0_CREATECOLLECTION_LOAD2(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) the following chains were created:

• We consider the chain 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]), COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))) which results in the following constraint:
  

  (77)    (<(x2[14], x1[14])=TRUE∧java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14])))=java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))∧x1[14]=x1[15]∧x2[14]=x2[15] ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥))

  
  
  We simplified constraint (77) using rules (I), (II), (IV) which results in the following new constraint:
  

  (78)    (<(x2[14], x1[14])=TRUE ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])≥COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥))

  
  
  We simplified constraint (78) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (79)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (79) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (80)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (80) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (81)    (x1[14] + [-1] + [-1]x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]x2[14] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (82)    (x1[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  We simplified constraint (82) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (83)    (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  

  (84)    (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)

  
  
  

For Pair COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) the following chains were created:

• We consider the chain COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15])))) which results in the following constraint:
  

  (85)    (COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15])≥NonInfC∧COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15])≥14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥))

  
  
  We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (86)    ((U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (86) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (87)    ((U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (87) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (88)    ((U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧[(-1)bso_79] ≥ 0)

  
  
  We simplified constraint (88) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (89)    ((U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_79] ≥ 0)

  
  
  

For Pair 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14162_0_CREATECOLLECTION_LOAD3(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) the following chains were created:

• We consider the chain 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]), COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17]) which results in the following constraint:
  

  (90)    (<(x1[16], x0[16])=TRUE∧x0[16]=x0[17]∧x1[16]=x1[17] ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥))

  
  
  We simplified constraint (90) using rule (IV) which results in the following new constraint:
  

  (91)    (<(x1[16], x0[16])=TRUE ⇒ 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥NonInfC∧14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])≥COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])∧(U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥))

  
  
  We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (92)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (93)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (93) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (94)    (x0[16] + [-1] + [-1]x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)bni_80 + (-1)Bound*bni_80] + [(-1)bni_80]x1[16] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (94) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (95)    (x0[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  We simplified constraint (95) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (96)    (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  

  (97)    (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)

  
  
  

For Pair COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0, x1) the following chains were created:

• We consider the chain COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17]) which results in the following constraint:
  

  (98)    (COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17])≥NonInfC∧COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17])≥14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])∧(U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥))

  
  
  We simplified constraint (98) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (99)    ((U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (99) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (100)    ((U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (100) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (101)    ((U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥)∧[(-1)bso_83] ≥ 0)

  
  
  We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (102)    ((U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_83] ≥ 0)

  
  
  

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

• 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_49] ≥ 0)
    
  
  
• 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)
    
  
  
• 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 0)
    
  
  
• 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)
    
  
  
• 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)
    
  
  
• 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_59] ≥ 0)
    
  
  
• 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_61] ≥ 0)
    
  
  
• 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_63] ≥ 0)
    
  
  
• 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0)))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1, +(x2, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_65] ≥ 0)
    
  
  
• 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0, x1) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0, +(x1, 1))
  
  • ((U^Increasing(14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_67] ≥ 0)
    
  
  
• 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14162_0_CREATECOLLECTION_LOAD(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2)
  
  • (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)
    
  • (x1[10] ≥ 0∧x2[10] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])), ≥)∧[(-1)Bound*bni_68] + [bni_68]x1[10] ≥ 0∧[(-1)bso_69] ≥ 0)
    
  
  
• COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))))
  
  • ((U^Increasing(15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)
    
  
  
• 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14162_0_CREATECOLLECTION_LOAD1(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1)
  
  • (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)
    
  • (x0[12] ≥ 0∧x1[12] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])), ≥)∧[(-1)Bound*bni_72] + [bni_72]x0[12] ≥ 0∧[(-1)bso_73] ≥ 0)
    
  
  
• COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0, x1)
  
  • ((U^Increasing(15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)
    
  
  
• 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → COND_14162_0_CREATECOLLECTION_LOAD2(<(x2, x1), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2)
  
  • (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)
    
  • (x1[14] ≥ 0∧x2[14] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])), ≥)∧[(-1)Bound*bni_76] + [bni_76]x1[14] ≥ 0∧[(-1)bso_77] ≥ 0)
    
  
  
• COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), x1, x2) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))), java.lang.Object(x0)), x1, x2, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0))))
  
  • ((U^Increasing(14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_79] ≥ 0)
    
  
  
• 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → COND_14162_0_CREATECOLLECTION_LOAD3(<(x1, x0), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1)
  
  • (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)
    
  • (x0[16] ≥ 0∧x1[16] ≥ 0 ⇒ (U^Increasing(COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])), ≥)∧[(-1)Bound*bni_80] + [bni_80]x0[16] ≥ 0∧[(-1)bso_81] ≥ 0)
    
  
  
• COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0, x1) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0, x1)
  
  • ((U^Increasing(14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_83] ≥ 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(15556_0_insert_Load(x₁, x₂)) = [-1]   
POL(NULL) = [-1]   
POL(java.lang.Object(x₁)) = [-1]   
POL(15561_0_insert_Return(x₁)) = [-1]   
POL(15646_0_insert_Load) = [-1]   
POL(15658_0_insert_Return) = [-1]   
POL(15660_0_insert_Return) = [-1]   
POL(15666_0_insert_Return) = [-1]   
POL(15672_0_insert_Return) = [-1]   
POL(14869_0_insert_Return(x₁)) = [-1]   
POL(14946_0_insert_Return) = [-1]   
POL(14948_0_insert_Return) = [-1]   
POL(14954_0_insert_Return) = [-1]   
POL(14959_0_insert_Return) = [-1]   
POL(OrderedCollection.IntValue) = [-1]   
POL(9579_0_insert_NONNULL(x₁)) = [-1]   
POL(10063_0_insert_Return(x₁)) = [-1]   
POL(10223_1_insert_InvokeMethod(x₁, x₂)) = [-1]   
POL(11929_0_insert_Return) = [-1]   
POL(11986_0_insert_Return) = [-1]   
POL(10469_0_insert_Return) = [-1]   
POL(10473_0_insert_Return) = [-1]   
POL(10207_1_insert_InvokeMethod(x₁, x₂)) = [-1]   
POL(15556_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₂ + [-1]x₃   
POL(15556_1_insert_InvokeMethod(x₁, x₂, x₃)) = [-1]   
POL(OrderedCollection.OrderedCollection(x₁)) = [-1]   
POL(14162_0_CREATECOLLECTION_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂   
POL(OrderedCollection.Element) = [-1]   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(15646_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃   
POL(15646_1_insert_InvokeMethod(x₁)) = [-1]   
POL(14864_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₂ + [-1]x₃   
POL(14864_1_insert_InvokeMethod(x₁, x₂, x₃)) = [-1]   
POL(14938_2_CREATECOLLECTION_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃   
POL(14938_1_insert_InvokeMethod(x₁)) = [-1]   
POL(COND_14162_0_CREATECOLLECTION_LOAD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(<(x₁, x₂)) = [-1]   
POL(COND_14162_0_CREATECOLLECTION_LOAD1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(COND_14162_0_CREATECOLLECTION_LOAD2(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   
POL(COND_14162_0_CREATECOLLECTION_LOAD3(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃   

The following pairs are in P_>:

15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], +(x2[0], 1))
15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], +(x2[1], 1))
15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], +(x2[2], 1))
15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], +(x2[3], 1))
15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], +(x1[4], 1))
14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], +(x2[5], 1))
14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], +(x2[6], 1))
14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], +(x2[7], 1))
14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], +(x2[8], 1))
14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], +(x1[9], 1))

The following pairs are in P_bound:

14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])

The following pairs are in P_≥:

14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14162_0_CREATECOLLECTION_LOAD(<(x2[10], x1[10]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14162_0_CREATECOLLECTION_LOAD1(<(x1[12], x0[12]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14162_0_CREATECOLLECTION_LOAD2(<(x2[14], x1[14]), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14162_0_CREATECOLLECTION_LOAD3(<(x1[16], x0[16]), java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])

There are no usable rules.

(43) Complex Obligation (AND)

(44) 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

The ITRS R consists of the following rules:
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 15561_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 15658_0_insert_Return
15646_0_insert_Load → 15660_0_insert_Return
15646_0_insert_Load → 15666_0_insert_Return
15646_0_insert_Load → 15672_0_insert_Return
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 14869_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 14946_0_insert_Return
15646_0_insert_Load → 14948_0_insert_Return
15646_0_insert_Load → 14954_0_insert_Return
15646_0_insert_Load → 14959_0_insert_Return
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15646_0_insert_Load → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10063_0_insert_Return(java.lang.Object(x0))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10223_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10473_0_insert_Return
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10207_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10469_0_insert_Return

The integer pair graph contains the following rules and edges:
(10): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10]) → COND_14162_0_CREATECOLLECTION_LOAD(x2[10] < x1[10], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))), x1[10], x2[10])
(11): COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(12): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12]) → COND_14162_0_CREATECOLLECTION_LOAD1(x1[12] < x0[12], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[12], x1[12])
(13): COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])
(14): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14]) → COND_14162_0_CREATECOLLECTION_LOAD2(x2[14] < x1[14], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))), x1[14], x2[14])
(15): COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(16): 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16]) → COND_14162_0_CREATECOLLECTION_LOAD3(x1[16] < x0[16], java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[16], x1[16])
(17): COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])

(10) -> (11), if ((x2[10] < x1[10] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[10]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))∧(x1[10] →^* x1[11])∧(x2[10] →^* x2[11]))

(12) -> (13), if ((x1[12] < x0[12] →^* TRUE)∧(x0[12] →^* x0[13])∧(x1[12] →^* x1[13]))

(14) -> (15), if ((x2[14] < x1[14] →^* TRUE)∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[14]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))∧(x1[14] →^* x1[15])∧(x2[14] →^* x2[15]))

(16) -> (17), if ((x1[16] < x0[16] →^* TRUE)∧(x0[16] →^* x0[17])∧(x1[16] →^* x1[17]))

The set Q consists of the following terms:
15556_0_insert_Load(NULL, java.lang.Object(x0))
15646_0_insert_Load
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(45) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 8 less nodes.

(46) TRUE

(47) 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

The ITRS R consists of the following rules:
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 15561_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 15658_0_insert_Return
15646_0_insert_Load → 15660_0_insert_Return
15646_0_insert_Load → 15666_0_insert_Return
15646_0_insert_Load → 15672_0_insert_Return
15556_0_insert_Load(NULL, java.lang.Object(o2794)) → 14869_0_insert_Return(java.lang.Object(o2794))
15646_0_insert_Load → 14946_0_insert_Return
15646_0_insert_Load → 14948_0_insert_Return
15646_0_insert_Load → 14954_0_insert_Return
15646_0_insert_Load → 14959_0_insert_Return
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue)) → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
15646_0_insert_Load → 9579_0_insert_NONNULL(java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10063_0_insert_Return(java.lang.Object(x0))
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10223_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11986_0_insert_Return
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10473_0_insert_Return
9579_0_insert_NONNULL(java.lang.Object(x0)) → 10207_1_insert_InvokeMethod(9579_0_insert_NONNULL(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x1)) → 11929_0_insert_Return
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0)) → 10469_0_insert_Return

The integer pair graph contains the following rules and edges:
(0): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])), x1[0], x2[0], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[0], x2[0] + 1)
(1): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])), x1[1], x2[1], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[1], x2[1] + 1)
(2): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])), x1[2], x2[2], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[2], x2[2] + 1)
(3): 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])), x1[3], x2[3], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[3], x2[3] + 1)
(4): 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[4], x1[4]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[4], x1[4] + 1)
(5): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])), x1[5], x2[5], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[5], x2[5] + 1)
(6): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])), x1[6], x2[6], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[6], x2[6] + 1)
(7): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])), x1[7], x2[7], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[7], x2[7] + 1)
(8): 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])), x1[8], x2[8], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x1[8], x2[8] + 1)
(9): 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))), x0[9], x1[9]) → 14162_0_CREATECOLLECTION_LOAD(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(OrderedCollection.Element))), x0[9], x1[9] + 1)
(11): COND_14162_0_CREATECOLLECTION_LOAD(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), x1[11], x2[11]) → 15556_2_CREATECOLLECTION_INVOKEMETHOD(15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])), x1[11], x2[11], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))))
(13): COND_14162_0_CREATECOLLECTION_LOAD1(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[13], x1[13]) → 15646_2_CREATECOLLECTION_INVOKEMETHOD(15646_1_insert_InvokeMethod(15646_0_insert_Load), x0[13], x1[13])
(15): COND_14162_0_CREATECOLLECTION_LOAD2(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), x1[15], x2[15]) → 14864_2_CREATECOLLECTION_INVOKEMETHOD(14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])), x1[15], x2[15], java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))))
(17): COND_14162_0_CREATECOLLECTION_LOAD3(TRUE, java.lang.Object(OrderedCollection.OrderedCollection(NULL)), x0[17], x1[17]) → 14938_2_CREATECOLLECTION_INVOKEMETHOD(14938_1_insert_InvokeMethod(15646_0_insert_Load), x0[17], x1[17])

(11) -> (0), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0]))), java.lang.Object(x0[0])))∧(x1[11] →^* x1[0])∧(x2[11] →^* x2[0])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[0])))))

(11) -> (1), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1]))), java.lang.Object(x0[1])))∧(x1[11] →^* x1[1])∧(x2[11] →^* x2[1])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[1])))))

(11) -> (2), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2]))), java.lang.Object(x0[2])))∧(x1[11] →^* x1[2])∧(x2[11] →^* x2[2])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[2])))))

(11) -> (3), if ((15556_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[11]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))), java.lang.Object(x0[11])) →^* 15556_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3]))), java.lang.Object(x0[3])))∧(x1[11] →^* x1[3])∧(x2[11] →^* x2[3])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[11]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[3])))))

(13) -> (4), if ((15646_1_insert_InvokeMethod(15646_0_insert_Load) →^* 15646_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[13] →^* x0[4])∧(x1[13] →^* x1[4]))

(15) -> (5), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5]))), java.lang.Object(x0[5])))∧(x1[15] →^* x1[5])∧(x2[15] →^* x2[5])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[5])))))

(15) -> (6), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6]))), java.lang.Object(x0[6])))∧(x1[15] →^* x1[6])∧(x2[15] →^* x2[6])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[6])))))

(15) -> (7), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7]))), java.lang.Object(x0[7])))∧(x1[15] →^* x1[7])∧(x2[15] →^* x2[7])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[7])))))

(15) -> (8), if ((14864_1_insert_InvokeMethod(15556_0_insert_Load(java.lang.Object(x0[15]), java.lang.Object(OrderedCollection.IntValue)), java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))), java.lang.Object(x0[15])) →^* 14864_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8]))), java.lang.Object(x0[8])))∧(x1[15] →^* x1[8])∧(x2[15] →^* x2[8])∧(java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[15]))) →^* java.lang.Object(OrderedCollection.OrderedCollection(java.lang.Object(x0[8])))))

(17) -> (9), if ((14938_1_insert_InvokeMethod(15646_0_insert_Load) →^* 14938_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(OrderedCollection.IntValue))))∧(x0[17] →^* x0[9])∧(x1[17] →^* x1[9]))

The set Q consists of the following terms:
15556_0_insert_Load(NULL, java.lang.Object(x0))
15646_0_insert_Load
15556_0_insert_Load(java.lang.Object(x0), java.lang.Object(OrderedCollection.IntValue))
9579_0_insert_NONNULL(java.lang.Object(x0))
10223_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10223_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))
10207_1_insert_InvokeMethod(11929_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(11986_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10469_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10473_0_insert_Return, java.lang.Object(x0))
10207_1_insert_InvokeMethod(10063_0_insert_Return(java.lang.Object(x0)), java.lang.Object(x0))

(48) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 14 less nodes.

(49) TRUE