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_22 (Sun Microsystems Inc.) Main-Class: LessLeavesRec/LessLeavesRec

package LessLeavesRec;
public class LessLeavesRec {
    public static Tree append(Tree x, Tree y) {
                // adds y to the right bottom of x
                if (x == null) return y;
                else return new Tree(x.l, append(x.r,y));
    }

    // checks whether one tree has less leaves than the other
    public static boolean lessleaves(Tree x, Tree y){
                if (y == null) {
                        return false;
                } else {
                        if (x == null) {
                                return true;
                        } else {
                                return lessleaves(append(x.l,x.r), append(y.l,y.r));
                        }
            }
        }

        public static void main(String[] args) {
                Random.args = args;
                Tree x = Tree.createTree();
                Tree y = Tree.createTree();
          
                boolean b = lessleaves(x,y);
        }
}


package LessLeavesRec;
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 LessLeavesRec;

public class Tree {
    Tree l;
    Tree r;
    int value;

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

    public Tree() {
    }

    public static Tree createNode() {
        final Tree result = new Tree();
        result.value = Random.random();
        return result;
    }




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

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

        return result;
    }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
LessLeavesRec.LessLeavesRec.main([Ljava/lang/String;)V: Graph of 212 nodes with 0 SCCs.

LessLeavesRec.Tree.createTree()LLessLeavesRec/Tree;: Graph of 396 nodes with 1 SCC.

LessLeavesRec.LessLeavesRec.lessleaves(LLessLeavesRec/Tree;LLessLeavesRec/Tree;)Z: Graph of 134 nodes with 0 SCCs.

LessLeavesRec.Tree.createNode()LLessLeavesRec/Tree;: Graph of 99 nodes with 0 SCCs.

LessLeavesRec.LessLeavesRec.append(LLessLeavesRec/Tree;LLessLeavesRec/Tree;)LLessLeavesRec/Tree;: Graph of 46 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

---

Log for SCC 0:

Generated 15 rules for P and 30 rules for R.

Combined rules. Obtained 1 rules for P and 4 rules for R.

Filtered ground terms:

4490_1_append_InvokeMethod(x1, x2, x3, x4, x5, x6) → 4490_1_append_InvokeMethod(x1, x4, x5, x6)
LessLeavesRec.Tree(x1, x2, x3) → LessLeavesRec.Tree(x2, x3)
4159_0_append_NONNULL(x1, x2, x3, x4) → 4159_0_append_NONNULL(x2, x3, x4)
9986_0_append_Return(x1, x2) → 9986_0_append_Return(x2)
6162_0_append_Return(x1, x2) → 6162_0_append_Return(x2)
4219_0_append_Return(x1, x2, x3, x4) → 4219_0_append_Return(x3, x4)

Filtered duplicate args:

4159_0_append_NONNULL(x1, x2, x3) → 4159_0_append_NONNULL(x2, x3)
4219_0_append_Return(x1, x2) → 4219_0_append_Return(x2)

Filtered unneeded arguments:

4490_1_append_InvokeMethod(x1, x2, x3, x4) → 4490_1_append_InvokeMethod(x1, x3, x4)

Filtered all free variables:

6162_0_append_Return(x1) → 6162_0_append_Return
9986_0_append_Return(x1) → 9986_0_append_Return

Finished conversion. Obtained 1 rules for P and 4 rules for R. System has no predefined symbols.

---

Log for SCC 1:

Generated 61 rules for P and 152 rules for R.

Combined rules. Obtained 9 rules for P and 44 rules for R.

Filtered ground terms:

LessLeavesRec.Tree(x1, x2, x3) → LessLeavesRec.Tree(x2, x3)
4141_0_append_Load(x1, x2, x3) → 4141_0_append_Load(x2, x3)
9986_0_append_Return(x1, x2) → 9986_0_append_Return(x2)
6162_0_append_Return(x1, x2) → 6162_0_append_Return(x2)
4219_0_append_Return(x1, x2, x3, x4) → 4219_0_append_Return(x3, x4)
8914_0_append_Load(x1, x2, x3) → 8914_0_append_Load(x2, x3)
4505_0_append_Load(x1, x2, x3) → 4505_0_append_Load(x2, x3)
4490_1_append_InvokeMethod(x1, x2, x3, x4, x5, x6) → 4490_1_append_InvokeMethod(x1, x4, x5, x6)
4159_0_append_NONNULL(x1, x2, x3, x4) → 4159_0_append_NONNULL(x2, x3, x4)
11095_0_lessleaves_Return(x1) → 11095_0_lessleaves_Return
10213_0_lessleaves_Return(x1) → 10213_0_lessleaves_Return
10190_0_lessleaves_Return(x1) → 10190_0_lessleaves_Return
9516_0_lessleaves_Return(x1) → 9516_0_lessleaves_Return
8962_0_lessleaves_Return(x1) → 8962_0_lessleaves_Return
8507_0_lessleaves_Return(x1) → 8507_0_lessleaves_Return
4742_0_lessleaves_Return(x1) → 4742_0_lessleaves_Return
4737_0_lessleaves_Return(x1) → 4737_0_lessleaves_Return
3714_0_lessleaves_Return(x1, x2, x3) → 3714_0_lessleaves_Return(x2)
3835_0_lessleaves_Return(x1, x2, x3) → 3835_0_lessleaves_Return(x3)

Filtered duplicate args:

4219_0_append_Return(x1, x2) → 4219_0_append_Return(x2)
4159_0_append_NONNULL(x1, x2, x3) → 4159_0_append_NONNULL(x2, x3)

Finished conversion. Obtained 9 rules for P and 44 rules for R. System has no predefined symbols.

---

Log for SCC 2:

Generated 204 rules for P and 195 rules for R.

Combined rules. Obtained 37 rules for P and 34 rules for R.

Filtered ground terms:

17086_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → 17086_0_createTree_FieldAccess(x2, x3, x4, x5)
LessLeavesRec.Tree(x1, x2, x3) → LessLeavesRec.Tree(x2, x3)
16786_0_random_GT(x1, x2, x3) → 16786_0_random_GT(x2, x3)
17161_0_random_IntArithmetic(x1, x2, x3, x4) → 17161_0_random_IntArithmetic(x2, x3)
16685_0_createTree_LE(x1, x2, x3, x4, x5) → 16685_0_createTree_LE(x2, x3, x4, x5)
Cond_19955_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_19955_1_createTree_InvokeMethod1(x1, x3, x4, x5)
3247_0_createNode_Return(x1, x2) → 3247_0_createNode_Return
Cond_19955_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_19955_1_createTree_InvokeMethod(x1, x3, x4, x5)
2562_0_createNode_Return(x1, x2) → 2562_0_createNode_Return
19955_0_createNode_New(x1) → 19955_0_createNode_New
Cond_20061_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_20061_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_20061_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_20061_1_createTree_InvokeMethod(x1, x3, x4, x5)
20061_0_createNode_New(x1) → 20061_0_createNode_New
Cond_19922_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_19922_1_createTree_InvokeMethod1(x1, x3)
19922_1_createTree_InvokeMethod(x1, x2, x3, x4) → 19922_1_createTree_InvokeMethod(x1, x2)
Cond_19922_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_19922_1_createTree_InvokeMethod(x1, x3)
19922_0_createNode_New(x1) → 19922_0_createNode_New
Cond_17161_1_createTree_InvokeMethod3(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod3(x1, x2, x3)
Cond_20129_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_20129_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_20129_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_20129_1_createTree_InvokeMethod(x1, x3, x4, x5)
20129_0_createNode_New(x1) → 20129_0_createNode_New
Cond_17727_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_17727_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_17727_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_17727_1_createTree_InvokeMethod(x1, x3, x4, x5)
17727_0_createNode_New(x1) → 17727_0_createNode_New
Cond_17086_0_createTree_FieldAccess2(x1, x2, x3, x4, x5, x6) → Cond_17086_0_createTree_FieldAccess2(x1, x3, x4, x5, x6)
Cond_17930_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_17930_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_17930_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_17930_1_createTree_InvokeMethod(x1, x3, x4, x5)
17930_0_createNode_New(x1) → 17930_0_createNode_New
Cond_17086_0_createTree_FieldAccess1(x1, x2, x3, x4, x5, x6) → Cond_17086_0_createTree_FieldAccess1(x1, x3, x4, x5, x6)
Cond_17698_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_17698_1_createTree_InvokeMethod1(x1, x3)
17698_1_createTree_InvokeMethod(x1, x2, x3, x4) → 17698_1_createTree_InvokeMethod(x1, x2)
Cond_17698_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_17698_1_createTree_InvokeMethod(x1, x3)
17698_0_createNode_New(x1) → 17698_0_createNode_New
Cond_18104_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_18104_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_18104_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_18104_1_createTree_InvokeMethod(x1, x3, x4, x5)
18104_0_createNode_New(x1) → 18104_0_createNode_New
Cond_17086_0_createTree_FieldAccess(x1, x2, x3, x4, x5, x6) → Cond_17086_0_createTree_FieldAccess(x1, x3, x4, x5, x6)
16950_0_random_ArrayAccess(x1, x2, x3) → 16950_0_random_ArrayAccess(x2, x3)
16781_0_random_GT(x1, x2, x3) → 16781_0_random_GT(x2, x3)
Cond_16685_0_createTree_LE1(x1, x2, x3, x4, x5, x6) → Cond_16685_0_createTree_LE1(x1, x3, x4, x5, x6)
Cond_16685_0_createTree_LE(x1, x2, x3, x4, x5, x6) → Cond_16685_0_createTree_LE(x1, x3, x4, x5, x6)
3580_0_createNode_InvokeMethod(x1, x2, x3, x4) → 3580_0_createNode_InvokeMethod
java.lang.ArrayIndexOutOfBoundsException(x1) → java.lang.ArrayIndexOutOfBoundsException
java.lang.IndexOutOfBoundsException(x1) → java.lang.IndexOutOfBoundsException
java.lang.RuntimeException(x1) → java.lang.RuntimeException
java.lang.Exception(x1) → java.lang.Exception
java.lang.Throwable(x1) → java.lang.Throwable
Cond_2507_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_2507_1_createNode_InvokeMethod(x1, x2)
2507_0_random_ArrayAccess(x1, x2, x3) → 2507_0_random_ArrayAccess(x2, x3)
2507_1_createNode_InvokeMethod(x1, x2, x3) → 2507_1_createNode_InvokeMethod(x1)
Cond_2645_1_createNode_InvokeMethod1(x1, x2, x3, x4) → Cond_2645_1_createNode_InvokeMethod1(x1, x2)
2645_0_random_IntArithmetic(x1, x2, x3, x4) → 2645_0_random_IntArithmetic(x2, x3)
2645_1_createNode_InvokeMethod(x1, x2, x3) → 2645_1_createNode_InvokeMethod(x1)
Cond_2645_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_2645_1_createNode_InvokeMethod(x1, x2)
Cond_2559_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_2559_1_createNode_InvokeMethod(x1, x2)
2559_0_random_ArrayAccess(x1, x2, x3) → 2559_0_random_ArrayAccess(x2, x3)
2559_1_createNode_InvokeMethod(x1, x2, x3) → 2559_1_createNode_InvokeMethod(x1)
3636_0_createNode_InvokeMethod(x1, x2, x3, x4) → 3636_0_createNode_InvokeMethod
Cond_2560_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_2560_1_createNode_InvokeMethod(x1, x2)
2560_0_random_ArrayAccess(x1, x2, x3) → 2560_0_random_ArrayAccess(x2, x3)
2560_1_createNode_InvokeMethod(x1, x2, x3) → 2560_1_createNode_InvokeMethod(x1)
Cond_2339_1_createNode_InvokeMethod3(x1, x2, x3, x4) → Cond_2339_1_createNode_InvokeMethod3(x1, x2)
2339_0_random_GT(x1, x2, x3) → 2339_0_random_GT(x2, x3)
2339_1_createNode_InvokeMethod(x1, x2, x3) → 2339_1_createNode_InvokeMethod(x1)
Cond_2339_1_createNode_InvokeMethod2(x1, x2, x3, x4) → Cond_2339_1_createNode_InvokeMethod2(x1, x2)
Cond_2339_1_createNode_InvokeMethod1(x1, x2, x3, x4) → Cond_2339_1_createNode_InvokeMethod1(x1, x2)
Cond_2339_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_2339_1_createNode_InvokeMethod(x1, x2)
20098_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 20098_0_createTree_InvokeMethod(x3, x4, x5)
20208_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 20208_0_createTree_InvokeMethod(x3, x4, x5)
20055_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 20055_0_createTree_InvokeMethod(x3)
20333_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 20333_0_createTree_InvokeMethod(x3, x4, x5)
17975_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 17975_0_createTree_InvokeMethod(x3, x4, x5)
18223_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 18223_0_createTree_InvokeMethod(x3, x4, x5)
17926_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 17926_0_createTree_InvokeMethod(x3)
18394_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 18394_0_createTree_InvokeMethod(x3, x4, x5)
16708_0_createTree_Return(x1, x2) → 16708_0_createTree_Return(x2)
19972_0_createNode_InvokeMethod(x1, x2, x3, x4) → 19972_0_createNode_InvokeMethod
20077_0_createNode_InvokeMethod(x1, x2, x3, x4) → 20077_0_createNode_InvokeMethod
19939_0_createNode_InvokeMethod(x1, x2, x3, x4) → 19939_0_createNode_InvokeMethod
20161_0_createNode_InvokeMethod(x1, x2, x3, x4) → 20161_0_createNode_InvokeMethod

Filtered duplicate args:

17086_0_createTree_FieldAccess(x1, x2, x3, x4) → 17086_0_createTree_FieldAccess(x1, x2, x4)
16685_0_createTree_LE(x1, x2, x3, x4) → 16685_0_createTree_LE(x2, x3, x4)
Cond_17086_0_createTree_FieldAccess2(x1, x2, x3, x4, x5) → Cond_17086_0_createTree_FieldAccess2(x1, x2, x3, x5)
Cond_17086_0_createTree_FieldAccess1(x1, x2, x3, x4, x5) → Cond_17086_0_createTree_FieldAccess1(x1, x2, x3, x5)
Cond_17086_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → Cond_17086_0_createTree_FieldAccess(x1, x2, x3, x5)
Cond_16685_0_createTree_LE1(x1, x2, x3, x4, x5) → Cond_16685_0_createTree_LE1(x1, x3, x4, x5)
Cond_16685_0_createTree_LE(x1, x2, x3, x4, x5) → Cond_16685_0_createTree_LE(x1, x3, x4, x5)

Filtered all non-integer terms:

16685_0_createTree_LE(x1, x2, x3) → 16685_0_createTree_LE(x3)
Cond_16685_0_createTree_LE(x1, x2, x3, x4) → Cond_16685_0_createTree_LE(x1, x4)
16781_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16781_1_createTree_InvokeMethod(x1, x2)
Cond_16685_0_createTree_LE1(x1, x2, x3, x4) → Cond_16685_0_createTree_LE1(x1, x4)
16786_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16786_1_createTree_InvokeMethod(x1, x2)
Cond_16781_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16781_1_createTree_InvokeMethod(x1, x2, x3)
16950_1_createTree_InvokeMethod(x1, x2, x3, x4) → 16950_1_createTree_InvokeMethod(x1, x2)
Cond_16950_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16950_1_createTree_InvokeMethod(x1, x2, x3)
17161_1_createTree_InvokeMethod(x1, x2, x3, x4) → 17161_1_createTree_InvokeMethod(x1, x2)
17161_0_random_IntArithmetic(x1, x2) → 17161_0_random_IntArithmetic(x2)
Cond_17161_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod(x1, x2, x3)
17086_0_createTree_FieldAccess(x1, x2, x3) → 17086_0_createTree_FieldAccess(x1)
LessLeavesRec.Tree(x1, x2) → LessLeavesRec.Tree
Cond_17086_0_createTree_FieldAccess(x1, x2, x3, x4) → Cond_17086_0_createTree_FieldAccess(x1, x2)
18104_1_createTree_InvokeMethod(x1, x2, x3, x4) → 18104_1_createTree_InvokeMethod(x1, x2)
Cond_18104_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_18104_1_createTree_InvokeMethod(x1, x2)
Cond_18104_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_18104_1_createTree_InvokeMethod1(x1, x2)
Cond_17086_0_createTree_FieldAccess1(x1, x2, x3, x4) → Cond_17086_0_createTree_FieldAccess1(x1, x2)
17930_1_createTree_InvokeMethod(x1, x2, x3, x4) → 17930_1_createTree_InvokeMethod(x1, x2)
Cond_17930_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_17930_1_createTree_InvokeMethod(x1, x2)
Cond_17930_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_17930_1_createTree_InvokeMethod1(x1, x2)
Cond_17086_0_createTree_FieldAccess2(x1, x2, x3, x4) → Cond_17086_0_createTree_FieldAccess2(x1, x2)
17727_1_createTree_InvokeMethod(x1, x2, x3, x4) → 17727_1_createTree_InvokeMethod(x1, x2)
Cond_17727_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_17727_1_createTree_InvokeMethod(x1, x2)
Cond_17727_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_17727_1_createTree_InvokeMethod1(x1, x2)
Cond_17161_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod1(x1, x2, x3)
Cond_17161_1_createTree_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod2(x1, x2, x3)
20129_1_createTree_InvokeMethod(x1, x2, x3, x4) → 20129_1_createTree_InvokeMethod(x1, x2)
Cond_20129_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_20129_1_createTree_InvokeMethod(x1, x2)
Cond_20129_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_20129_1_createTree_InvokeMethod1(x1, x2)
Cond_17161_1_createTree_InvokeMethod4(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod4(x1, x2, x3)
Cond_17161_1_createTree_InvokeMethod5(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod5(x1, x2, x3)
20061_1_createTree_InvokeMethod(x1, x2, x3, x4) → 20061_1_createTree_InvokeMethod(x1, x2)
Cond_20061_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_20061_1_createTree_InvokeMethod(x1, x2)
Cond_20061_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_20061_1_createTree_InvokeMethod1(x1, x2)
Cond_17161_1_createTree_InvokeMethod6(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod6(x1, x2, x3)
Cond_17161_1_createTree_InvokeMethod7(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod7(x1, x2, x3)
19955_1_createTree_InvokeMethod(x1, x2, x3, x4) → 19955_1_createTree_InvokeMethod(x1, x2)
Cond_19955_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_19955_1_createTree_InvokeMethod(x1, x2)
Cond_19955_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_19955_1_createTree_InvokeMethod1(x1, x2)
Cond_17161_1_createTree_InvokeMethod8(x1, x2, x3, x4, x5) → Cond_17161_1_createTree_InvokeMethod8(x1, x2, x3)
Cond_16786_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_16786_1_createTree_InvokeMethod(x1, x2, x3)
16708_0_createTree_Return(x1) → 16708_0_createTree_Return
18394_0_createTree_InvokeMethod(x1, x2, x3) → 18394_0_createTree_InvokeMethod(x1)
18223_0_createTree_InvokeMethod(x1, x2, x3) → 18223_0_createTree_InvokeMethod(x1)
17975_0_createTree_InvokeMethod(x1, x2, x3) → 17975_0_createTree_InvokeMethod(x1)
20333_0_createTree_InvokeMethod(x1, x2, x3) → 20333_0_createTree_InvokeMethod(x1)
20208_0_createTree_InvokeMethod(x1, x2, x3) → 20208_0_createTree_InvokeMethod(x1)
20098_0_createTree_InvokeMethod(x1, x2, x3) → 20098_0_createTree_InvokeMethod(x1)
2645_0_random_IntArithmetic(x1, x2) → 2645_0_random_IntArithmetic(x2)

Filtered all free variables:

16781_1_createTree_InvokeMethod(x1, x2) → 16781_1_createTree_InvokeMethod(x2)
16786_1_createTree_InvokeMethod(x1, x2) → 16786_1_createTree_InvokeMethod(x2)
Cond_16781_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16781_1_createTree_InvokeMethod(x1, x3)
16950_1_createTree_InvokeMethod(x1, x2) → 16950_1_createTree_InvokeMethod(x2)
Cond_16950_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16950_1_createTree_InvokeMethod(x1, x3)
17161_1_createTree_InvokeMethod(x1, x2) → 17161_1_createTree_InvokeMethod(x2)
Cond_17161_1_createTree_InvokeMethod(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod(x1, x3)
Cond_17161_1_createTree_InvokeMethod1(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod1(x1, x3)
Cond_17161_1_createTree_InvokeMethod2(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod2(x1, x3)
Cond_17161_1_createTree_InvokeMethod3(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod3(x1, x3)
Cond_17161_1_createTree_InvokeMethod4(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod4(x1, x3)
Cond_17161_1_createTree_InvokeMethod5(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod5(x1, x3)
Cond_17161_1_createTree_InvokeMethod6(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod6(x1, x3)
Cond_17161_1_createTree_InvokeMethod7(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod7(x1, x3)
Cond_17161_1_createTree_InvokeMethod8(x1, x2, x3) → Cond_17161_1_createTree_InvokeMethod8(x1, x3)
Cond_16786_1_createTree_InvokeMethod(x1, x2, x3) → Cond_16786_1_createTree_InvokeMethod(x1, x3)
2339_0_random_GT(x1, x2) → 2339_0_random_GT
2507_0_random_ArrayAccess(x1, x2) → 2507_0_random_ArrayAccess(x1)
ARRAY(x1, x2) → ARRAY(x1)
2559_0_random_ArrayAccess(x1, x2) → 2559_0_random_ArrayAccess(x1)
2560_0_random_ArrayAccess(x1, x2) → 2560_0_random_ArrayAccess(x1)
2645_0_random_IntArithmetic(x1) → 2645_0_random_IntArithmetic

Filtered ground terms:

Cond_2645_1_createNode_InvokeMethod1(x1, x2) → Cond_2645_1_createNode_InvokeMethod1(x1)
2645_1_createNode_InvokeMethod(x1) → 2645_1_createNode_InvokeMethod
Cond_2645_1_createNode_InvokeMethod(x1, x2) → Cond_2645_1_createNode_InvokeMethod(x1)
Cond_2339_1_createNode_InvokeMethod3(x1, x2) → Cond_2339_1_createNode_InvokeMethod3(x1)
2339_1_createNode_InvokeMethod(x1) → 2339_1_createNode_InvokeMethod
Cond_2339_1_createNode_InvokeMethod2(x1, x2) → Cond_2339_1_createNode_InvokeMethod2(x1)
Cond_2339_1_createNode_InvokeMethod1(x1, x2) → Cond_2339_1_createNode_InvokeMethod1(x1)
Cond_2339_1_createNode_InvokeMethod(x1, x2) → Cond_2339_1_createNode_InvokeMethod(x1)

Combined rules. Obtained 25 rules for P and 29 rules for R.

Finished conversion. Obtained 25 rules for P and 29 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:
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0) → 6162_0_append_Return
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return

The integer pair graph contains the following rules and edges:
(0): 4159_0_APPEND_NONNULL(x2[0], java.lang.Object(LessLeavesRec.Tree(x0[0], x1[0]))) → 4159_0_APPEND_NONNULL(x2[0], x1[0])

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

The set Q consists of the following terms:
4159_0_append_NONNULL(x0, NULL)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0)
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))), x3)

(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:

4159_0_APPEND_NONNULL(x2[0], java.lang.Object(LessLeavesRec.Tree(x0[0], x1[0]))) → 4159_0_APPEND_NONNULL(x2[0], x1[0])

The TRS R consists of the following rules:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0) → 6162_0_append_Return
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return

The set Q consists of the following terms:

4159_0_append_NONNULL(x0, NULL)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0)
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))), x3)

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:

4159_0_APPEND_NONNULL(x2[0], java.lang.Object(LessLeavesRec.Tree(x0[0], x1[0]))) → 4159_0_APPEND_NONNULL(x2[0], x1[0])

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

4159_0_append_NONNULL(x0, NULL)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0)
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))), x3)

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].

4159_0_append_NONNULL(x0, NULL)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), NULL, x0)
4490_1_append_InvokeMethod(6162_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))), x3)

(11) Obligation:

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

4159_0_APPEND_NONNULL(x2[0], java.lang.Object(LessLeavesRec.Tree(x0[0], x1[0]))) → 4159_0_APPEND_NONNULL(x2[0], x1[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:

• 4159_0_APPEND_NONNULL(x2[0], java.lang.Object(LessLeavesRec.Tree(x0[0], x1[0]))) → 4159_0_APPEND_NONNULL(x2[0], x1[0])
  The graph contains the following edges 1 >= 1, 2 > 2

(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:
4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL) → 4737_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0)) → 4742_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 8962_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 8507_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 10190_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL) → 9516_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 10213_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 11095_0_lessleaves_Return
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The integer pair graph contains the following rules and edges:
(0): 4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[0], x2[0]), x0[0], x1[0], x2[0])
(1): 4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1])
(2): 4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
(3): 4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
(4): 4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
(5): 4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

(0) -> (1), if ((4141_0_append_Load(x1[0], x2[0]) →^* 4219_0_append_Return(java.lang.Object(x0[1])))∧(x0[0] →^* java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])))∧(x1[0] →^* NULL)∧(x2[0] →^* java.lang.Object(x0[1])))

(0) -> (2), if ((4141_0_append_Load(x1[0], x2[0]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))))∧(x0[0] →^* java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])))∧(x1[0] →^* java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)))∧(x2[0] →^* x1[2]))

(0) -> (3), if ((4141_0_append_Load(x1[0], x2[0]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))))∧(x0[0] →^* java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])))∧(x1[0] →^* java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))))∧(x2[0] →^* x6[3]))

(1) -> (0), if ((4141_0_append_Load(x1[1], x2[1]) →^* 4219_0_append_Return(x0[0]))∧(java.lang.Object(x0[1]) →^* java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])))∧(x1[1] →^* NULL)∧(x2[1] →^* x0[0]))

(1) -> (4), if ((4141_0_append_Load(x1[1], x2[1]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))))∧(java.lang.Object(x0[1]) →^* java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])))∧(x1[1] →^* java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)))∧(x2[1] →^* x1[4]))

(1) -> (5), if ((4141_0_append_Load(x1[1], x2[1]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))))∧(java.lang.Object(x0[1]) →^* java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])))∧(x1[1] →^* java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))))∧(x2[1] →^* x6[5]))

(2) -> (0), if ((4141_0_append_Load(x2[2], x3[2]) →^* 4219_0_append_Return(x0[0]))∧(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])) →^* java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])))∧(x2[2] →^* NULL)∧(x3[2] →^* x0[0]))

(2) -> (4), if ((4141_0_append_Load(x2[2], x3[2]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))))∧(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])) →^* java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])))∧(x2[2] →^* java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)))∧(x3[2] →^* x1[4]))

(2) -> (5), if ((4141_0_append_Load(x2[2], x3[2]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))))∧(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])) →^* java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])))∧(x2[2] →^* java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))))∧(x3[2] →^* x6[5]))

(3) -> (0), if ((4141_0_append_Load(x3[3], x4[3]) →^* 4219_0_append_Return(x0[0]))∧(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))) →^* java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])))∧(x3[3] →^* NULL)∧(x4[3] →^* x0[0]))

(3) -> (4), if ((4141_0_append_Load(x3[3], x4[3]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))))∧(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))) →^* java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])))∧(x3[3] →^* java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)))∧(x4[3] →^* x1[4]))

(3) -> (5), if ((4141_0_append_Load(x3[3], x4[3]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))))∧(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))) →^* java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])))∧(x3[3] →^* java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))))∧(x4[3] →^* x6[5]))

(4) -> (1), if ((4141_0_append_Load(x2[4], x3[4]) →^* 4219_0_append_Return(java.lang.Object(x0[1])))∧(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])) →^* java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])))∧(x2[4] →^* NULL)∧(x3[4] →^* java.lang.Object(x0[1])))

(4) -> (2), if ((4141_0_append_Load(x2[4], x3[4]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))))∧(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])) →^* java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])))∧(x2[4] →^* java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)))∧(x3[4] →^* x1[2]))

(4) -> (3), if ((4141_0_append_Load(x2[4], x3[4]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))))∧(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])) →^* java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])))∧(x2[4] →^* java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))))∧(x3[4] →^* x6[3]))

(5) -> (1), if ((4141_0_append_Load(x3[5], x4[5]) →^* 4219_0_append_Return(java.lang.Object(x0[1])))∧(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))) →^* java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])))∧(x3[5] →^* NULL)∧(x4[5] →^* java.lang.Object(x0[1])))

(5) -> (2), if ((4141_0_append_Load(x3[5], x4[5]) →^* 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))))∧(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))) →^* java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])))∧(x3[5] →^* java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)))∧(x4[5] →^* x1[2]))

(5) -> (3), if ((4141_0_append_Load(x3[5], x4[5]) →^* 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))))∧(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))) →^* java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])))∧(x3[5] →^* java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))))∧(x4[5] →^* x6[3]))

The set Q consists of the following terms:
4141_0_append_Load(x0, x1)
4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL)
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0))
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL)
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

(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:

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[0], x2[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL) → 4737_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0)) → 4742_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 8962_0_lessleaves_Return
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 8962_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 8507_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 10190_0_lessleaves_Return
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 10190_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL) → 9516_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 10213_0_lessleaves_Return
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 10213_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0)))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3))))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4))))) → 11095_0_lessleaves_Return
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5))) → 11095_0_lessleaves_Return
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL)
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0))
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL)
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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:

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[0], x2[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL)
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0))
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL)
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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].

4653_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(x0), x0, NULL)
4653_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(x0)), NULL, java.lang.Object(x0))
4653_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
4653_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
4653_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
4653_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
4653_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
4653_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
4653_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
8384_1_lessleaves_InvokeMethod(3835_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))
8384_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
8384_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
8384_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
8384_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
8384_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
8384_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
8384_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
9206_1_lessleaves_InvokeMethod(3714_0_lessleaves_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), java.lang.Object(LessLeavesRec.Tree(x0, x1)), NULL)
9206_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
9206_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
9206_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
9206_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
9206_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
9206_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
9206_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))
10776_1_lessleaves_InvokeMethod(4737_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, x0)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(4742_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(x0))))
10776_1_lessleaves_InvokeMethod(8507_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, NULL)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)))
10776_1_lessleaves_InvokeMethod(8962_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x2, x3)))))
10776_1_lessleaves_InvokeMethod(9516_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, NULL)))
10776_1_lessleaves_InvokeMethod(10190_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x0, x1)))), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x2, x3)), x4)))
10776_1_lessleaves_InvokeMethod(10213_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(NULL, java.lang.Object(LessLeavesRec.Tree(x3, x4)))))
10776_1_lessleaves_InvokeMethod(11095_0_lessleaves_Return, java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x0, x1)), x2)), java.lang.Object(LessLeavesRec.Tree(java.lang.Object(LessLeavesRec.Tree(x3, x4)), x5)))

(20) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[0], x2[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(21) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[0], x2[0]), x0[0], x1[0], x2[0]) at position [0] we obtained the following new rules [LPAR04]:

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])

(22) Obligation:

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

4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])
4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(23) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x1[1], x2[1]), java.lang.Object(x0[1]), x1[1], x2[1]) at position [0] we obtained the following new rules [LPAR04]:

4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])

(24) Obligation:

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

4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])
4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(25) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[2], x3[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2]) at position [0] we obtained the following new rules [LPAR04]:

4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])

(26) Obligation:

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

4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])
4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(27) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[3], x4[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3]) at position [0] we obtained the following new rules [LPAR04]:

4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])

(28) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])
4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(29) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x2[4], x3[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4]) at position [0] we obtained the following new rules [LPAR04]:

4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])

(30) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])
4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(31) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule 4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4141_0_append_Load(x3[5], x4[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5]) at position [0] we obtained the following new rules [LPAR04]:

4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

(32) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4141_0_append_Load(x0, x1) → 4159_0_append_NONNULL(x1, x0)
4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(33) 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.

(34) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4141_0_append_Load(x0, x1)
4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(35) 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].

4141_0_append_Load(x0, x1)

(36) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(37) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

4505_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(java.lang.Object(x0[1])), java.lang.Object(LessLeavesRec.Tree(x1[1], x2[1])), NULL, java.lang.Object(x0[1])) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[1], x1[1]), java.lang.Object(x0[1]), x1[1], x2[1])

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(4141_1_LESSLEAVES_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = x₂   
POL(4159_0_append_NONNULL(x₁, x₂)) = x₁ + x₂   
POL(4219_0_append_Return(x₁)) = 1 + x₁   
POL(4490_1_append_InvokeMethod(x₁, x₂, x₃, x₄)) = x₁ + x₂   
POL(4505_1_LESSLEAVES_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = x₁   
POL(6162_0_append_Return(x₁)) = x₁   
POL(9986_0_append_Return(x₁)) = x₁   
POL(LessLeavesRec.Tree(x₁, x₂)) = x₁ + x₂   
POL(NULL) = 1   
POL(java.lang.Object(x₁)) = x₁   

The following usable rules [FROCOS05] were oriented:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

(38) Obligation:

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

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The TRS R consists of the following rules:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(39) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

4141_1_LESSLEAVES_INVOKEMETHOD(4219_0_append_Return(x0[0]), java.lang.Object(LessLeavesRec.Tree(x1[0], x2[0])), NULL, x0[0]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x2[0], x1[0]), x0[0], x1[0], x2[0])
4141_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4]))), java.lang.Object(LessLeavesRec.Tree(x2[4], x3[4])), java.lang.Object(LessLeavesRec.Tree(x0[4], NULL)), x1[4]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[4], x2[4]), java.lang.Object(LessLeavesRec.Tree(x0[4], x1[4])), x2[4], x3[4])
4141_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5]))))), java.lang.Object(LessLeavesRec.Tree(x3[5], x4[5])), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x5[5])))), x6[5]) → 4505_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[5], x3[5]), java.lang.Object(LessLeavesRec.Tree(x0[5], java.lang.Object(LessLeavesRec.Tree(x1[5], x2[5])))), x3[5], x4[5])

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(4141_1_LESSLEAVES_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = x₂   
POL(4159_0_append_NONNULL(x₁, x₂)) = 0   
POL(4219_0_append_Return(x₁)) = 0   
POL(4490_1_append_InvokeMethod(x₁, x₂, x₃, x₄)) = 0   
POL(4505_1_LESSLEAVES_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = x₃   
POL(6162_0_append_Return(x₁)) = 0   
POL(9986_0_append_Return(x₁)) = 0   
POL(LessLeavesRec.Tree(x₁, x₂)) = x₁   
POL(NULL) = 0   
POL(java.lang.Object(x₁)) = 1 + x₁   

The following usable rules [FROCOS05] were oriented: none

(40) Obligation:

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

4505_1_LESSLEAVES_INVOKEMETHOD(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2]))), java.lang.Object(LessLeavesRec.Tree(x2[2], x3[2])), java.lang.Object(LessLeavesRec.Tree(x0[2], NULL)), x1[2]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x3[2], x2[2]), java.lang.Object(LessLeavesRec.Tree(x0[2], x1[2])), x2[2], x3[2])
4505_1_LESSLEAVES_INVOKEMETHOD(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3]))))), java.lang.Object(LessLeavesRec.Tree(x3[3], x4[3])), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x5[3])))), x6[3]) → 4141_1_LESSLEAVES_INVOKEMETHOD(4159_0_append_NONNULL(x4[3], x3[3]), java.lang.Object(LessLeavesRec.Tree(x0[3], java.lang.Object(LessLeavesRec.Tree(x1[3], x2[3])))), x3[3], x4[3])

The TRS R consists of the following rules:

4159_0_append_NONNULL(x0, NULL) → 4219_0_append_Return(x0)
4159_0_append_NONNULL(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1))) → 4490_1_append_InvokeMethod(4159_0_append_NONNULL(x2, x1), x0, x1, x2)
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x2, java.lang.Object(LessLeavesRec.Tree(x0, x1)))))
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5) → 9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))))))
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0) → 6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x1, x0)))

The set Q consists of the following terms:

4159_0_append_NONNULL(x0, NULL)
4159_0_append_NONNULL(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2)))
4490_1_append_InvokeMethod(6162_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, x1))), x2, java.lang.Object(LessLeavesRec.Tree(x0, NULL)), x1)
4490_1_append_InvokeMethod(9986_0_append_Return(java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x2))))), x3, java.lang.Object(LessLeavesRec.Tree(x0, java.lang.Object(LessLeavesRec.Tree(x1, x4)))), x5)
4490_1_append_InvokeMethod(4219_0_append_Return(x0), x1, NULL, x0)

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

(41) DependencyGraphProof (EQUIVALENT transformation)

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

(42) TRUE

(43) 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:
18104_0_createNode_New → 20161_0_createNode_InvokeMethod
18104_0_createNode_New → 19939_0_createNode_InvokeMethod
18104_0_createNode_New → 20077_0_createNode_InvokeMethod
18104_0_createNode_New → 19972_0_createNode_InvokeMethod
16685_0_createTree_LE(0) → 16708_0_createTree_Return
18104_0_createNode_New → 2339_1_createNode_InvokeMethod
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20333_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20055_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20208_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20098_0_createTree_InvokeMethod(x0)
2339_1_createNode_InvokeMethod → 2562_0_createNode_Return
2339_1_createNode_InvokeMethod → 3580_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3636_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3247_0_createNode_Return

The integer pair graph contains the following rules and edges:
(0): 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0]) → COND_18104_1_CREATETREE_INVOKEMETHOD(x0[0] > 0, 2562_0_createNode_Return, x0[0])
(1): COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1]) → 16685_0_CREATETREE_LE(x0[1] + -1)
(2): 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2]) → COND_18104_1_CREATETREE_INVOKEMETHOD1(x0[2] > 0, 3247_0_createNode_Return, x0[2])
(3): COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3]) → 16685_0_CREATETREE_LE(x0[3] + -1)
(4): 16685_0_CREATETREE_LE(x0[4]) → COND_16685_0_CREATETREE_LE(x0[4] > 0, x0[4])
(5): COND_16685_0_CREATETREE_LE(TRUE, x0[5]) → 16685_0_CREATETREE_LE(x0[5] + -1)
(6): 16685_0_CREATETREE_LE(x0[6]) → COND_16685_0_CREATETREE_LE1(x0[6] > 0, x0[6])
(7): COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])
(8): 16685_0_CREATETREE_LE(x0[8]) → COND_16685_0_CREATETREE_LE2(x0[8] > 0, x0[8])
(9): COND_16685_0_CREATETREE_LE2(TRUE, x0[9]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])
(10): 16685_0_CREATETREE_LE(x0[10]) → COND_16685_0_CREATETREE_LE3(x0[10] > 0, x0[10])
(11): COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])
(12): 16685_0_CREATETREE_LE(x0[12]) → COND_16685_0_CREATETREE_LE4(x0[12] > 0, x0[12])
(13): COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])
(14): 16685_0_CREATETREE_LE(x0[14]) → COND_16685_0_CREATETREE_LE5(x0[14] > 0, x0[14])
(15): COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])
(16): 16685_0_CREATETREE_LE(x0[16]) → COND_16685_0_CREATETREE_LE6(x0[16] > 0, x0[16])
(17): COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])
(18): 16685_0_CREATETREE_LE(x0[18]) → COND_16685_0_CREATETREE_LE7(x0[18] > 0, x0[18])
(19): COND_16685_0_CREATETREE_LE7(TRUE, x0[19]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])
(20): 16685_0_CREATETREE_LE(x0[20]) → COND_16685_0_CREATETREE_LE8(x0[20] > 0, x0[20])
(21): COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])

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

(1) -> (4), if ((x0[1] + -1 →^* x0[4]))

(1) -> (6), if ((x0[1] + -1 →^* x0[6]))

(1) -> (8), if ((x0[1] + -1 →^* x0[8]))

(1) -> (10), if ((x0[1] + -1 →^* x0[10]))

(1) -> (12), if ((x0[1] + -1 →^* x0[12]))

(1) -> (14), if ((x0[1] + -1 →^* x0[14]))

(1) -> (16), if ((x0[1] + -1 →^* x0[16]))

(1) -> (18), if ((x0[1] + -1 →^* x0[18]))

(1) -> (20), if ((x0[1] + -1 →^* x0[20]))

(2) -> (3), if ((x0[2] > 0 →^* TRUE)∧(x0[2] →^* x0[3]))

(3) -> (4), if ((x0[3] + -1 →^* x0[4]))

(3) -> (6), if ((x0[3] + -1 →^* x0[6]))

(3) -> (8), if ((x0[3] + -1 →^* x0[8]))

(3) -> (10), if ((x0[3] + -1 →^* x0[10]))

(3) -> (12), if ((x0[3] + -1 →^* x0[12]))

(3) -> (14), if ((x0[3] + -1 →^* x0[14]))

(3) -> (16), if ((x0[3] + -1 →^* x0[16]))

(3) -> (18), if ((x0[3] + -1 →^* x0[18]))

(3) -> (20), if ((x0[3] + -1 →^* x0[20]))

(4) -> (5), if ((x0[4] > 0 →^* TRUE)∧(x0[4] →^* x0[5]))

(5) -> (4), if ((x0[5] + -1 →^* x0[4]))

(5) -> (6), if ((x0[5] + -1 →^* x0[6]))

(5) -> (8), if ((x0[5] + -1 →^* x0[8]))

(5) -> (10), if ((x0[5] + -1 →^* x0[10]))

(5) -> (12), if ((x0[5] + -1 →^* x0[12]))

(5) -> (14), if ((x0[5] + -1 →^* x0[14]))

(5) -> (16), if ((x0[5] + -1 →^* x0[16]))

(5) -> (18), if ((x0[5] + -1 →^* x0[18]))

(5) -> (20), if ((x0[5] + -1 →^* x0[20]))

(6) -> (7), if ((x0[6] > 0 →^* TRUE)∧(x0[6] →^* x0[7]))

(7) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[7] →^* x0[0]))

(7) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[7] →^* x0[2]))

(8) -> (9), if ((x0[8] > 0 →^* TRUE)∧(x0[8] →^* x0[9]))

(9) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[9] →^* x0[0]))

(9) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[9] →^* x0[2]))

(10) -> (11), if ((x0[10] > 0 →^* TRUE)∧(x0[10] →^* x0[11]))

(11) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[11] →^* x0[0]))

(11) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[11] →^* x0[2]))

(12) -> (13), if ((x0[12] > 0 →^* TRUE)∧(x0[12] →^* x0[13]))

(13) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[13] →^* x0[0]))

(13) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[13] →^* x0[2]))

(14) -> (15), if ((x0[14] > 0 →^* TRUE)∧(x0[14] →^* x0[15]))

(15) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[15] →^* x0[0]))

(15) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[15] →^* x0[2]))

(16) -> (17), if ((x0[16] > 0 →^* TRUE)∧(x0[16] →^* x0[17]))

(17) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[17] →^* x0[0]))

(17) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[17] →^* x0[2]))

(18) -> (19), if ((x0[18] > 0 →^* TRUE)∧(x0[18] →^* x0[19]))

(19) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[19] →^* x0[0]))

(19) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[19] →^* x0[2]))

(20) -> (21), if ((x0[20] > 0 →^* TRUE)∧(x0[20] →^* x0[21]))

(21) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[21] →^* x0[0]))

(21) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[21] →^* x0[2]))

The set Q consists of the following terms:
18104_0_createNode_New
16685_0_createTree_LE(0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0)
2339_1_createNode_InvokeMethod

(44) 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 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0) → COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0, 0), 2562_0_createNode_Return, x0) the following chains were created:

• We consider the chain 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0]) → COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0]), COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1]) → 16685_0_CREATETREE_LE(+(x0[1], -1)) which results in the following constraint:
  

  (1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0])≥NonInfC∧18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0])≥COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])∧(U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥))

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

  (2)    (>(x0[0], 0)=TRUE ⇒ 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0])≥NonInfC∧18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0])≥COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])∧(U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥))

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

  (3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)

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

  (4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)

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

  (5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)

  
  
  We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)

  
  
  

For Pair COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0) → 16685_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

• We consider the chain COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1]) → 16685_0_CREATETREE_LE(+(x0[1], -1)) which results in the following constraint:
  

  (7)    (COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1])≥NonInfC∧COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1])≥16685_0_CREATETREE_LE(+(x0[1], -1))∧(U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥))

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

  (8)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧[1 + (-1)bso_54] ≥ 0)

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

  (9)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧[1 + (-1)bso_54] ≥ 0)

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

  (10)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧[1 + (-1)bso_54] ≥ 0)

  
  
  We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (11)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_54] ≥ 0)

  
  
  

For Pair 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0) → COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0, 0), 3247_0_createNode_Return, x0) the following chains were created:

• We consider the chain 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2]) → COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2]), COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3]) → 16685_0_CREATETREE_LE(+(x0[3], -1)) which results in the following constraint:
  

  (12)    (>(x0[2], 0)=TRUE∧x0[2]=x0[3] ⇒ 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2])≥NonInfC∧18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2])≥COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])∧(U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥))

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

  (13)    (>(x0[2], 0)=TRUE ⇒ 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2])≥NonInfC∧18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2])≥COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])∧(U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥))

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

  (14)    (x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)

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

  (15)    (x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (15) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (16)    (x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)

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

  (17)    (x0[2] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥)∧[bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)

  
  
  

For Pair COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0) → 16685_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

• We consider the chain COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3]) → 16685_0_CREATETREE_LE(+(x0[3], -1)) which results in the following constraint:
  

  (18)    (COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3])≥NonInfC∧COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3])≥16685_0_CREATETREE_LE(+(x0[3], -1))∧(U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥))

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

  (19)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧[1 + (-1)bso_58] ≥ 0)

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

  (20)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧[1 + (-1)bso_58] ≥ 0)

  
  
  We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (21)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧[1 + (-1)bso_58] ≥ 0)

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

  (22)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_58] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[4]) → COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4]), COND_16685_0_CREATETREE_LE(TRUE, x0[5]) → 16685_0_CREATETREE_LE(+(x0[5], -1)) which results in the following constraint:
  

  (23)    (>(x0[4], 0)=TRUE∧x0[4]=x0[5] ⇒ 16685_0_CREATETREE_LE(x0[4])≥NonInfC∧16685_0_CREATETREE_LE(x0[4])≥COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])∧(U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥))

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

  (24)    (>(x0[4], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[4])≥NonInfC∧16685_0_CREATETREE_LE(x0[4])≥COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])∧(U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥))

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

  (25)    (x0[4] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥)∧[(-1)Bound*bni_59] + [(2)bni_59]x0[4] ≥ 0∧[1 + (-1)bso_60] ≥ 0)

  
  
  We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (26)    (x0[4] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥)∧[(-1)Bound*bni_59] + [(2)bni_59]x0[4] ≥ 0∧[1 + (-1)bso_60] ≥ 0)

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

  (27)    (x0[4] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥)∧[(-1)Bound*bni_59] + [(2)bni_59]x0[4] ≥ 0∧[1 + (-1)bso_60] ≥ 0)

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

  (28)    (x0[4] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥)∧[(-1)Bound*bni_59 + (2)bni_59] + [(2)bni_59]x0[4] ≥ 0∧[1 + (-1)bso_60] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE(TRUE, x0) → 16685_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE(TRUE, x0[5]) → 16685_0_CREATETREE_LE(+(x0[5], -1)) which results in the following constraint:
  

  (29)    (COND_16685_0_CREATETREE_LE(TRUE, x0[5])≥NonInfC∧COND_16685_0_CREATETREE_LE(TRUE, x0[5])≥16685_0_CREATETREE_LE(+(x0[5], -1))∧(U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥))

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

  (30)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧[1 + (-1)bso_62] ≥ 0)

  
  
  We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (31)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧[1 + (-1)bso_62] ≥ 0)

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

  (32)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧[1 + (-1)bso_62] ≥ 0)

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

  (33)    ((U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧0 = 0∧[1 + (-1)bso_62] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE1(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[6]) → COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6]), COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7]) which results in the following constraint:
  

  (34)    (>(x0[6], 0)=TRUE∧x0[6]=x0[7] ⇒ 16685_0_CREATETREE_LE(x0[6])≥NonInfC∧16685_0_CREATETREE_LE(x0[6])≥COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])∧(U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥))

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

  (35)    (>(x0[6], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[6])≥NonInfC∧16685_0_CREATETREE_LE(x0[6])≥COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])∧(U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥))

  
  
  We simplified constraint (35) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (36)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[6] ≥ 0∧[1 + (-1)bso_64] ≥ 0)

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

  (37)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[6] ≥ 0∧[1 + (-1)bso_64] ≥ 0)

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

  (38)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[6] ≥ 0∧[1 + (-1)bso_64] ≥ 0)

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

  (39)    (x0[6] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥)∧[(-1)Bound*bni_63 + (2)bni_63] + [(2)bni_63]x0[6] ≥ 0∧[1 + (-1)bso_64] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE1(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7]) which results in the following constraint:
  

  (40)    (COND_16685_0_CREATETREE_LE1(TRUE, x0[7])≥NonInfC∧COND_16685_0_CREATETREE_LE1(TRUE, x0[7])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥))

  
  
  We simplified constraint (40) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (41)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥)∧[(-1)bso_66] ≥ 0)

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

  (42)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥)∧[(-1)bso_66] ≥ 0)

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

  (43)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥)∧[(-1)bso_66] ≥ 0)

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

  (44)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥)∧0 = 0∧[(-1)bso_66] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE2(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[8]) → COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8]), COND_16685_0_CREATETREE_LE2(TRUE, x0[9]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9]) which results in the following constraint:
  

  (45)    (>(x0[8], 0)=TRUE∧x0[8]=x0[9] ⇒ 16685_0_CREATETREE_LE(x0[8])≥NonInfC∧16685_0_CREATETREE_LE(x0[8])≥COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])∧(U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥))

  
  
  We simplified constraint (45) using rule (IV) which results in the following new constraint:
  

  (46)    (>(x0[8], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[8])≥NonInfC∧16685_0_CREATETREE_LE(x0[8])≥COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])∧(U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥))

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

  (47)    (x0[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥)∧[(-1)Bound*bni_67] + [(2)bni_67]x0[8] ≥ 0∧[(-1)bso_68] ≥ 0)

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

  (48)    (x0[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥)∧[(-1)Bound*bni_67] + [(2)bni_67]x0[8] ≥ 0∧[(-1)bso_68] ≥ 0)

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

  (49)    (x0[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥)∧[(-1)Bound*bni_67] + [(2)bni_67]x0[8] ≥ 0∧[(-1)bso_68] ≥ 0)

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

  (50)    (x0[8] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥)∧[(-1)Bound*bni_67 + (2)bni_67] + [(2)bni_67]x0[8] ≥ 0∧[(-1)bso_68] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE2(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE2(TRUE, x0[9]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9]) which results in the following constraint:
  

  (51)    (COND_16685_0_CREATETREE_LE2(TRUE, x0[9])≥NonInfC∧COND_16685_0_CREATETREE_LE2(TRUE, x0[9])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥))

  
  
  We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (52)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥)∧[1 + (-1)bso_70] ≥ 0)

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

  (53)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥)∧[1 + (-1)bso_70] ≥ 0)

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

  (54)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥)∧[1 + (-1)bso_70] ≥ 0)

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

  (55)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥)∧0 = 0∧[1 + (-1)bso_70] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE3(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[10]) → COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10]), COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11]) which results in the following constraint:
  

  (56)    (>(x0[10], 0)=TRUE∧x0[10]=x0[11] ⇒ 16685_0_CREATETREE_LE(x0[10])≥NonInfC∧16685_0_CREATETREE_LE(x0[10])≥COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])∧(U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥))

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

  (57)    (>(x0[10], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[10])≥NonInfC∧16685_0_CREATETREE_LE(x0[10])≥COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])∧(U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥))

  
  
  We simplified constraint (57) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (58)    (x0[10] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥)∧[(-1)Bound*bni_71] + [(2)bni_71]x0[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

  
  
  We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (59)    (x0[10] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥)∧[(-1)Bound*bni_71] + [(2)bni_71]x0[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

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

  (60)    (x0[10] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥)∧[(-1)Bound*bni_71] + [(2)bni_71]x0[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

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

  (61)    (x0[10] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥)∧[(-1)Bound*bni_71 + (2)bni_71] + [(2)bni_71]x0[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE3(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11]) which results in the following constraint:
  

  (62)    (COND_16685_0_CREATETREE_LE3(TRUE, x0[11])≥NonInfC∧COND_16685_0_CREATETREE_LE3(TRUE, x0[11])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥))

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

  (63)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥)∧[(-1)bso_74] ≥ 0)

  
  
  We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (64)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥)∧[(-1)bso_74] ≥ 0)

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

  (65)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥)∧[(-1)bso_74] ≥ 0)

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

  (66)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥)∧0 = 0∧[(-1)bso_74] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE4(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[12]) → COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12]), COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13]) which results in the following constraint:
  

  (67)    (>(x0[12], 0)=TRUE∧x0[12]=x0[13] ⇒ 16685_0_CREATETREE_LE(x0[12])≥NonInfC∧16685_0_CREATETREE_LE(x0[12])≥COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])∧(U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥))

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

  (68)    (>(x0[12], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[12])≥NonInfC∧16685_0_CREATETREE_LE(x0[12])≥COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])∧(U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥))

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

  (69)    (x0[12] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥)∧[(-1)Bound*bni_75] + [(2)bni_75]x0[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)

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

  (70)    (x0[12] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥)∧[(-1)Bound*bni_75] + [(2)bni_75]x0[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)

  
  
  We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (71)    (x0[12] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥)∧[(-1)Bound*bni_75] + [(2)bni_75]x0[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)

  
  
  We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (72)    (x0[12] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥)∧[(-1)Bound*bni_75 + (2)bni_75] + [(2)bni_75]x0[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE4(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13]) which results in the following constraint:
  

  (73)    (COND_16685_0_CREATETREE_LE4(TRUE, x0[13])≥NonInfC∧COND_16685_0_CREATETREE_LE4(TRUE, x0[13])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥))

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

  (74)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥)∧[(-1)bso_78] ≥ 0)

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

  (75)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥)∧[(-1)bso_78] ≥ 0)

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

  (76)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥)∧[(-1)bso_78] ≥ 0)

  
  
  We simplified constraint (76) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (77)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥)∧0 = 0∧[(-1)bso_78] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE5(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[14]) → COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14]), COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15]) which results in the following constraint:
  

  (78)    (>(x0[14], 0)=TRUE∧x0[14]=x0[15] ⇒ 16685_0_CREATETREE_LE(x0[14])≥NonInfC∧16685_0_CREATETREE_LE(x0[14])≥COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])∧(U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥))

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

  (79)    (>(x0[14], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[14])≥NonInfC∧16685_0_CREATETREE_LE(x0[14])≥COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])∧(U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥))

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

  (80)    (x0[14] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥)∧[(-1)Bound*bni_79] + [(2)bni_79]x0[14] ≥ 0∧[1 + (-1)bso_80] ≥ 0)

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

  (81)    (x0[14] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥)∧[(-1)Bound*bni_79] + [(2)bni_79]x0[14] ≥ 0∧[1 + (-1)bso_80] ≥ 0)

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

  (82)    (x0[14] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥)∧[(-1)Bound*bni_79] + [(2)bni_79]x0[14] ≥ 0∧[1 + (-1)bso_80] ≥ 0)

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

  (83)    (x0[14] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥)∧[(-1)Bound*bni_79 + (2)bni_79] + [(2)bni_79]x0[14] ≥ 0∧[1 + (-1)bso_80] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE5(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15]) which results in the following constraint:
  

  (84)    (COND_16685_0_CREATETREE_LE5(TRUE, x0[15])≥NonInfC∧COND_16685_0_CREATETREE_LE5(TRUE, x0[15])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥))

  
  
  We simplified constraint (84) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (85)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥)∧[(-1)bso_82] ≥ 0)

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

  (86)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥)∧[(-1)bso_82] ≥ 0)

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

  (87)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥)∧[(-1)bso_82] ≥ 0)

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

  (88)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥)∧0 = 0∧[(-1)bso_82] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE6(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[16]) → COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16]), COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17]) which results in the following constraint:
  

  (89)    (>(x0[16], 0)=TRUE∧x0[16]=x0[17] ⇒ 16685_0_CREATETREE_LE(x0[16])≥NonInfC∧16685_0_CREATETREE_LE(x0[16])≥COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])∧(U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥))

  
  
  We simplified constraint (89) using rule (IV) which results in the following new constraint:
  

  (90)    (>(x0[16], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[16])≥NonInfC∧16685_0_CREATETREE_LE(x0[16])≥COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])∧(U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥))

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

  (91)    (x0[16] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥)∧[(-1)Bound*bni_83] + [(2)bni_83]x0[16] ≥ 0∧[1 + (-1)bso_84] ≥ 0)

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

  (92)    (x0[16] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥)∧[(-1)Bound*bni_83] + [(2)bni_83]x0[16] ≥ 0∧[1 + (-1)bso_84] ≥ 0)

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

  (93)    (x0[16] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥)∧[(-1)Bound*bni_83] + [(2)bni_83]x0[16] ≥ 0∧[1 + (-1)bso_84] ≥ 0)

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

  (94)    (x0[16] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥)∧[(-1)Bound*bni_83 + (2)bni_83] + [(2)bni_83]x0[16] ≥ 0∧[1 + (-1)bso_84] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE6(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17]) which results in the following constraint:
  

  (95)    (COND_16685_0_CREATETREE_LE6(TRUE, x0[17])≥NonInfC∧COND_16685_0_CREATETREE_LE6(TRUE, x0[17])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥))

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

  (96)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥)∧[(-1)bso_86] ≥ 0)

  
  
  We simplified constraint (96) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (97)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥)∧[(-1)bso_86] ≥ 0)

  
  
  We simplified constraint (97) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (98)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥)∧[(-1)bso_86] ≥ 0)

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

  (99)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥)∧0 = 0∧[(-1)bso_86] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE7(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[18]) → COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18]), COND_16685_0_CREATETREE_LE7(TRUE, x0[19]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19]) which results in the following constraint:
  

  (100)    (>(x0[18], 0)=TRUE∧x0[18]=x0[19] ⇒ 16685_0_CREATETREE_LE(x0[18])≥NonInfC∧16685_0_CREATETREE_LE(x0[18])≥COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])∧(U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥))

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

  (101)    (>(x0[18], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[18])≥NonInfC∧16685_0_CREATETREE_LE(x0[18])≥COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])∧(U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥))

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

  (102)    (x0[18] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥)∧[(-1)Bound*bni_87] + [(2)bni_87]x0[18] ≥ 0∧[(-1)bso_88] ≥ 0)

  
  
  We simplified constraint (102) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (103)    (x0[18] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥)∧[(-1)Bound*bni_87] + [(2)bni_87]x0[18] ≥ 0∧[(-1)bso_88] ≥ 0)

  
  
  We simplified constraint (103) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (104)    (x0[18] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥)∧[(-1)Bound*bni_87] + [(2)bni_87]x0[18] ≥ 0∧[(-1)bso_88] ≥ 0)

  
  
  We simplified constraint (104) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (105)    (x0[18] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥)∧[(-1)Bound*bni_87 + (2)bni_87] + [(2)bni_87]x0[18] ≥ 0∧[(-1)bso_88] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE7(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE7(TRUE, x0[19]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19]) which results in the following constraint:
  

  (106)    (COND_16685_0_CREATETREE_LE7(TRUE, x0[19])≥NonInfC∧COND_16685_0_CREATETREE_LE7(TRUE, x0[19])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥))

  
  
  We simplified constraint (106) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (107)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥)∧[1 + (-1)bso_90] ≥ 0)

  
  
  We simplified constraint (107) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (108)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥)∧[1 + (-1)bso_90] ≥ 0)

  
  
  We simplified constraint (108) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (109)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥)∧[1 + (-1)bso_90] ≥ 0)

  
  
  We simplified constraint (109) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (110)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥)∧0 = 0∧[1 + (-1)bso_90] ≥ 0)

  
  
  

For Pair 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE8(>(x0, 0), x0) the following chains were created:

• We consider the chain 16685_0_CREATETREE_LE(x0[20]) → COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20]), COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21]) which results in the following constraint:
  

  (111)    (>(x0[20], 0)=TRUE∧x0[20]=x0[21] ⇒ 16685_0_CREATETREE_LE(x0[20])≥NonInfC∧16685_0_CREATETREE_LE(x0[20])≥COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])∧(U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥))

  
  
  We simplified constraint (111) using rule (IV) which results in the following new constraint:
  

  (112)    (>(x0[20], 0)=TRUE ⇒ 16685_0_CREATETREE_LE(x0[20])≥NonInfC∧16685_0_CREATETREE_LE(x0[20])≥COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])∧(U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥))

  
  
  We simplified constraint (112) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (113)    (x0[20] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥)∧[(-1)Bound*bni_91] + [(2)bni_91]x0[20] ≥ 0∧[1 + (-1)bso_92] ≥ 0)

  
  
  We simplified constraint (113) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (114)    (x0[20] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥)∧[(-1)Bound*bni_91] + [(2)bni_91]x0[20] ≥ 0∧[1 + (-1)bso_92] ≥ 0)

  
  
  We simplified constraint (114) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (115)    (x0[20] + [-1] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥)∧[(-1)Bound*bni_91] + [(2)bni_91]x0[20] ≥ 0∧[1 + (-1)bso_92] ≥ 0)

  
  
  We simplified constraint (115) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (116)    (x0[20] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥)∧[(-1)Bound*bni_91 + (2)bni_91] + [(2)bni_91]x0[20] ≥ 0∧[1 + (-1)bso_92] ≥ 0)

  
  
  

For Pair COND_16685_0_CREATETREE_LE8(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0) the following chains were created:

• We consider the chain COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21]) which results in the following constraint:
  

  (117)    (COND_16685_0_CREATETREE_LE8(TRUE, x0[21])≥NonInfC∧COND_16685_0_CREATETREE_LE8(TRUE, x0[21])≥18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])∧(U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥))

  
  
  We simplified constraint (117) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (118)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥)∧[(-1)bso_94] ≥ 0)

  
  
  We simplified constraint (118) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (119)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥)∧[(-1)bso_94] ≥ 0)

  
  
  We simplified constraint (119) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (120)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥)∧[(-1)bso_94] ≥ 0)

  
  
  We simplified constraint (120) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (121)    ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥)∧0 = 0∧[(-1)bso_94] ≥ 0)

  
  
  

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

• 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0) → COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0, 0), 2562_0_createNode_Return, x0)
  
  • (x0[0] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)
    
  
  
• COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0) → 16685_0_CREATETREE_LE(+(x0, -1))
  
  • ((U^Increasing(16685_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_54] ≥ 0)
    
  
  
• 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0) → COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0, 0), 3247_0_createNode_Return, x0)
  
  • (x0[2] ≥ 0 ⇒ (U^Increasing(COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])), ≥)∧[bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)
    
  
  
• COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0) → 16685_0_CREATETREE_LE(+(x0, -1))
  
  • ((U^Increasing(16685_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_58] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE(>(x0, 0), x0)
  
  • (x0[4] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])), ≥)∧[(-1)Bound*bni_59 + (2)bni_59] + [(2)bni_59]x0[4] ≥ 0∧[1 + (-1)bso_60] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE(TRUE, x0) → 16685_0_CREATETREE_LE(+(x0, -1))
  
  • ((U^Increasing(16685_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧0 = 0∧[1 + (-1)bso_62] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE1(>(x0, 0), x0)
  
  • (x0[6] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])), ≥)∧[(-1)Bound*bni_63 + (2)bni_63] + [(2)bni_63]x0[6] ≥ 0∧[1 + (-1)bso_64] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE1(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])), ≥)∧0 = 0∧[(-1)bso_66] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE2(>(x0, 0), x0)
  
  • (x0[8] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])), ≥)∧[(-1)Bound*bni_67 + (2)bni_67] + [(2)bni_67]x0[8] ≥ 0∧[(-1)bso_68] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE2(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])), ≥)∧0 = 0∧[1 + (-1)bso_70] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE3(>(x0, 0), x0)
  
  • (x0[10] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])), ≥)∧[(-1)Bound*bni_71 + (2)bni_71] + [(2)bni_71]x0[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE3(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])), ≥)∧0 = 0∧[(-1)bso_74] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE4(>(x0, 0), x0)
  
  • (x0[12] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])), ≥)∧[(-1)Bound*bni_75 + (2)bni_75] + [(2)bni_75]x0[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE4(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])), ≥)∧0 = 0∧[(-1)bso_78] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE5(>(x0, 0), x0)
  
  • (x0[14] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])), ≥)∧[(-1)Bound*bni_79 + (2)bni_79] + [(2)bni_79]x0[14] ≥ 0∧[1 + (-1)bso_80] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE5(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])), ≥)∧0 = 0∧[(-1)bso_82] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE6(>(x0, 0), x0)
  
  • (x0[16] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])), ≥)∧[(-1)Bound*bni_83 + (2)bni_83] + [(2)bni_83]x0[16] ≥ 0∧[1 + (-1)bso_84] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE6(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])), ≥)∧0 = 0∧[(-1)bso_86] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE7(>(x0, 0), x0)
  
  • (x0[18] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])), ≥)∧[(-1)Bound*bni_87 + (2)bni_87] + [(2)bni_87]x0[18] ≥ 0∧[(-1)bso_88] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE7(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])), ≥)∧0 = 0∧[1 + (-1)bso_90] ≥ 0)
    
  
  
• 16685_0_CREATETREE_LE(x0) → COND_16685_0_CREATETREE_LE8(>(x0, 0), x0)
  
  • (x0[20] ≥ 0 ⇒ (U^Increasing(COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])), ≥)∧[(-1)Bound*bni_91 + (2)bni_91] + [(2)bni_91]x0[20] ≥ 0∧[1 + (-1)bso_92] ≥ 0)
    
  
  
• COND_16685_0_CREATETREE_LE8(TRUE, x0) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0)
  
  • ((U^Increasing(18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])), ≥)∧0 = 0∧[(-1)bso_94] ≥ 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(18104_0_createNode_New) = [-1]   
POL(20161_0_createNode_InvokeMethod) = [-1]   
POL(19939_0_createNode_InvokeMethod) = [-1]   
POL(20077_0_createNode_InvokeMethod) = [-1]   
POL(19972_0_createNode_InvokeMethod) = [-1]   
POL(16685_0_createTree_LE(x₁)) = [-1]   
POL(0) = 0   
POL(16708_0_createTree_Return) = [-1]   
POL(2339_1_createNode_InvokeMethod) = [-1]   
POL(18104_1_createTree_InvokeMethod(x₁, x₂)) = [-1]   
POL(3580_0_createNode_InvokeMethod) = [-1]   
POL(18394_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(3636_0_createNode_InvokeMethod) = [-1]   
POL(17926_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(18223_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(17975_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(20333_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(20055_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(20208_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(20098_0_createTree_InvokeMethod(x₁)) = [-1]   
POL(2562_0_createNode_Return) = [-1]   
POL(3247_0_createNode_Return) = [-1]   
POL(18104_1_CREATETREE_INVOKEMETHOD(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_18104_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [2]x₃   
POL(>(x₁, x₂)) = [-1]   
POL(16685_0_CREATETREE_LE(x₁)) = [2]x₁   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(-1) = [-1]   
POL(COND_18104_1_CREATETREE_INVOKEMETHOD1(x₁, x₂, x₃)) = [-1] + [2]x₃   
POL(COND_16685_0_CREATETREE_LE(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE1(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE2(x₁, x₂)) = [2]x₂   
POL(COND_16685_0_CREATETREE_LE3(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE4(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE5(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE6(x₁, x₂)) = [-1] + [2]x₂   
POL(COND_16685_0_CREATETREE_LE7(x₁, x₂)) = [2]x₂   
POL(COND_16685_0_CREATETREE_LE8(x₁, x₂)) = [-1] + [2]x₂   

The following pairs are in P_>:

COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1]) → 16685_0_CREATETREE_LE(+(x0[1], -1))
COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3]) → 16685_0_CREATETREE_LE(+(x0[3], -1))
16685_0_CREATETREE_LE(x0[4]) → COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])
COND_16685_0_CREATETREE_LE(TRUE, x0[5]) → 16685_0_CREATETREE_LE(+(x0[5], -1))
16685_0_CREATETREE_LE(x0[6]) → COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])
COND_16685_0_CREATETREE_LE2(TRUE, x0[9]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])
16685_0_CREATETREE_LE(x0[10]) → COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])
16685_0_CREATETREE_LE(x0[12]) → COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])
16685_0_CREATETREE_LE(x0[14]) → COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])
16685_0_CREATETREE_LE(x0[16]) → COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])
COND_16685_0_CREATETREE_LE7(TRUE, x0[19]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])
16685_0_CREATETREE_LE(x0[20]) → COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])

The following pairs are in P_bound:

18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0]) → COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])
18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2]) → COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])
16685_0_CREATETREE_LE(x0[4]) → COND_16685_0_CREATETREE_LE(>(x0[4], 0), x0[4])
16685_0_CREATETREE_LE(x0[6]) → COND_16685_0_CREATETREE_LE1(>(x0[6], 0), x0[6])
16685_0_CREATETREE_LE(x0[8]) → COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])
16685_0_CREATETREE_LE(x0[10]) → COND_16685_0_CREATETREE_LE3(>(x0[10], 0), x0[10])
16685_0_CREATETREE_LE(x0[12]) → COND_16685_0_CREATETREE_LE4(>(x0[12], 0), x0[12])
16685_0_CREATETREE_LE(x0[14]) → COND_16685_0_CREATETREE_LE5(>(x0[14], 0), x0[14])
16685_0_CREATETREE_LE(x0[16]) → COND_16685_0_CREATETREE_LE6(>(x0[16], 0), x0[16])
16685_0_CREATETREE_LE(x0[18]) → COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])
16685_0_CREATETREE_LE(x0[20]) → COND_16685_0_CREATETREE_LE8(>(x0[20], 0), x0[20])

The following pairs are in P_≥:

18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0]) → COND_18104_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 2562_0_createNode_Return, x0[0])
18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2]) → COND_18104_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 3247_0_createNode_Return, x0[2])
COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])
16685_0_CREATETREE_LE(x0[8]) → COND_16685_0_CREATETREE_LE2(>(x0[8], 0), x0[8])
COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])
COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])
COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])
COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])
16685_0_CREATETREE_LE(x0[18]) → COND_16685_0_CREATETREE_LE7(>(x0[18], 0), x0[18])
COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])

There are no usable rules.

(45) Complex Obligation (AND)

(46) 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:
18104_0_createNode_New → 20161_0_createNode_InvokeMethod
18104_0_createNode_New → 19939_0_createNode_InvokeMethod
18104_0_createNode_New → 20077_0_createNode_InvokeMethod
18104_0_createNode_New → 19972_0_createNode_InvokeMethod
16685_0_createTree_LE(0) → 16708_0_createTree_Return
18104_0_createNode_New → 2339_1_createNode_InvokeMethod
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20333_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20055_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20208_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20098_0_createTree_InvokeMethod(x0)
2339_1_createNode_InvokeMethod → 2562_0_createNode_Return
2339_1_createNode_InvokeMethod → 3580_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3636_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3247_0_createNode_Return

The integer pair graph contains the following rules and edges:
(0): 18104_1_CREATETREE_INVOKEMETHOD(2562_0_createNode_Return, x0[0]) → COND_18104_1_CREATETREE_INVOKEMETHOD(x0[0] > 0, 2562_0_createNode_Return, x0[0])
(2): 18104_1_CREATETREE_INVOKEMETHOD(3247_0_createNode_Return, x0[2]) → COND_18104_1_CREATETREE_INVOKEMETHOD1(x0[2] > 0, 3247_0_createNode_Return, x0[2])
(7): COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])
(8): 16685_0_CREATETREE_LE(x0[8]) → COND_16685_0_CREATETREE_LE2(x0[8] > 0, x0[8])
(11): COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])
(13): COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])
(15): COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])
(17): COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])
(18): 16685_0_CREATETREE_LE(x0[18]) → COND_16685_0_CREATETREE_LE7(x0[18] > 0, x0[18])
(21): COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])

(7) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[7] →^* x0[0]))

(11) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[11] →^* x0[0]))

(13) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[13] →^* x0[0]))

(15) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[15] →^* x0[0]))

(17) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[17] →^* x0[0]))

(21) -> (0), if ((18104_0_createNode_New →^* 2562_0_createNode_Return)∧(x0[21] →^* x0[0]))

(7) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[7] →^* x0[2]))

(11) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[11] →^* x0[2]))

(13) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[13] →^* x0[2]))

(15) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[15] →^* x0[2]))

(17) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[17] →^* x0[2]))

(21) -> (2), if ((18104_0_createNode_New →^* 3247_0_createNode_Return)∧(x0[21] →^* x0[2]))

The set Q consists of the following terms:
18104_0_createNode_New
16685_0_createTree_LE(0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0)
2339_1_createNode_InvokeMethod

(47) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 10 less nodes.

(48) TRUE

(49) 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:
18104_0_createNode_New → 20161_0_createNode_InvokeMethod
18104_0_createNode_New → 19939_0_createNode_InvokeMethod
18104_0_createNode_New → 20077_0_createNode_InvokeMethod
18104_0_createNode_New → 19972_0_createNode_InvokeMethod
16685_0_createTree_LE(0) → 16708_0_createTree_Return
18104_0_createNode_New → 2339_1_createNode_InvokeMethod
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18394_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17926_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 18223_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 17975_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20333_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20055_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20208_0_createTree_InvokeMethod(x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0) → 20098_0_createTree_InvokeMethod(x0)
2339_1_createNode_InvokeMethod → 2562_0_createNode_Return
2339_1_createNode_InvokeMethod → 3580_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3636_0_createNode_InvokeMethod
2339_1_createNode_InvokeMethod → 3247_0_createNode_Return

The integer pair graph contains the following rules and edges:
(1): COND_18104_1_CREATETREE_INVOKEMETHOD(TRUE, 2562_0_createNode_Return, x0[1]) → 16685_0_CREATETREE_LE(x0[1] + -1)
(3): COND_18104_1_CREATETREE_INVOKEMETHOD1(TRUE, 3247_0_createNode_Return, x0[3]) → 16685_0_CREATETREE_LE(x0[3] + -1)
(5): COND_16685_0_CREATETREE_LE(TRUE, x0[5]) → 16685_0_CREATETREE_LE(x0[5] + -1)
(7): COND_16685_0_CREATETREE_LE1(TRUE, x0[7]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[7])
(9): COND_16685_0_CREATETREE_LE2(TRUE, x0[9]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[9])
(11): COND_16685_0_CREATETREE_LE3(TRUE, x0[11]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[11])
(13): COND_16685_0_CREATETREE_LE4(TRUE, x0[13]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[13])
(15): COND_16685_0_CREATETREE_LE5(TRUE, x0[15]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[15])
(17): COND_16685_0_CREATETREE_LE6(TRUE, x0[17]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[17])
(19): COND_16685_0_CREATETREE_LE7(TRUE, x0[19]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[19])
(21): COND_16685_0_CREATETREE_LE8(TRUE, x0[21]) → 18104_1_CREATETREE_INVOKEMETHOD(18104_0_createNode_New, x0[21])


The set Q consists of the following terms:
18104_0_createNode_New
16685_0_createTree_LE(0)
18104_1_createTree_InvokeMethod(3580_0_createNode_InvokeMethod, x0)
18104_1_createTree_InvokeMethod(3636_0_createNode_InvokeMethod, x0)
2339_1_createNode_InvokeMethod

(50) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 11 less nodes.

(51) TRUE