Termination proof of /tmp/tmpxkznqH/MirrorBinTreeRec.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 AND

    ↳5 IDP

        ↳6 IDPtoQDPProof (⇒)

        ↳7 QDP

        ↳8 DependencyGraphProof (⇔)

        ↳9 QDP

        ↳10 UsableRulesProof (⇔)

        ↳11 QDP

        ↳12 QReductionProof (⇔)

        ↳13 QDP

        ↳14 UsableRulesReductionPairsProof (⇔)

        ↳15 QDP

        ↳16 DependencyGraphProof (⇔)

        ↳17 QDP

        ↳18 QReductionProof (⇔)

        ↳19 QDP

        ↳20 QDPSizeChangeProof (⇔)

        ↳21 YES

    ↳22 IDP

        ↳23 IDPNonInfProof (⇒)

        ↳24 AND

            ↳25 IDP

                ↳26 IDependencyGraphProof (⇔)

                ↳27 TRUE

            ↳28 IDP

                ↳29 IDependencyGraphProof (⇔)

                ↳30 TRUE

(0) Obligation:

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

package MirrorBinTreeRec;

/**
 * Mirror a binary tree
 * @author cotto
 */
public class MirrorBinTreeRec {
    public static void main(final String[] args) {
        Random.args = args;
        final Tree tree = Tree.createTree();
        mirror(tree);
    }

    public static void mirror(final Tree tree) {
        if (tree == null) {
            return;
        }
        final Tree temp = tree.right;
        tree.right = tree.left;
        tree.left = temp;
        mirror(tree.left);
        mirror(tree.right);
    }
}


package MirrorBinTreeRec;
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 MirrorBinTreeRec;

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

    public Tree(final Tree l, final Tree r) {
        this.left = l;
        this.right = 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.left == null) {
                    t.left = createNode();
                    t = result;
                } else {
                    t = t.left;
                }
            } else {
                if (t.right == null) {
                    t.right = createNode();
                    t = result;
                } else {
                    t = t.right;
                }
            }
            counter--;
        }

        return result;
    }

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
MirrorBinTreeRec.MirrorBinTreeRec.main([Ljava/lang/String;)V: Graph of 81 nodes with 0 SCCs.

MirrorBinTreeRec.Tree.createTree()LMirrorBinTreeRec/Tree;: Graph of 346 nodes with 1 SCC.

MirrorBinTreeRec.MirrorBinTreeRec.mirror(LMirrorBinTreeRec/Tree;)V: Graph of 61 nodes with 0 SCCs.

MirrorBinTreeRec.Tree.createNode()LMirrorBinTreeRec/Tree;: Graph of 99 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 44 rules for P and 26 rules for R.

Combined rules. Obtained 6 rules for P and 11 rules for R.

Filtered ground terms:

1935_0_mirror_NONNULL(x1, x2, x3) → 1935_0_mirror_NONNULL(x2, x3)
MirrorBinTreeRec.Tree(x1, x2, x3) → MirrorBinTreeRec.Tree(x2, x3)
2333_0_mirror_Return(x1) → 2333_0_mirror_Return
3416_0_mirror_Return(x1) → 3416_0_mirror_Return
3128_0_mirror_Return(x1) → 3128_0_mirror_Return
2821_0_mirror_Return(x1) → 2821_0_mirror_Return
1978_0_mirror_Return(x1, x2) → 1978_0_mirror_Return

Filtered duplicate args:

1935_0_mirror_NONNULL(x1, x2) → 1935_0_mirror_NONNULL(x2)

Finished conversion. Obtained 6 rules for P and 11 rules for R. System has no predefined symbols.

Log for SCC 1:

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:

9511_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → 9511_0_createTree_FieldAccess(x2, x3, x4, x5)
MirrorBinTreeRec.Tree(x1, x2, x3) → MirrorBinTreeRec.Tree(x2, x3)
9284_0_random_GT(x1, x2, x3) → 9284_0_random_GT(x2, x3)
9574_0_random_IntArithmetic(x1, x2, x3, x4) → 9574_0_random_IntArithmetic(x2, x3)
9177_0_createTree_LE(x1, x2, x3, x4, x5) → 9177_0_createTree_LE(x2, x3, x4, x5)
Cond_11896_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_11896_1_createTree_InvokeMethod1(x1, x3, x4, x5)
1925_0_createNode_Return(x1, x2) → 1925_0_createNode_Return
Cond_11896_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_11896_1_createTree_InvokeMethod(x1, x3, x4, x5)
1621_0_createNode_Return(x1, x2) → 1621_0_createNode_Return
11896_0_createNode_New(x1) → 11896_0_createNode_New
Cond_11999_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_11999_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_11999_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_11999_1_createTree_InvokeMethod(x1, x3, x4, x5)
11999_0_createNode_New(x1) → 11999_0_createNode_New
Cond_11868_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_11868_1_createTree_InvokeMethod1(x1, x3)
11868_1_createTree_InvokeMethod(x1, x2, x3, x4) → 11868_1_createTree_InvokeMethod(x1, x2)
Cond_11868_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_11868_1_createTree_InvokeMethod(x1, x3)
11868_0_createNode_New(x1) → 11868_0_createNode_New
Cond_9574_1_createTree_InvokeMethod3(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod3(x1, x2, x3)
Cond_12092_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_12092_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_12092_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_12092_1_createTree_InvokeMethod(x1, x3, x4, x5)
12092_0_createNode_New(x1) → 12092_0_createNode_New
Cond_10100_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_10100_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_10100_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_10100_1_createTree_InvokeMethod(x1, x3, x4, x5)
10100_0_createNode_New(x1) → 10100_0_createNode_New
Cond_9511_0_createTree_FieldAccess2(x1, x2, x3, x4, x5, x6) → Cond_9511_0_createTree_FieldAccess2(x1, x3, x4, x5, x6)
Cond_10307_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_10307_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_10307_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_10307_1_createTree_InvokeMethod(x1, x3, x4, x5)
10307_0_createNode_New(x1) → 10307_0_createNode_New
Cond_9511_0_createTree_FieldAccess1(x1, x2, x3, x4, x5, x6) → Cond_9511_0_createTree_FieldAccess1(x1, x3, x4, x5, x6)
Cond_10057_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_10057_1_createTree_InvokeMethod1(x1, x3)
10057_1_createTree_InvokeMethod(x1, x2, x3, x4) → 10057_1_createTree_InvokeMethod(x1, x2)
Cond_10057_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_10057_1_createTree_InvokeMethod(x1, x3)
10057_0_createNode_New(x1) → 10057_0_createNode_New
Cond_10501_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_10501_1_createTree_InvokeMethod1(x1, x3, x4, x5)
Cond_10501_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_10501_1_createTree_InvokeMethod(x1, x3, x4, x5)
10501_0_createNode_New(x1) → 10501_0_createNode_New
Cond_9511_0_createTree_FieldAccess(x1, x2, x3, x4, x5, x6) → Cond_9511_0_createTree_FieldAccess(x1, x3, x4, x5, x6)
9414_0_random_ArrayAccess(x1, x2, x3) → 9414_0_random_ArrayAccess(x2, x3)
9278_0_random_GT(x1, x2, x3) → 9278_0_random_GT(x2, x3)
Cond_9177_0_createTree_LE1(x1, x2, x3, x4, x5, x6) → Cond_9177_0_createTree_LE1(x1, x3, x4, x5, x6)
Cond_9177_0_createTree_LE(x1, x2, x3, x4, x5, x6) → Cond_9177_0_createTree_LE(x1, x3, x4, x5, x6)
2014_0_createNode_InvokeMethod(x1, x2, x3, x4) → 2014_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_1587_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_1587_1_createNode_InvokeMethod(x1, x2)
1587_0_random_ArrayAccess(x1, x2, x3) → 1587_0_random_ArrayAccess(x2, x3)
1587_1_createNode_InvokeMethod(x1, x2, x3) → 1587_1_createNode_InvokeMethod(x1)
Cond_1678_1_createNode_InvokeMethod1(x1, x2, x3, x4) → Cond_1678_1_createNode_InvokeMethod1(x1, x2)
1678_0_random_IntArithmetic(x1, x2, x3, x4) → 1678_0_random_IntArithmetic(x2, x3)
1678_1_createNode_InvokeMethod(x1, x2, x3) → 1678_1_createNode_InvokeMethod(x1)
Cond_1678_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_1678_1_createNode_InvokeMethod(x1, x2)
Cond_1618_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_1618_1_createNode_InvokeMethod(x1, x2)
1618_0_random_ArrayAccess(x1, x2, x3) → 1618_0_random_ArrayAccess(x2, x3)
1618_1_createNode_InvokeMethod(x1, x2, x3) → 1618_1_createNode_InvokeMethod(x1)
2043_0_createNode_InvokeMethod(x1, x2, x3, x4) → 2043_0_createNode_InvokeMethod
Cond_1619_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_1619_1_createNode_InvokeMethod(x1, x2)
1619_0_random_ArrayAccess(x1, x2, x3) → 1619_0_random_ArrayAccess(x2, x3)
1619_1_createNode_InvokeMethod(x1, x2, x3) → 1619_1_createNode_InvokeMethod(x1)
Cond_1502_1_createNode_InvokeMethod3(x1, x2, x3, x4) → Cond_1502_1_createNode_InvokeMethod3(x1, x2)
1502_0_random_GT(x1, x2, x3) → 1502_0_random_GT(x2, x3)
1502_1_createNode_InvokeMethod(x1, x2, x3) → 1502_1_createNode_InvokeMethod(x1)
Cond_1502_1_createNode_InvokeMethod2(x1, x2, x3, x4) → Cond_1502_1_createNode_InvokeMethod2(x1, x2)
Cond_1502_1_createNode_InvokeMethod1(x1, x2, x3, x4) → Cond_1502_1_createNode_InvokeMethod1(x1, x2)
Cond_1502_1_createNode_InvokeMethod(x1, x2, x3, x4) → Cond_1502_1_createNode_InvokeMethod(x1, x2)
12050_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 12050_0_createTree_InvokeMethod(x3, x4, x5)
12189_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 12189_0_createTree_InvokeMethod(x3, x4, x5)
11992_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 11992_0_createTree_InvokeMethod(x3)
12277_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 12277_0_createTree_InvokeMethod(x3, x4, x5)
10396_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 10396_0_createTree_InvokeMethod(x3, x4, x5)
10647_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 10647_0_createTree_InvokeMethod(x3, x4, x5)
10301_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 10301_0_createTree_InvokeMethod(x3)
10799_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 10799_0_createTree_InvokeMethod(x3, x4, x5)
9203_0_createTree_Return(x1, x2) → 9203_0_createTree_Return(x2)
11910_0_createNode_InvokeMethod(x1, x2, x3, x4) → 11910_0_createNode_InvokeMethod
12023_0_createNode_InvokeMethod(x1, x2, x3, x4) → 12023_0_createNode_InvokeMethod
11882_0_createNode_InvokeMethod(x1, x2, x3, x4) → 11882_0_createNode_InvokeMethod
12141_0_createNode_InvokeMethod(x1, x2, x3, x4) → 12141_0_createNode_InvokeMethod

Filtered duplicate args:

9511_0_createTree_FieldAccess(x1, x2, x3, x4) → 9511_0_createTree_FieldAccess(x1, x2, x4)
9177_0_createTree_LE(x1, x2, x3, x4) → 9177_0_createTree_LE(x2, x3, x4)
Cond_9511_0_createTree_FieldAccess2(x1, x2, x3, x4, x5) → Cond_9511_0_createTree_FieldAccess2(x1, x2, x3, x5)
Cond_9511_0_createTree_FieldAccess1(x1, x2, x3, x4, x5) → Cond_9511_0_createTree_FieldAccess1(x1, x2, x3, x5)
Cond_9511_0_createTree_FieldAccess(x1, x2, x3, x4, x5) → Cond_9511_0_createTree_FieldAccess(x1, x2, x3, x5)
Cond_9177_0_createTree_LE1(x1, x2, x3, x4, x5) → Cond_9177_0_createTree_LE1(x1, x3, x4, x5)
Cond_9177_0_createTree_LE(x1, x2, x3, x4, x5) → Cond_9177_0_createTree_LE(x1, x3, x4, x5)

Filtered all non-integer terms:

9177_0_createTree_LE(x1, x2, x3) → 9177_0_createTree_LE(x3)
Cond_9177_0_createTree_LE(x1, x2, x3, x4) → Cond_9177_0_createTree_LE(x1, x4)
9278_1_createTree_InvokeMethod(x1, x2, x3, x4) → 9278_1_createTree_InvokeMethod(x1, x2)
Cond_9177_0_createTree_LE1(x1, x2, x3, x4) → Cond_9177_0_createTree_LE1(x1, x4)
9284_1_createTree_InvokeMethod(x1, x2, x3, x4) → 9284_1_createTree_InvokeMethod(x1, x2)
Cond_9278_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_9278_1_createTree_InvokeMethod(x1, x2, x3)
9414_1_createTree_InvokeMethod(x1, x2, x3, x4) → 9414_1_createTree_InvokeMethod(x1, x2)
Cond_9414_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_9414_1_createTree_InvokeMethod(x1, x2, x3)
9574_1_createTree_InvokeMethod(x1, x2, x3, x4) → 9574_1_createTree_InvokeMethod(x1, x2)
9574_0_random_IntArithmetic(x1, x2) → 9574_0_random_IntArithmetic(x2)
Cond_9574_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod(x1, x2, x3)
9511_0_createTree_FieldAccess(x1, x2, x3) → 9511_0_createTree_FieldAccess(x1)
MirrorBinTreeRec.Tree(x1, x2) → MirrorBinTreeRec.Tree
Cond_9511_0_createTree_FieldAccess(x1, x2, x3, x4) → Cond_9511_0_createTree_FieldAccess(x1, x2)
10501_1_createTree_InvokeMethod(x1, x2, x3, x4) → 10501_1_createTree_InvokeMethod(x1, x2)
Cond_10501_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_10501_1_createTree_InvokeMethod(x1, x2)
Cond_10501_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_10501_1_createTree_InvokeMethod1(x1, x2)
Cond_9511_0_createTree_FieldAccess1(x1, x2, x3, x4) → Cond_9511_0_createTree_FieldAccess1(x1, x2)
10307_1_createTree_InvokeMethod(x1, x2, x3, x4) → 10307_1_createTree_InvokeMethod(x1, x2)
Cond_10307_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_10307_1_createTree_InvokeMethod(x1, x2)
Cond_10307_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_10307_1_createTree_InvokeMethod1(x1, x2)
Cond_9511_0_createTree_FieldAccess2(x1, x2, x3, x4) → Cond_9511_0_createTree_FieldAccess2(x1, x2)
10100_1_createTree_InvokeMethod(x1, x2, x3, x4) → 10100_1_createTree_InvokeMethod(x1, x2)
Cond_10100_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_10100_1_createTree_InvokeMethod(x1, x2)
Cond_10100_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_10100_1_createTree_InvokeMethod1(x1, x2)
Cond_9574_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod1(x1, x2, x3)
Cond_9574_1_createTree_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod2(x1, x2, x3)
12092_1_createTree_InvokeMethod(x1, x2, x3, x4) → 12092_1_createTree_InvokeMethod(x1, x2)
Cond_12092_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_12092_1_createTree_InvokeMethod(x1, x2)
Cond_12092_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_12092_1_createTree_InvokeMethod1(x1, x2)
Cond_9574_1_createTree_InvokeMethod4(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod4(x1, x2, x3)
Cond_9574_1_createTree_InvokeMethod5(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod5(x1, x2, x3)
11999_1_createTree_InvokeMethod(x1, x2, x3, x4) → 11999_1_createTree_InvokeMethod(x1, x2)
Cond_11999_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_11999_1_createTree_InvokeMethod(x1, x2)
Cond_11999_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_11999_1_createTree_InvokeMethod1(x1, x2)
Cond_9574_1_createTree_InvokeMethod6(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod6(x1, x2, x3)
Cond_9574_1_createTree_InvokeMethod7(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod7(x1, x2, x3)
11896_1_createTree_InvokeMethod(x1, x2, x3, x4) → 11896_1_createTree_InvokeMethod(x1, x2)
Cond_11896_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_11896_1_createTree_InvokeMethod(x1, x2)
Cond_11896_1_createTree_InvokeMethod1(x1, x2, x3, x4) → Cond_11896_1_createTree_InvokeMethod1(x1, x2)
Cond_9574_1_createTree_InvokeMethod8(x1, x2, x3, x4, x5) → Cond_9574_1_createTree_InvokeMethod8(x1, x2, x3)
Cond_9284_1_createTree_InvokeMethod(x1, x2, x3, x4, x5) → Cond_9284_1_createTree_InvokeMethod(x1, x2, x3)
9203_0_createTree_Return(x1) → 9203_0_createTree_Return
10799_0_createTree_InvokeMethod(x1, x2, x3) → 10799_0_createTree_InvokeMethod(x1)
10647_0_createTree_InvokeMethod(x1, x2, x3) → 10647_0_createTree_InvokeMethod(x1)
10396_0_createTree_InvokeMethod(x1, x2, x3) → 10396_0_createTree_InvokeMethod(x1)
12277_0_createTree_InvokeMethod(x1, x2, x3) → 12277_0_createTree_InvokeMethod(x1)
12189_0_createTree_InvokeMethod(x1, x2, x3) → 12189_0_createTree_InvokeMethod(x1)
12050_0_createTree_InvokeMethod(x1, x2, x3) → 12050_0_createTree_InvokeMethod(x1)
1678_0_random_IntArithmetic(x1, x2) → 1678_0_random_IntArithmetic(x2)

Filtered all free variables:

9278_1_createTree_InvokeMethod(x1, x2) → 9278_1_createTree_InvokeMethod(x2)
9284_1_createTree_InvokeMethod(x1, x2) → 9284_1_createTree_InvokeMethod(x2)
Cond_9278_1_createTree_InvokeMethod(x1, x2, x3) → Cond_9278_1_createTree_InvokeMethod(x1, x3)
9414_1_createTree_InvokeMethod(x1, x2) → 9414_1_createTree_InvokeMethod(x2)
Cond_9414_1_createTree_InvokeMethod(x1, x2, x3) → Cond_9414_1_createTree_InvokeMethod(x1, x3)
9574_1_createTree_InvokeMethod(x1, x2) → 9574_1_createTree_InvokeMethod(x2)
Cond_9574_1_createTree_InvokeMethod(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod(x1, x3)
Cond_9574_1_createTree_InvokeMethod1(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod1(x1, x3)
Cond_9574_1_createTree_InvokeMethod2(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod2(x1, x3)
Cond_9574_1_createTree_InvokeMethod3(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod3(x1, x3)
Cond_9574_1_createTree_InvokeMethod4(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod4(x1, x3)
Cond_9574_1_createTree_InvokeMethod5(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod5(x1, x3)
Cond_9574_1_createTree_InvokeMethod6(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod6(x1, x3)
Cond_9574_1_createTree_InvokeMethod7(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod7(x1, x3)
Cond_9574_1_createTree_InvokeMethod8(x1, x2, x3) → Cond_9574_1_createTree_InvokeMethod8(x1, x3)
Cond_9284_1_createTree_InvokeMethod(x1, x2, x3) → Cond_9284_1_createTree_InvokeMethod(x1, x3)
1502_0_random_GT(x1, x2) → 1502_0_random_GT
1587_0_random_ArrayAccess(x1, x2) → 1587_0_random_ArrayAccess(x1)
ARRAY(x1, x2) → ARRAY(x1)
1618_0_random_ArrayAccess(x1, x2) → 1618_0_random_ArrayAccess(x1)
1619_0_random_ArrayAccess(x1, x2) → 1619_0_random_ArrayAccess(x1)
1678_0_random_IntArithmetic(x1) → 1678_0_random_IntArithmetic

Filtered ground terms:

Cond_1678_1_createNode_InvokeMethod1(x1, x2) → Cond_1678_1_createNode_InvokeMethod1(x1)
1678_1_createNode_InvokeMethod(x1) → 1678_1_createNode_InvokeMethod
Cond_1678_1_createNode_InvokeMethod(x1, x2) → Cond_1678_1_createNode_InvokeMethod(x1)
Cond_1502_1_createNode_InvokeMethod3(x1, x2) → Cond_1502_1_createNode_InvokeMethod3(x1)
1502_1_createNode_InvokeMethod(x1) → 1502_1_createNode_InvokeMethod
Cond_1502_1_createNode_InvokeMethod2(x1, x2) → Cond_1502_1_createNode_InvokeMethod2(x1)
Cond_1502_1_createNode_InvokeMethod1(x1, x2) → Cond_1502_1_createNode_InvokeMethod1(x1)
Cond_1502_1_createNode_InvokeMethod(x1, x2) → Cond_1502_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:
1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 2333_0_mirror_Return
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 2821_0_mirror_Return
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 3128_0_mirror_Return
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 3416_0_mirror_Return

The integer pair graph contains the following rules and edges:
(0): 1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
(1): 1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])
(2): 2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])
(3): 2258_1_MIRROR_INVOKEMETHOD(2821_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[3], x1[3])), x1[3]) → 1935_0_MIRROR_NONNULL(x0[3])
(4): 2258_1_MIRROR_INVOKEMETHOD(3128_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[4], x1[4])), x1[4]) → 1935_0_MIRROR_NONNULL(x0[4])
(5): 2258_1_MIRROR_INVOKEMETHOD(3416_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[5], x1[5])), x1[5]) → 1935_0_MIRROR_NONNULL(x0[5])
(6): 2258_1_MIRROR_INVOKEMETHOD(2333_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[6], x1[6])), x1[6]) → 1935_0_MIRROR_NONNULL(x0[6])

(0) -> (2), if ((1935_0_mirror_NONNULL(x0[0]) →^* 1978_0_mirror_Return)∧(java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])) →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)))∧(x0[0] →^* NULL))

(0) -> (3), if ((1935_0_mirror_NONNULL(x0[0]) →^* 2821_0_mirror_Return)∧(java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])) →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[3], x1[3])))∧(x0[0] →^* x1[3]))

(0) -> (4), if ((1935_0_mirror_NONNULL(x0[0]) →^* 3128_0_mirror_Return)∧(java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])) →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[4], x1[4])))∧(x0[0] →^* x1[4]))

(0) -> (5), if ((1935_0_mirror_NONNULL(x0[0]) →^* 3416_0_mirror_Return)∧(java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])) →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[5], x1[5])))∧(x0[0] →^* x1[5]))

(0) -> (6), if ((1935_0_mirror_NONNULL(x0[0]) →^* 2333_0_mirror_Return)∧(java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])) →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[6], x1[6])))∧(x0[0] →^* x1[6]))

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

(1) -> (1), if ((x0[1] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1]', x1[1]'))))

(2) -> (0), if ((x0[2] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))))

(2) -> (1), if ((x0[2] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))))

(3) -> (0), if ((x0[3] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))))

(3) -> (1), if ((x0[3] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))))

(4) -> (0), if ((x0[4] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))))

(4) -> (1), if ((x0[4] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))))

(5) -> (0), if ((x0[5] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))))

(5) -> (1), if ((x0[5] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))))

(6) -> (0), if ((x0[6] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))))

(6) -> (1), if ((x0[6] →^* java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))))

The set Q consists of the following terms:
1935_0_mirror_NONNULL(NULL)
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)

(6) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(7) Obligation:

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

1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])
2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])
2258_1_MIRROR_INVOKEMETHOD(2821_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[3], x1[3])), x1[3]) → 1935_0_MIRROR_NONNULL(x0[3])
2258_1_MIRROR_INVOKEMETHOD(3128_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[4], x1[4])), x1[4]) → 1935_0_MIRROR_NONNULL(x0[4])
2258_1_MIRROR_INVOKEMETHOD(3416_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[5], x1[5])), x1[5]) → 1935_0_MIRROR_NONNULL(x0[5])
2258_1_MIRROR_INVOKEMETHOD(2333_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[6], x1[6])), x1[6]) → 1935_0_MIRROR_NONNULL(x0[6])

The TRS R consists of the following rules:

1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 2333_0_mirror_Return
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 2821_0_mirror_Return
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 3128_0_mirror_Return
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 3416_0_mirror_Return

The set Q consists of the following terms:

1935_0_mirror_NONNULL(NULL)
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)

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

(8) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.

(9) Obligation:

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

2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

The TRS R consists of the following rules:

1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 2333_0_mirror_Return
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 2821_0_mirror_Return
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 2821_0_mirror_Return
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL) → 3128_0_mirror_Return
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0) → 3416_0_mirror_Return
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0) → 3416_0_mirror_Return

The set Q consists of the following terms:

1935_0_mirror_NONNULL(NULL)
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)

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

(10) 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.

(11) Obligation:

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

2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

The TRS R consists of the following rules:

1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return

The set Q consists of the following terms:

1935_0_mirror_NONNULL(NULL)
2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)

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

(12) 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].

2315_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
2315_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
2315_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(1978_0_mirror_Return, NULL)
3018_1_mirror_InvokeMethod(2333_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(2821_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3128_0_mirror_Return, x0)
3018_1_mirror_InvokeMethod(3416_0_mirror_Return, x0)

(13) Obligation:

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

2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

The TRS R consists of the following rules:

1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return

The set Q consists of the following terms:

1935_0_mirror_NONNULL(NULL)

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

(14) UsableRulesReductionPairsProof (EQUIVALENT transformation)

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

The following dependency pairs can be deleted:

2258_1_MIRROR_INVOKEMETHOD(1978_0_mirror_Return, java.lang.Object(MirrorBinTreeRec.Tree(x0[2], NULL)), NULL) → 1935_0_MIRROR_NONNULL(x0[2])

The following rules are removed from R:

1935_0_mirror_NONNULL(NULL) → 1978_0_mirror_Return

Used ordering: POLO with Polynomial interpretation [POLO]:

POL(1935_0_MIRROR_NONNULL(x₁)) = 2·x₁
POL(1935_0_mirror_NONNULL(x₁)) = x₁
POL(1978_0_mirror_Return) = 0
POL(2258_1_MIRROR_INVOKEMETHOD(x₁, x₂, x₃)) = x₁ + x₂ + x₃
POL(MirrorBinTreeRec.Tree(x₁, x₂)) = 2·x₁ + 2·x₂
POL(NULL) = 0
POL(java.lang.Object(x₁)) = 2·x₁

(15) Obligation:

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

1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[0], x1[0]))) → 2258_1_MIRROR_INVOKEMETHOD(1935_0_mirror_NONNULL(x0[0]), java.lang.Object(MirrorBinTreeRec.Tree(x1[0], x0[0])), x0[0])
1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

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

1935_0_mirror_NONNULL(NULL)

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

(16) DependencyGraphProof (EQUIVALENT transformation)

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

(17) Obligation:

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

1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

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

1935_0_mirror_NONNULL(NULL)

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

(18) 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].

1935_0_mirror_NONNULL(NULL)

(19) Obligation:

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

1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])

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

(20) 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:

1935_0_MIRROR_NONNULL(java.lang.Object(MirrorBinTreeRec.Tree(x0[1], x1[1]))) → 1935_0_MIRROR_NONNULL(x0[1])
The graph contains the following edges 1 > 1

(21) YES

(22) 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:
10501_0_createNode_New → 12141_0_createNode_InvokeMethod
10501_0_createNode_New → 11882_0_createNode_InvokeMethod
10501_0_createNode_New → 12023_0_createNode_InvokeMethod
10501_0_createNode_New → 11910_0_createNode_InvokeMethod
9177_0_createTree_LE(0) → 9203_0_createTree_Return
10501_0_createNode_New → 1502_1_createNode_InvokeMethod
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10799_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10799_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10301_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10301_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10647_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10647_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10396_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10396_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12277_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 11992_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12189_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12050_0_createTree_InvokeMethod(x0)
1502_1_createNode_InvokeMethod → 1621_0_createNode_Return
1502_1_createNode_InvokeMethod → 2014_0_createNode_InvokeMethod
1502_1_createNode_InvokeMethod → 2043_0_createNode_InvokeMethod
1502_1_createNode_InvokeMethod → 1925_0_createNode_Return

The integer pair graph contains the following rules and edges:
(0): 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0]) → COND_10501_1_CREATETREE_INVOKEMETHOD(x0[0] > 0, 1621_0_createNode_Return, x0[0])
(1): COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1]) → 9177_0_CREATETREE_LE(x0[1] + -1)
(2): 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2]) → COND_10501_1_CREATETREE_INVOKEMETHOD1(x0[2] > 0, 1925_0_createNode_Return, x0[2])
(3): COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3]) → 9177_0_CREATETREE_LE(x0[3] + -1)
(4): 9177_0_CREATETREE_LE(x0[4]) → COND_9177_0_CREATETREE_LE(x0[4] > 0, x0[4])
(5): COND_9177_0_CREATETREE_LE(TRUE, x0[5]) → 9177_0_CREATETREE_LE(x0[5] + -1)
(6): 9177_0_CREATETREE_LE(x0[6]) → COND_9177_0_CREATETREE_LE1(x0[6] > 0, x0[6])
(7): COND_9177_0_CREATETREE_LE1(TRUE, x0[7]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])
(8): 9177_0_CREATETREE_LE(x0[8]) → COND_9177_0_CREATETREE_LE2(x0[8] > 0, x0[8])
(9): COND_9177_0_CREATETREE_LE2(TRUE, x0[9]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])
(10): 9177_0_CREATETREE_LE(x0[10]) → COND_9177_0_CREATETREE_LE3(x0[10] > 0, x0[10])
(11): COND_9177_0_CREATETREE_LE3(TRUE, x0[11]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])
(12): 9177_0_CREATETREE_LE(x0[12]) → COND_9177_0_CREATETREE_LE4(x0[12] > 0, x0[12])
(13): COND_9177_0_CREATETREE_LE4(TRUE, x0[13]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])
(14): 9177_0_CREATETREE_LE(x0[14]) → COND_9177_0_CREATETREE_LE5(x0[14] > 0, x0[14])
(15): COND_9177_0_CREATETREE_LE5(TRUE, x0[15]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])
(16): 9177_0_CREATETREE_LE(x0[16]) → COND_9177_0_CREATETREE_LE6(x0[16] > 0, x0[16])
(17): COND_9177_0_CREATETREE_LE6(TRUE, x0[17]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])
(18): 9177_0_CREATETREE_LE(x0[18]) → COND_9177_0_CREATETREE_LE7(x0[18] > 0, x0[18])
(19): COND_9177_0_CREATETREE_LE7(TRUE, x0[19]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])
(20): 9177_0_CREATETREE_LE(x0[20]) → COND_9177_0_CREATETREE_LE8(x0[20] > 0, x0[20])
(21): COND_9177_0_CREATETREE_LE8(TRUE, x0[21]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_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 ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[7] →^* x0[0]))

(7) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[7] →^* x0[2]))

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

(9) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[9] →^* x0[0]))

(9) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[9] →^* x0[2]))

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

(11) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[11] →^* x0[0]))

(11) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[11] →^* x0[2]))

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

(13) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[13] →^* x0[0]))

(13) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[13] →^* x0[2]))

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

(15) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[15] →^* x0[0]))

(15) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[15] →^* x0[2]))

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

(17) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[17] →^* x0[0]))

(17) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[17] →^* x0[2]))

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

(19) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[19] →^* x0[0]))

(19) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[19] →^* x0[2]))

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

(21) -> (0), if ((10501_0_createNode_New →^* 1621_0_createNode_Return)∧(x0[21] →^* x0[0]))

(21) -> (2), if ((10501_0_createNode_New →^* 1925_0_createNode_Return)∧(x0[21] →^* x0[2]))

The set Q consists of the following terms:
10501_0_createNode_New
9177_0_createTree_LE(0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0)
1502_1_createNode_InvokeMethod

(23) 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 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0) → COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0, 0), 1621_0_createNode_Return, x0) the following chains were created:

We consider the chain 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0]) → COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0]), COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1]) → 9177_0_CREATETREE_LE(+(x0[1], -1)) which results in the following constraint:
(1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0])≥NonInfC∧10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0])≥COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])∧(U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE ⇒ 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0])≥NonInfC∧10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0])≥COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])∧(U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_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_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_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_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_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_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_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_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)

For Pair COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0) → 9177_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

We consider the chain COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1]) → 9177_0_CREATETREE_LE(+(x0[1], -1)) which results in the following constraint:
(7)    (COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1])≥NonInfC∧COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1])≥9177_0_CREATETREE_LE(+(x0[1], -1))∧(U^Increasing(9177_0_CREATETREE_LE(+(x0[1], -1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(9177_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(9177_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(9177_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(9177_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_54] ≥ 0)

For Pair 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0) → COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0, 0), 1925_0_createNode_Return, x0) the following chains were created:

We consider the chain 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2]) → COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2]), COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3]) → 9177_0_CREATETREE_LE(+(x0[3], -1)) which results in the following constraint:
(12)    (>(x0[2], 0)=TRUE∧x0[2]=x0[3] ⇒ 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2])≥NonInfC∧10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2])≥COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])∧(U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])), ≥))

We simplified constraint (12) using rule (IV) which results in the following new constraint:
(13)    (>(x0[2], 0)=TRUE ⇒ 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2])≥NonInfC∧10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2])≥COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])∧(U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_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_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_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_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_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_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_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_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])), ≥)∧[bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)

For Pair COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0) → 9177_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

We consider the chain COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3]) → 9177_0_CREATETREE_LE(+(x0[3], -1)) which results in the following constraint:
(18)    (COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3])≥NonInfC∧COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3])≥9177_0_CREATETREE_LE(+(x0[3], -1))∧(U^Increasing(9177_0_CREATETREE_LE(+(x0[3], -1))), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    ((U^Increasing(9177_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(9177_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(9177_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(9177_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_58] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[4]) → COND_9177_0_CREATETREE_LE(>(x0[4], 0), x0[4]), COND_9177_0_CREATETREE_LE(TRUE, x0[5]) → 9177_0_CREATETREE_LE(+(x0[5], -1)) which results in the following constraint:
(23)    (>(x0[4], 0)=TRUE∧x0[4]=x0[5] ⇒ 9177_0_CREATETREE_LE(x0[4])≥NonInfC∧9177_0_CREATETREE_LE(x0[4])≥COND_9177_0_CREATETREE_LE(>(x0[4], 0), x0[4])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[4])≥NonInfC∧9177_0_CREATETREE_LE(x0[4])≥COND_9177_0_CREATETREE_LE(>(x0[4], 0), x0[4])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE(TRUE, x0) → 9177_0_CREATETREE_LE(+(x0, -1)) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE(TRUE, x0[5]) → 9177_0_CREATETREE_LE(+(x0[5], -1)) which results in the following constraint:
(29)    (COND_9177_0_CREATETREE_LE(TRUE, x0[5])≥NonInfC∧COND_9177_0_CREATETREE_LE(TRUE, x0[5])≥9177_0_CREATETREE_LE(+(x0[5], -1))∧(U^Increasing(9177_0_CREATETREE_LE(+(x0[5], -1))), ≥))

We simplified constraint (29) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(30)    ((U^Increasing(9177_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(9177_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(9177_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(9177_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧0 = 0∧[1 + (-1)bso_62] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE1(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[6]) → COND_9177_0_CREATETREE_LE1(>(x0[6], 0), x0[6]), COND_9177_0_CREATETREE_LE1(TRUE, x0[7]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7]) which results in the following constraint:
(34)    (>(x0[6], 0)=TRUE∧x0[6]=x0[7] ⇒ 9177_0_CREATETREE_LE(x0[6])≥NonInfC∧9177_0_CREATETREE_LE(x0[6])≥COND_9177_0_CREATETREE_LE1(>(x0[6], 0), x0[6])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[6])≥NonInfC∧9177_0_CREATETREE_LE(x0[6])≥COND_9177_0_CREATETREE_LE1(>(x0[6], 0), x0[6])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE1(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE1(TRUE, x0[7]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7]) which results in the following constraint:
(40)    (COND_9177_0_CREATETREE_LE1(TRUE, x0[7])≥NonInfC∧COND_9177_0_CREATETREE_LE1(TRUE, x0[7])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])), ≥))

We simplified constraint (40) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(41)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])), ≥)∧0 = 0∧[(-1)bso_66] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE2(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[8]) → COND_9177_0_CREATETREE_LE2(>(x0[8], 0), x0[8]), COND_9177_0_CREATETREE_LE2(TRUE, x0[9]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9]) which results in the following constraint:
(45)    (>(x0[8], 0)=TRUE∧x0[8]=x0[9] ⇒ 9177_0_CREATETREE_LE(x0[8])≥NonInfC∧9177_0_CREATETREE_LE(x0[8])≥COND_9177_0_CREATETREE_LE2(>(x0[8], 0), x0[8])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[8])≥NonInfC∧9177_0_CREATETREE_LE(x0[8])≥COND_9177_0_CREATETREE_LE2(>(x0[8], 0), x0[8])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE2(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE2(TRUE, x0[9]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9]) which results in the following constraint:
(51)    (COND_9177_0_CREATETREE_LE2(TRUE, x0[9])≥NonInfC∧COND_9177_0_CREATETREE_LE2(TRUE, x0[9])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])), ≥)∧0 = 0∧[1 + (-1)bso_70] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE3(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[10]) → COND_9177_0_CREATETREE_LE3(>(x0[10], 0), x0[10]), COND_9177_0_CREATETREE_LE3(TRUE, x0[11]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11]) which results in the following constraint:
(56)    (>(x0[10], 0)=TRUE∧x0[10]=x0[11] ⇒ 9177_0_CREATETREE_LE(x0[10])≥NonInfC∧9177_0_CREATETREE_LE(x0[10])≥COND_9177_0_CREATETREE_LE3(>(x0[10], 0), x0[10])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[10])≥NonInfC∧9177_0_CREATETREE_LE(x0[10])≥COND_9177_0_CREATETREE_LE3(>(x0[10], 0), x0[10])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE3(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE3(TRUE, x0[11]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11]) which results in the following constraint:
(62)    (COND_9177_0_CREATETREE_LE3(TRUE, x0[11])≥NonInfC∧COND_9177_0_CREATETREE_LE3(TRUE, x0[11])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])), ≥)∧0 = 0∧[(-1)bso_74] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE4(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[12]) → COND_9177_0_CREATETREE_LE4(>(x0[12], 0), x0[12]), COND_9177_0_CREATETREE_LE4(TRUE, x0[13]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13]) which results in the following constraint:
(67)    (>(x0[12], 0)=TRUE∧x0[12]=x0[13] ⇒ 9177_0_CREATETREE_LE(x0[12])≥NonInfC∧9177_0_CREATETREE_LE(x0[12])≥COND_9177_0_CREATETREE_LE4(>(x0[12], 0), x0[12])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[12])≥NonInfC∧9177_0_CREATETREE_LE(x0[12])≥COND_9177_0_CREATETREE_LE4(>(x0[12], 0), x0[12])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE4(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE4(TRUE, x0[13]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13]) which results in the following constraint:
(73)    (COND_9177_0_CREATETREE_LE4(TRUE, x0[13])≥NonInfC∧COND_9177_0_CREATETREE_LE4(TRUE, x0[13])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])), ≥))

We simplified constraint (73) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(74)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])), ≥)∧0 = 0∧[(-1)bso_78] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE5(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[14]) → COND_9177_0_CREATETREE_LE5(>(x0[14], 0), x0[14]), COND_9177_0_CREATETREE_LE5(TRUE, x0[15]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15]) which results in the following constraint:
(78)    (>(x0[14], 0)=TRUE∧x0[14]=x0[15] ⇒ 9177_0_CREATETREE_LE(x0[14])≥NonInfC∧9177_0_CREATETREE_LE(x0[14])≥COND_9177_0_CREATETREE_LE5(>(x0[14], 0), x0[14])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[14])≥NonInfC∧9177_0_CREATETREE_LE(x0[14])≥COND_9177_0_CREATETREE_LE5(>(x0[14], 0), x0[14])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE5(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE5(TRUE, x0[15]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15]) which results in the following constraint:
(84)    (COND_9177_0_CREATETREE_LE5(TRUE, x0[15])≥NonInfC∧COND_9177_0_CREATETREE_LE5(TRUE, x0[15])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])), ≥))

We simplified constraint (84) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(85)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])), ≥)∧0 = 0∧[(-1)bso_82] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE6(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[16]) → COND_9177_0_CREATETREE_LE6(>(x0[16], 0), x0[16]), COND_9177_0_CREATETREE_LE6(TRUE, x0[17]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17]) which results in the following constraint:
(89)    (>(x0[16], 0)=TRUE∧x0[16]=x0[17] ⇒ 9177_0_CREATETREE_LE(x0[16])≥NonInfC∧9177_0_CREATETREE_LE(x0[16])≥COND_9177_0_CREATETREE_LE6(>(x0[16], 0), x0[16])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[16])≥NonInfC∧9177_0_CREATETREE_LE(x0[16])≥COND_9177_0_CREATETREE_LE6(>(x0[16], 0), x0[16])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE6(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE6(TRUE, x0[17]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17]) which results in the following constraint:
(95)    (COND_9177_0_CREATETREE_LE6(TRUE, x0[17])≥NonInfC∧COND_9177_0_CREATETREE_LE6(TRUE, x0[17])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])), ≥))

We simplified constraint (95) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(96)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])), ≥)∧0 = 0∧[(-1)bso_86] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE7(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[18]) → COND_9177_0_CREATETREE_LE7(>(x0[18], 0), x0[18]), COND_9177_0_CREATETREE_LE7(TRUE, x0[19]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19]) which results in the following constraint:
(100)    (>(x0[18], 0)=TRUE∧x0[18]=x0[19] ⇒ 9177_0_CREATETREE_LE(x0[18])≥NonInfC∧9177_0_CREATETREE_LE(x0[18])≥COND_9177_0_CREATETREE_LE7(>(x0[18], 0), x0[18])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[18])≥NonInfC∧9177_0_CREATETREE_LE(x0[18])≥COND_9177_0_CREATETREE_LE7(>(x0[18], 0), x0[18])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE7(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE7(TRUE, x0[19]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19]) which results in the following constraint:
(106)    (COND_9177_0_CREATETREE_LE7(TRUE, x0[19])≥NonInfC∧COND_9177_0_CREATETREE_LE7(TRUE, x0[19])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])), ≥))

We simplified constraint (106) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(107)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])), ≥)∧0 = 0∧[1 + (-1)bso_90] ≥ 0)

For Pair 9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE8(>(x0, 0), x0) the following chains were created:

We consider the chain 9177_0_CREATETREE_LE(x0[20]) → COND_9177_0_CREATETREE_LE8(>(x0[20], 0), x0[20]), COND_9177_0_CREATETREE_LE8(TRUE, x0[21]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21]) which results in the following constraint:
(111)    (>(x0[20], 0)=TRUE∧x0[20]=x0[21] ⇒ 9177_0_CREATETREE_LE(x0[20])≥NonInfC∧9177_0_CREATETREE_LE(x0[20])≥COND_9177_0_CREATETREE_LE8(>(x0[20], 0), x0[20])∧(U^Increasing(COND_9177_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 ⇒ 9177_0_CREATETREE_LE(x0[20])≥NonInfC∧9177_0_CREATETREE_LE(x0[20])≥COND_9177_0_CREATETREE_LE8(>(x0[20], 0), x0[20])∧(U^Increasing(COND_9177_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_9177_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_9177_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_9177_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_9177_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_9177_0_CREATETREE_LE8(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0) the following chains were created:

We consider the chain COND_9177_0_CREATETREE_LE8(TRUE, x0[21]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21]) which results in the following constraint:
(117)    (COND_9177_0_CREATETREE_LE8(TRUE, x0[21])≥NonInfC∧COND_9177_0_CREATETREE_LE8(TRUE, x0[21])≥10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21])∧(U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21])), ≥))

We simplified constraint (117) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(118)    ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21])), ≥)∧0 = 0∧[(-1)bso_94] ≥ 0)

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

10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0) → COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0, 0), 1621_0_createNode_Return, x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[0] ≥ 0∧[(-1)bso_52] ≥ 0)
COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0) → 9177_0_CREATETREE_LE(+(x0, -1))
- ((U^Increasing(9177_0_CREATETREE_LE(+(x0[1], -1))), ≥)∧0 = 0∧[1 + (-1)bso_54] ≥ 0)
10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0) → COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0, 0), 1925_0_createNode_Return, x0)
- (x0[2] ≥ 0 ⇒ (U^Increasing(COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])), ≥)∧[bni_55 + (-1)Bound*bni_55] + [(2)bni_55]x0[2] ≥ 0∧[(-1)bso_56] ≥ 0)
COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0) → 9177_0_CREATETREE_LE(+(x0, -1))
- ((U^Increasing(9177_0_CREATETREE_LE(+(x0[3], -1))), ≥)∧0 = 0∧[1 + (-1)bso_58] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE(>(x0, 0), x0)
- (x0[4] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE(TRUE, x0) → 9177_0_CREATETREE_LE(+(x0, -1))
- ((U^Increasing(9177_0_CREATETREE_LE(+(x0[5], -1))), ≥)∧0 = 0∧[1 + (-1)bso_62] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE1(>(x0, 0), x0)
- (x0[6] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE1(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])), ≥)∧0 = 0∧[(-1)bso_66] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE2(>(x0, 0), x0)
- (x0[8] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE2(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])), ≥)∧0 = 0∧[1 + (-1)bso_70] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE3(>(x0, 0), x0)
- (x0[10] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE3(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])), ≥)∧0 = 0∧[(-1)bso_74] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE4(>(x0, 0), x0)
- (x0[12] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE4(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])), ≥)∧0 = 0∧[(-1)bso_78] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE5(>(x0, 0), x0)
- (x0[14] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE5(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])), ≥)∧0 = 0∧[(-1)bso_82] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE6(>(x0, 0), x0)
- (x0[16] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE6(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])), ≥)∧0 = 0∧[(-1)bso_86] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE7(>(x0, 0), x0)
- (x0[18] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE7(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])), ≥)∧0 = 0∧[1 + (-1)bso_90] ≥ 0)
9177_0_CREATETREE_LE(x0) → COND_9177_0_CREATETREE_LE8(>(x0, 0), x0)
- (x0[20] ≥ 0 ⇒ (U^Increasing(COND_9177_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_9177_0_CREATETREE_LE8(TRUE, x0) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0)
- ((U^Increasing(10501_1_CREATETREE_INVOKEMETHOD(10501_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(10501_0_createNode_New) = [-1]
POL(12141_0_createNode_InvokeMethod) = [-1]
POL(11882_0_createNode_InvokeMethod) = [-1]
POL(12023_0_createNode_InvokeMethod) = [-1]
POL(11910_0_createNode_InvokeMethod) = [-1]
POL(9177_0_createTree_LE(x₁)) = [-1]
POL(0) = 0
POL(9203_0_createTree_Return) = [-1]
POL(1502_1_createNode_InvokeMethod) = [-1]
POL(10501_1_createTree_InvokeMethod(x₁, x₂)) = [-1]
POL(2014_0_createNode_InvokeMethod) = [-1]
POL(10799_0_createTree_InvokeMethod(x₁)) = [-1]
POL(2043_0_createNode_InvokeMethod) = [-1]
POL(10301_0_createTree_InvokeMethod(x₁)) = [-1]
POL(10647_0_createTree_InvokeMethod(x₁)) = [-1]
POL(10396_0_createTree_InvokeMethod(x₁)) = [-1]
POL(12277_0_createTree_InvokeMethod(x₁)) = [-1]
POL(11992_0_createTree_InvokeMethod(x₁)) = [-1]
POL(12189_0_createTree_InvokeMethod(x₁)) = [-1]
POL(12050_0_createTree_InvokeMethod(x₁)) = [-1]
POL(1621_0_createNode_Return) = [-1]
POL(1925_0_createNode_Return) = [-1]
POL(10501_1_CREATETREE_INVOKEMETHOD(x₁, x₂)) = [-1] + [2]x₂
POL(COND_10501_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [2]x₃
POL(>(x₁, x₂)) = [-1]
POL(9177_0_CREATETREE_LE(x₁)) = [2]x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(COND_10501_1_CREATETREE_INVOKEMETHOD1(x₁, x₂, x₃)) = [-1] + [2]x₃
POL(COND_9177_0_CREATETREE_LE(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE1(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE2(x₁, x₂)) = [2]x₂
POL(COND_9177_0_CREATETREE_LE3(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE4(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE5(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE6(x₁, x₂)) = [-1] + [2]x₂
POL(COND_9177_0_CREATETREE_LE7(x₁, x₂)) = [2]x₂
POL(COND_9177_0_CREATETREE_LE8(x₁, x₂)) = [-1] + [2]x₂

The following pairs are in P_>:

COND_10501_1_CREATETREE_INVOKEMETHOD(TRUE, 1621_0_createNode_Return, x0[1]) → 9177_0_CREATETREE_LE(+(x0[1], -1))
COND_10501_1_CREATETREE_INVOKEMETHOD1(TRUE, 1925_0_createNode_Return, x0[3]) → 9177_0_CREATETREE_LE(+(x0[3], -1))
9177_0_CREATETREE_LE(x0[4]) → COND_9177_0_CREATETREE_LE(>(x0[4], 0), x0[4])
COND_9177_0_CREATETREE_LE(TRUE, x0[5]) → 9177_0_CREATETREE_LE(+(x0[5], -1))
9177_0_CREATETREE_LE(x0[6]) → COND_9177_0_CREATETREE_LE1(>(x0[6], 0), x0[6])
COND_9177_0_CREATETREE_LE2(TRUE, x0[9]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[9])
9177_0_CREATETREE_LE(x0[10]) → COND_9177_0_CREATETREE_LE3(>(x0[10], 0), x0[10])
9177_0_CREATETREE_LE(x0[12]) → COND_9177_0_CREATETREE_LE4(>(x0[12], 0), x0[12])
9177_0_CREATETREE_LE(x0[14]) → COND_9177_0_CREATETREE_LE5(>(x0[14], 0), x0[14])
9177_0_CREATETREE_LE(x0[16]) → COND_9177_0_CREATETREE_LE6(>(x0[16], 0), x0[16])
COND_9177_0_CREATETREE_LE7(TRUE, x0[19]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[19])
9177_0_CREATETREE_LE(x0[20]) → COND_9177_0_CREATETREE_LE8(>(x0[20], 0), x0[20])

The following pairs are in P_bound:

10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0]) → COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])
10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2]) → COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])
9177_0_CREATETREE_LE(x0[4]) → COND_9177_0_CREATETREE_LE(>(x0[4], 0), x0[4])
9177_0_CREATETREE_LE(x0[6]) → COND_9177_0_CREATETREE_LE1(>(x0[6], 0), x0[6])
9177_0_CREATETREE_LE(x0[8]) → COND_9177_0_CREATETREE_LE2(>(x0[8], 0), x0[8])
9177_0_CREATETREE_LE(x0[10]) → COND_9177_0_CREATETREE_LE3(>(x0[10], 0), x0[10])
9177_0_CREATETREE_LE(x0[12]) → COND_9177_0_CREATETREE_LE4(>(x0[12], 0), x0[12])
9177_0_CREATETREE_LE(x0[14]) → COND_9177_0_CREATETREE_LE5(>(x0[14], 0), x0[14])
9177_0_CREATETREE_LE(x0[16]) → COND_9177_0_CREATETREE_LE6(>(x0[16], 0), x0[16])
9177_0_CREATETREE_LE(x0[18]) → COND_9177_0_CREATETREE_LE7(>(x0[18], 0), x0[18])
9177_0_CREATETREE_LE(x0[20]) → COND_9177_0_CREATETREE_LE8(>(x0[20], 0), x0[20])

The following pairs are in P_≥:

10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0]) → COND_10501_1_CREATETREE_INVOKEMETHOD(>(x0[0], 0), 1621_0_createNode_Return, x0[0])
10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2]) → COND_10501_1_CREATETREE_INVOKEMETHOD1(>(x0[2], 0), 1925_0_createNode_Return, x0[2])
COND_9177_0_CREATETREE_LE1(TRUE, x0[7]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])
9177_0_CREATETREE_LE(x0[8]) → COND_9177_0_CREATETREE_LE2(>(x0[8], 0), x0[8])
COND_9177_0_CREATETREE_LE3(TRUE, x0[11]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])
COND_9177_0_CREATETREE_LE4(TRUE, x0[13]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])
COND_9177_0_CREATETREE_LE5(TRUE, x0[15]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])
COND_9177_0_CREATETREE_LE6(TRUE, x0[17]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])
9177_0_CREATETREE_LE(x0[18]) → COND_9177_0_CREATETREE_LE7(>(x0[18], 0), x0[18])
COND_9177_0_CREATETREE_LE8(TRUE, x0[21]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21])

There are no usable rules.

(24) Complex Obligation (AND)

(25) 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:
10501_0_createNode_New → 12141_0_createNode_InvokeMethod
10501_0_createNode_New → 11882_0_createNode_InvokeMethod
10501_0_createNode_New → 12023_0_createNode_InvokeMethod
10501_0_createNode_New → 11910_0_createNode_InvokeMethod
9177_0_createTree_LE(0) → 9203_0_createTree_Return
10501_0_createNode_New → 1502_1_createNode_InvokeMethod
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10799_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10799_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10301_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10301_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10647_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10647_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2014_0_createNode_InvokeMethod, x0) → 10396_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 10396_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12277_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 11992_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12189_0_createTree_InvokeMethod(x0)
10501_1_createTree_InvokeMethod(2043_0_createNode_InvokeMethod, x0) → 12050_0_createTree_InvokeMethod(x0)
1502_1_createNode_InvokeMethod → 1621_0_createNode_Return
1502_1_createNode_InvokeMethod → 2014_0_createNode_InvokeMethod
1502_1_createNode_InvokeMethod → 2043_0_createNode_InvokeMethod
1502_1_createNode_InvokeMethod → 1925_0_createNode_Return

The integer pair graph contains the following rules and edges:
(0): 10501_1_CREATETREE_INVOKEMETHOD(1621_0_createNode_Return, x0[0]) → COND_10501_1_CREATETREE_INVOKEMETHOD(x0[0] > 0, 1621_0_createNode_Return, x0[0])
(2): 10501_1_CREATETREE_INVOKEMETHOD(1925_0_createNode_Return, x0[2]) → COND_10501_1_CREATETREE_INVOKEMETHOD1(x0[2] > 0, 1925_0_createNode_Return, x0[2])
(7): COND_9177_0_CREATETREE_LE1(TRUE, x0[7]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[7])
(8): 9177_0_CREATETREE_LE(x0[8]) → COND_9177_0_CREATETREE_LE2(x0[8] > 0, x0[8])
(11): COND_9177_0_CREATETREE_LE3(TRUE, x0[11]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[11])
(13): COND_9177_0_CREATETREE_LE4(TRUE, x0[13]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[13])
(15): COND_9177_0_CREATETREE_LE5(TRUE, x0[15]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[15])
(17): COND_9177_0_CREATETREE_LE6(TRUE, x0[17]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[17])
(18): 9177_0_CREATETREE_LE(x0[18]) → COND_9177_0_CREATETREE_LE7(x0[18] > 0, x0[18])
(21): COND_9177_0_CREATETREE_LE8(TRUE, x0[21]) → 10501_1_CREATETREE_INVOKEMETHOD(10501_0_createNode_New, x0[21])