Termination proof of /tmp/tmp6Jn3mt/DupTreeRec.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 QDPSizeChangeProof (⇔)

        ↳15 YES

    ↳16 IDP

        ↳17 IDPNonInfProof (⇒)

        ↳18 AND

            ↳19 IDP

                ↳20 IDependencyGraphProof (⇔)

                ↳21 IDP

                ↳22 UsableRulesProof (⇔)

                ↳23 IDP

                ↳24 IDPNonInfProof (⇒)

                ↳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: DupTreeRec/DupTreeRec

package DupTreeRec;

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

    final Tree t = Tree.createTree(Random.random());
    dupTree(t);
  }

  public static void dupTree(final Tree t) {
      dupList(t.children);
  }

  public static void dupList(final TreeList l) {
      if (l == null) return;
      dupTree(l.value);
      l.next = new TreeList(l.value, l.next);
      dupList(l.next.next);
  }
}


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

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


package DupTreeRec;
public class Tree {
    TreeList children;

    public Tree() {
        this.children = null;
    }

    public void addChild(final Tree t) {
        this.children = new TreeList(t, this.children);
    }

    public static Tree createNode() {
        final Tree result = new Tree();
        return result;
    }

    public static Tree createTree(int depth) {
        if (depth <= 0) {
            return null;
        }
        depth = depth - 1;

        final Tree result = new Tree();
        final int numberOfChildren = Random.random();

        for (int i = 0; i < numberOfChildren; i++) {
            result.addChild(createTree(depth - 1));
        }

        return result;
    }
}


package DupTreeRec;
public class TreeList {
  Tree value;
  TreeList next;

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
DupTreeRec.DupTreeRec.main([Ljava/lang/String;)V: Graph of 138 nodes with 0 SCCs.

DupTreeRec.Tree.createTree(I)LDupTreeRec/Tree;: Graph of 161 nodes with 1 SCC.

DupTreeRec.DupTreeRec.dupTree(LDupTreeRec/Tree;)V: Graph of 50 nodes with 0 SCCs.

DupTreeRec.DupTreeRec.dupList(LDupTreeRec/TreeList;)V: Graph of 69 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 49 rules for P and 68 rules for R.

Combined rules. Obtained 3 rules for P and 18 rules for R.

Filtered ground terms:

DupTreeRec.TreeList(x1, x2, x3) → DupTreeRec.TreeList(x2, x3)
2002_0_dupTree_FieldAccess(x1, x2) → 2002_0_dupTree_FieldAccess(x2)
2925_0_dupTree_Return(x1) → 2925_0_dupTree_Return
DupTreeRec.Tree(x1, x2) → DupTreeRec.Tree(x2)
2025_0_dupTree_Return(x1) → 2025_0_dupTree_Return
2952_0_dupList_InvokeMethod(x1, x2, x3) → 2952_0_dupList_InvokeMethod(x3)
java.lang.NullPointerException(x1) → java.lang.NullPointerException
java.lang.RuntimeException(x1) → java.lang.RuntimeException
java.lang.Exception(x1) → java.lang.Exception
java.lang.Throwable(x1) → java.lang.Throwable
2737_0_dupList_InvokeMethod(x1, x2, x3) → 2737_0_dupList_InvokeMethod(x3)
2934_0_dupList_InvokeMethod(x1, x2, x3, x4) → 2934_0_dupList_InvokeMethod(x3, x4)
2930_0_dupList_Return(x1) → 2930_0_dupList_Return
2731_0_dupList_Return(x1) → 2731_0_dupList_Return
2161_0_dupList_InvokeMethod(x1, x2, x3, x4) → 2161_0_dupList_InvokeMethod(x3)
1941_0_dupList_Return(x1, x2) → 1941_0_dupList_Return
2941_0_dupTree_InvokeMethod(x1, x2, x3) → 2941_0_dupTree_InvokeMethod(x3)
2553_0_dupTree_InvokeMethod(x1, x2, x3) → 2553_0_dupTree_InvokeMethod(x3)
2138_0_dupTree_FieldAccess(x1, x2, x3) → 2138_0_dupTree_FieldAccess

Filtered all free variables:

2941_0_dupTree_InvokeMethod(x1) → 2941_0_dupTree_InvokeMethod
2934_0_dupList_InvokeMethod(x1, x2) → 2934_0_dupList_InvokeMethod
2952_0_dupList_InvokeMethod(x1) → 2952_0_dupList_InvokeMethod
2737_0_dupList_InvokeMethod(x1) → 2737_0_dupList_InvokeMethod
2553_0_dupTree_InvokeMethod(x1) → 2553_0_dupTree_InvokeMethod

Finished conversion. Obtained 3 rules for P and 18 rules for R. System has no predefined symbols.

Log for SCC 1:

Generated 100 rules for P and 60 rules for R.

Combined rules. Obtained 4 rules for P and 3 rules for R.

Filtered ground terms:

DupTreeRec.TreeList(x1) → DupTreeRec.TreeList
DupTreeRec.Tree(x1, x2) → DupTreeRec.Tree(x2)
2696_0_random_ArrayAccess(x1, x2, x3) → 2696_0_random_ArrayAccess(x2, x3)
2696_1_createTree_InvokeMethod(x1, x2, x3) → 2696_1_createTree_InvokeMethod(x1, x2)
4367_0_createTree_Return(x1, x2) → 4367_0_createTree_Return(x2)
2555_0_createTree_Return(x1, x2, x3) → 2555_0_createTree_Return(x2)
Cond_2738_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_2738_1_createTree_InvokeMethod(x1, x2, x3)
2738_0_random_IntArithmetic(x1, x2, x3, x4) → 2738_0_random_IntArithmetic(x2, x3)
2738_1_createTree_InvokeMethod(x1, x2, x3) → 2738_1_createTree_InvokeMethod(x1, x2)
Cond_2696_1_createTree_InvokeMethod(x1, x2, x3, x4) → Cond_2696_1_createTree_InvokeMethod(x1, x2, x3)
4425_0_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 4425_0_createTree_InvokeMethod(x2, x3, x4, x5, x6, x7)
java.lang.NullPointerException(x1) → java.lang.NullPointerException
3344_0_createTree_InvokeMethod(x1, x2, x3, x4) → 3344_0_createTree_InvokeMethod(x3)
java.lang.ArrayIndexOutOfBoundsException(x1) → java.lang.ArrayIndexOutOfBoundsException
java.lang.IndexOutOfBoundsException(x1) → java.lang.IndexOutOfBoundsException
3215_0_createTree_InvokeMethod(x1, x2, x3, x4) → 3215_0_createTree_InvokeMethod(x3)

Filtered duplicate args:

4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 4386_1_createTree_InvokeMethod(x1, x2, x4, x5, x6, x7)
Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x5, x6, x7, x8)
Cond_4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4386_1_createTree_InvokeMethod(x1, x2, x3, x5, x6, x7, x8)
4425_0_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6) → 4425_0_createTree_InvokeMethod(x1, x2, x4, x5, x6)

Filtered unneeded arguments:

Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5, x6)

Filtered all non-integer terms:

2738_0_random_IntArithmetic(x1, x2) → 2738_0_random_IntArithmetic(x2)
4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6) → 4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x6)
Cond_4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_4386_1_createTree_InvokeMethod(x1, x2, x3, x4, x5, x7)
DupTreeRec.Tree(x1) → DupTreeRec.Tree
4367_0_createTree_Return(x1) → 4367_0_createTree_Return
Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_4386_1_createTree_InvokeMethod1(x1, x2, x3, x4, x5)
4425_0_createTree_InvokeMethod(x1, x2, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x2, x3, x4)

Combined rules. Obtained 4 rules for P and 3 rules for R.

Finished conversion. Obtained 4 rules for P and 3 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:
2002_0_dupTree_FieldAccess(NULL) → 2138_0_dupTree_FieldAccess
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL) → 2025_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2941_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2941_0_dupTree_InvokeMethod
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL) → 2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x2, x3)), x2) → 2934_0_dupList_InvokeMethod
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x3, x4)), x3) → 2934_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL) → 2731_0_dupList_Return
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2952_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2952_0_dupList_InvokeMethod

The integer pair graph contains the following rules and edges:
(0): 2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0]))))) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x0[0]), java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])), x0[0])
(1): 2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])
(2): 1988_1_DUPLIST_INVOKEMETHOD(2025_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])))), java.lang.Object(DupTreeRec.Tree(NULL))) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x0[2]), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])), x0[2])
(3): 1988_1_DUPLIST_INVOKEMETHOD(2025_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[3], x1[3])))), java.lang.Object(DupTreeRec.Tree(NULL))) → 2002_0_DUPTREE_FIELDACCESS(x0[3])
(4): 1988_1_DUPLIST_INVOKEMETHOD(2925_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(x0[4], java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])))), x0[4]) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x1[4]), java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])), x1[4])
(5): 1988_1_DUPLIST_INVOKEMETHOD(2925_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(x0[5], java.lang.Object(DupTreeRec.TreeList(x1[5], x2[5])))), x0[5]) → 2002_0_DUPTREE_FIELDACCESS(x1[5])

(0) -> (2), if ((2002_0_dupTree_FieldAccess(x0[0]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])))))∧(x0[0] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(0) -> (3), if ((2002_0_dupTree_FieldAccess(x0[0]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[3], x1[3])))))∧(x0[0] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(0) -> (4), if ((2002_0_dupTree_FieldAccess(x0[0]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])) →^* java.lang.Object(DupTreeRec.TreeList(x0[4], java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])))))∧(x0[0] →^* x0[4]))

(0) -> (5), if ((2002_0_dupTree_FieldAccess(x0[0]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])) →^* java.lang.Object(DupTreeRec.TreeList(x0[5], java.lang.Object(DupTreeRec.TreeList(x1[5], x2[5])))))∧(x0[0] →^* x0[5]))

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

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

(2) -> (2), if ((2002_0_dupTree_FieldAccess(x0[2]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[2]', x1[2]')))))∧(x0[2] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(2) -> (3), if ((2002_0_dupTree_FieldAccess(x0[2]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[3], x1[3])))))∧(x0[2] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(2) -> (4), if ((2002_0_dupTree_FieldAccess(x0[2]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])) →^* java.lang.Object(DupTreeRec.TreeList(x0[4], java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])))))∧(x0[2] →^* x0[4]))

(2) -> (5), if ((2002_0_dupTree_FieldAccess(x0[2]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])) →^* java.lang.Object(DupTreeRec.TreeList(x0[5], java.lang.Object(DupTreeRec.TreeList(x1[5], x2[5])))))∧(x0[2] →^* x0[5]))

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

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

(4) -> (2), if ((2002_0_dupTree_FieldAccess(x1[4]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])))))∧(x1[4] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(4) -> (3), if ((2002_0_dupTree_FieldAccess(x1[4]) →^* 2025_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])) →^* java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[3], x1[3])))))∧(x1[4] →^* java.lang.Object(DupTreeRec.Tree(NULL))))

(4) -> (4), if ((2002_0_dupTree_FieldAccess(x1[4]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])) →^* java.lang.Object(DupTreeRec.TreeList(x0[4]', java.lang.Object(DupTreeRec.TreeList(x1[4]', x2[4]')))))∧(x1[4] →^* x0[4]'))

(4) -> (5), if ((2002_0_dupTree_FieldAccess(x1[4]) →^* 2925_0_dupTree_Return)∧(java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])) →^* java.lang.Object(DupTreeRec.TreeList(x0[5], java.lang.Object(DupTreeRec.TreeList(x1[5], x2[5])))))∧(x1[4] →^* x0[5]))

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

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

The set Q consists of the following terms:
2002_0_dupTree_FieldAccess(NULL)
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL)
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x0)
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL)
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL)
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, 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:

2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0]))))) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x0[0]), java.lang.Object(DupTreeRec.TreeList(x0[0], x1[0])), x0[0])
2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])
1988_1_DUPLIST_INVOKEMETHOD(2025_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])))), java.lang.Object(DupTreeRec.Tree(NULL))) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x0[2]), java.lang.Object(DupTreeRec.TreeList(x0[2], x1[2])), x0[2])
1988_1_DUPLIST_INVOKEMETHOD(2025_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(java.lang.Object(DupTreeRec.Tree(NULL)), java.lang.Object(DupTreeRec.TreeList(x0[3], x1[3])))), java.lang.Object(DupTreeRec.Tree(NULL))) → 2002_0_DUPTREE_FIELDACCESS(x0[3])
1988_1_DUPLIST_INVOKEMETHOD(2925_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(x0[4], java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])))), x0[4]) → 1988_1_DUPLIST_INVOKEMETHOD(2002_0_dupTree_FieldAccess(x1[4]), java.lang.Object(DupTreeRec.TreeList(x1[4], x2[4])), x1[4])
1988_1_DUPLIST_INVOKEMETHOD(2925_0_dupTree_Return, java.lang.Object(DupTreeRec.TreeList(x0[5], java.lang.Object(DupTreeRec.TreeList(x1[5], x2[5])))), x0[5]) → 2002_0_DUPTREE_FIELDACCESS(x1[5])

The TRS R consists of the following rules:

2002_0_dupTree_FieldAccess(NULL) → 2138_0_dupTree_FieldAccess
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL) → 2025_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2941_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2941_0_dupTree_InvokeMethod
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL) → 2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x2, x3)), x2) → 2934_0_dupList_InvokeMethod
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x3, x4)), x3) → 2934_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL) → 2731_0_dupList_Return
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2952_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2952_0_dupList_InvokeMethod

The set Q consists of the following terms:

2002_0_dupTree_FieldAccess(NULL)
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL)
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x0)
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL)
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL)
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, 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 5 less nodes.

(9) Obligation:

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

2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])

The TRS R consists of the following rules:

2002_0_dupTree_FieldAccess(NULL) → 2138_0_dupTree_FieldAccess
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL) → 2025_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2941_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0) → 2925_0_dupTree_Return
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2553_0_dupTree_InvokeMethod
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2941_0_dupTree_InvokeMethod
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL) → 2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x2, x3)), x2) → 2934_0_dupList_InvokeMethod
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x3, x4)), x3) → 2934_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL) → 2731_0_dupList_Return
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0))) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x2) → 2952_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0) → 2930_0_dupList_Return
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x3) → 2737_0_dupList_InvokeMethod
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, x3) → 2952_0_dupList_InvokeMethod

The set Q consists of the following terms:

2002_0_dupTree_FieldAccess(NULL)
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL)
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x0)
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL)
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL)
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, 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:

2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])

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

2002_0_dupTree_FieldAccess(NULL)
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL)
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x0)
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL)
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL)
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, 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].

2002_0_dupTree_FieldAccess(NULL)
2017_1_dupTree_InvokeMethod(1941_0_dupList_Return, NULL)
2017_1_dupTree_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2017_1_dupTree_InvokeMethod(2731_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2930_0_dupList_Return, x0)
2017_1_dupTree_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2017_1_dupTree_InvokeMethod(2952_0_dupList_InvokeMethod, x0)
1988_1_dupList_InvokeMethod(2138_0_dupTree_FieldAccess, java.lang.Object(DupTreeRec.TreeList(NULL, x0)), NULL)
1988_1_dupList_InvokeMethod(2553_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
1988_1_dupList_InvokeMethod(2941_0_dupTree_InvokeMethod, java.lang.Object(DupTreeRec.TreeList(x0, x1)), x0)
2706_1_dupList_InvokeMethod(1941_0_dupList_Return, NULL)
2706_1_dupList_InvokeMethod(2161_0_dupList_InvokeMethod(java.lang.Object(DupTreeRec.TreeList(NULL, x0))), java.lang.Object(DupTreeRec.TreeList(NULL, x0)))
2706_1_dupList_InvokeMethod(2731_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2737_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2930_0_dupList_Return, x0)
2706_1_dupList_InvokeMethod(2934_0_dupList_InvokeMethod, x0)
2706_1_dupList_InvokeMethod(2952_0_dupList_InvokeMethod, x0)

(13) Obligation:

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

2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])

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

(14) 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:

2002_0_DUPTREE_FIELDACCESS(java.lang.Object(DupTreeRec.Tree(java.lang.Object(DupTreeRec.TreeList(x0[1], x1[1]))))) → 2002_0_DUPTREE_FIELDACCESS(x0[1])
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
4386_1_createTree_InvokeMethod(3215_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(3344_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(4425_0_createTree_InvokeMethod(x1, x3, x4), x5, x7, x8, x9) → 4425_0_createTree_InvokeMethod(x5, x7, x8)

The integer pair graph contains the following rules and edges:
(0): 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]) → COND_2696_1_CREATETREE_INVOKEMETHOD(x2[0] >= 1 && x2[0] < x0[0], 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])
(1): COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1]) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])
(2): 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(x4[2] >= 0 && x2[2] > 0 && x1[2] > 0 && 0 < x4[2] - 1, 2738_0_random_IntArithmetic(x2[2]), x4[2])
(3): COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), x4[3] - 1 - 1), x4[3], x1[3], 0, x4[3] - 1)
(4): COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), x4[4] - 1 - 1)
(5): 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(x4[5] >= 0 && x3[5] > x4[5] + 1 && x1[5] >= 0 && 0 < x1[5] - 1, 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])
(6): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1), x1[6], x3[6], x4[6] + 1, x1[6] - 1)
(7): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x1[7] - 1 - 1)
(8): 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1, 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
(9): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1), x1[9], x3[9], x4[9] + 1, x1[9] - 1)
(10): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), x1[10] - 1 - 1)

(0) -> (1), if ((x2[0] >= 1 && x2[0] < x0[0] →^* TRUE)∧(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]))∧(x3[0] →^* x3[1]))

(1) -> (2), if ((2738_0_random_IntArithmetic(x5[1]) →^* 2738_0_random_IntArithmetic(x2[2]))∧(x3[1] →^* x4[2]))

(2) -> (3), if ((x4[2] >= 0 && x2[2] > 0 && x1[2] > 0 && 0 < x4[2] - 1 →^* TRUE)∧(2738_0_random_IntArithmetic(x2[2]) →^* 2738_0_random_IntArithmetic(x2[3]))∧(x4[2] →^* x4[3]))

(2) -> (4), if ((x4[2] >= 0 && x2[2] > 0 && x1[2] > 0 && 0 < x4[2] - 1 →^* TRUE)∧(2738_0_random_IntArithmetic(x2[2]) →^* 2738_0_random_IntArithmetic(x2[4]))∧(x4[2] →^* x4[4]))

(3) -> (5), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), x4[3] - 1 - 1) →^* 2555_0_createTree_Return(x0[5]))∧(x4[3] →^* x1[5])∧(x1[3] →^* x3[5])∧(0 →^* x4[5])∧(x4[3] - 1 →^* x0[5]))

(3) -> (8), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), x4[3] - 1 - 1) →^* 4367_0_createTree_Return)∧(x4[3] →^* x1[8])∧(x1[3] →^* x3[8])∧(0 →^* x4[8])∧(x4[3] - 1 →^* x5[8]))

(4) -> (0), if ((2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x4[4] - 1 - 1 →^* x3[0]))

(5) -> (6), if ((x4[5] >= 0 && x3[5] > x4[5] + 1 && x1[5] >= 0 && 0 < x1[5] - 1 →^* TRUE)∧(2555_0_createTree_Return(x0[5]) →^* 2555_0_createTree_Return(x0[6]))∧(x1[5] →^* x1[6])∧(x3[5] →^* x3[6])∧(x4[5] →^* x4[6])∧(x0[5] →^* x0[6]))

(5) -> (7), if ((x4[5] >= 0 && x3[5] > x4[5] + 1 && x1[5] >= 0 && 0 < x1[5] - 1 →^* TRUE)∧(2555_0_createTree_Return(x0[5]) →^* 2555_0_createTree_Return(x0[7]))∧(x1[5] →^* x1[7])∧(x3[5] →^* x3[7])∧(x4[5] →^* x4[7])∧(x0[5] →^* x0[7]))

(6) -> (5), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1) →^* 2555_0_createTree_Return(x0[5]))∧(x1[6] →^* x1[5])∧(x3[6] →^* x3[5])∧(x4[6] + 1 →^* x4[5])∧(x1[6] - 1 →^* x0[5]))

(6) -> (8), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1) →^* 4367_0_createTree_Return)∧(x1[6] →^* x1[8])∧(x3[6] →^* x3[8])∧(x4[6] + 1 →^* x4[8])∧(x1[6] - 1 →^* x5[8]))

(7) -> (0), if ((2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x1[7] - 1 - 1 →^* x3[0]))

(8) -> (9), if ((x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1 →^* TRUE)∧(x1[8] →^* x1[9])∧(x3[8] →^* x3[9])∧(x4[8] →^* x4[9])∧(x5[8] →^* x5[9]))

(8) -> (10), if ((x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1 →^* TRUE)∧(x1[8] →^* x1[10])∧(x3[8] →^* x3[10])∧(x4[8] →^* x4[10])∧(x5[8] →^* x5[10]))

(9) -> (5), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1) →^* 2555_0_createTree_Return(x0[5]))∧(x1[9] →^* x1[5])∧(x3[9] →^* x3[5])∧(x4[9] + 1 →^* x4[5])∧(x1[9] - 1 →^* x0[5]))

(9) -> (8), if ((2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1) →^* 4367_0_createTree_Return)∧(x1[9] →^* x1[8])∧(x3[9] →^* x3[8])∧(x4[9] + 1 →^* x4[8])∧(x1[9] - 1 →^* x5[8]))

(10) -> (0), if ((2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x1[10] - 1 - 1 →^* x3[0]))

The set Q consists of the following terms:
4386_1_createTree_InvokeMethod(3215_0_createTree_InvokeMethod(x0), x1, x2, x3, x4)
4386_1_createTree_InvokeMethod(3344_0_createTree_InvokeMethod(x0), x1, x2, x3, x4)
4386_1_createTree_InvokeMethod(4425_0_createTree_InvokeMethod(x0, x1, x2), x3, x4, x5, x6)

(17) 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 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2, 1), <(x2, x0)), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) the following chains were created:

We consider the chain 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]) → COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]), COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1]) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1]) which results in the following constraint:
(1)    (&&(>=(x2[0], 1), <(x2[0], x0[0]))=TRUE∧2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1] ⇒ 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])≥NonInfC∧2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])≥COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])∧(U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x2[0], 1)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])≥NonInfC∧2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])≥COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])∧(U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] + [-1] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x3[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] + [-1] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x3[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] + [-1] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x3[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x2[0] + [-1] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[bni_32] = 0∧0 = 0∧[(-1)Bound*bni_32] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x2[0] ≥ 0∧x0[0] + [-2] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[bni_32] = 0∧0 = 0∧[(-1)Bound*bni_32] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(8)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[bni_32] = 0∧0 = 0∧[(-1)Bound*bni_32] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)

For Pair COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5), x3) the following chains were created:

We consider the chain COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1]) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1]) which results in the following constraint:
(9)    (COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1])≥NonInfC∧COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1])≥2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])∧(U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    ((U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥)∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    ((U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥)∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    ((U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥)∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (12) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(13)    ((U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_35] ≥ 0)

For Pair 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2), x4) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4, 0), >(x2, 0)), >(x1, 0)), <(0, -(x4, 1))), 2738_0_random_IntArithmetic(x2), x4) the following chains were created:

We consider the chain 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2]), COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1)) which results in the following constraint:
(14)    (&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1)))=TRUE∧2738_0_random_IntArithmetic(x2[2])=2738_0_random_IntArithmetic(x2[3])∧x4[2]=x4[3] ⇒ 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥NonInfC∧2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])∧(U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥))

We simplified constraint (14) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(15)    (<(0, -(x4[2], 1))=TRUE∧>(x1[2], 0)=TRUE∧>=(x4[2], 0)=TRUE∧>(x2[2], 0)=TRUE ⇒ 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥NonInfC∧2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])∧(U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥))

We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(16)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(17)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (17) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(18)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(19)    (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(20)    (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)
We consider the chain 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2]), COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1)) which results in the following constraint:
(21)    (&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1)))=TRUE∧2738_0_random_IntArithmetic(x2[2])=2738_0_random_IntArithmetic(x2[4])∧x4[2]=x4[4] ⇒ 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥NonInfC∧2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])∧(U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥))

We simplified constraint (21) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(22)    (<(0, -(x4[2], 1))=TRUE∧>(x1[2], 0)=TRUE∧>=(x4[2], 0)=TRUE∧>(x2[2], 0)=TRUE ⇒ 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥NonInfC∧2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2])≥COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])∧(U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥))

We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(23)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(24)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(25)    (x4[2] + [-2] ≥ 0∧x1[2] + [-1] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(26)    (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)

For Pair COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2), x4) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x4, 1), 1)), x4, x1, 0, -(x4, 1)) the following chains were created:

We consider the chain COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1)) which results in the following constraint:
(28)    (COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3])≥NonInfC∧COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3])≥4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))∧(U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥))

We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(29)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(30)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(31)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(32)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)

For Pair COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2), x4) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x4, 1), 1)) the following chains were created:

We consider the chain COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1)) which results in the following constraint:
(33)    (COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4])≥NonInfC∧COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4])≥2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))∧(U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥))

We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(34)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (34) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(35)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (35) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(36)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (36) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(37)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)

For Pair 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0), x1, x3, x4, x0) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4, 0), >(x3, +(x4, 1))), >=(x1, 0)), <(0, -(x1, 1))), 2555_0_createTree_Return(x0), x1, x3, x4, x0) the following chains were created:

We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]), COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1)) which results in the following constraint:
(38)    (&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1)))=TRUE∧2555_0_createTree_Return(x0[5])=2555_0_createTree_Return(x0[6])∧x1[5]=x1[6]∧x3[5]=x3[6]∧x4[5]=x4[6]∧x0[5]=x0[6] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (38) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(39)    (<(0, -(x1[5], 1))=TRUE∧>=(x1[5], 0)=TRUE∧>=(x4[5], 0)=TRUE∧>(x3[5], +(x4[5], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (39) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(40)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (40) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(41)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (41) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(42)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (42) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(43)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (43) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(44)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(45)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)
We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]), COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1)) which results in the following constraint:
(46)    (&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1)))=TRUE∧2555_0_createTree_Return(x0[5])=2555_0_createTree_Return(x0[7])∧x1[5]=x1[7]∧x3[5]=x3[7]∧x4[5]=x4[7]∧x0[5]=x0[7] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (46) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(47)    (<(0, -(x1[5], 1))=TRUE∧>=(x1[5], 0)=TRUE∧>=(x4[5], 0)=TRUE∧>(x3[5], +(x4[5], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(48)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(49)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(50)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(51)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(52)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(53)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

For Pair COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0), x1, x3, x4, x0) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x1, 1), 1)), x1, x3, +(x4, 1), -(x1, 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1)) which results in the following constraint:
(54)    (COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6])≥4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))∧(U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥))

We simplified constraint (54) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(55)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_45] ≥ 0)

We simplified constraint (55) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(56)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_45] ≥ 0)

We simplified constraint (56) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(57)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_45] ≥ 0)

We simplified constraint (57) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(58)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

For Pair COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0), x1, x3, x4, x0) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x1, 1), 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1)) which results in the following constraint:
(59)    (COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7])≥2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))∧(U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥))

We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(60)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥)∧[1 + (-1)bso_47] ≥ 0)

We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(61)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥)∧[1 + (-1)bso_47] ≥ 0)

We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(62)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥)∧[1 + (-1)bso_47] ≥ 0)

We simplified constraint (62) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(63)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_47] ≥ 0)

For Pair 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1, x3, x4, x5) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4, 0), >(x3, +(x4, 1))), >=(x1, 0)), <(0, -(x1, 1))), 4367_0_createTree_Return, x1, x3, x4, x5) the following chains were created:

We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]), COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1)) which results in the following constraint:
(64)    (&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1)))=TRUE∧x1[8]=x1[9]∧x3[8]=x3[9]∧x4[8]=x4[9]∧x5[8]=x5[9] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (64) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(65)    (<(0, -(x1[8], 1))=TRUE∧>=(x1[8], 0)=TRUE∧>=(x4[8], 0)=TRUE∧>(x3[8], +(x4[8], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(66)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (66) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(67)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (67) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(68)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (68) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(69)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(70)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (70) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(71)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]), COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1)) which results in the following constraint:
(72)    (&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1)))=TRUE∧x1[8]=x1[10]∧x3[8]=x3[10]∧x4[8]=x4[10]∧x5[8]=x5[10] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (72) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(73)    (<(0, -(x1[8], 1))=TRUE∧>=(x1[8], 0)=TRUE∧>=(x4[8], 0)=TRUE∧>(x3[8], +(x4[8], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (73) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(74)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (74) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(75)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (75) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(76)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (76) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(77)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (77) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(78)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (78) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(79)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

For Pair COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1, x3, x4, x5) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(-(x1, 1), 1)), x1, x3, +(x4, 1), -(x1, 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1)) which results in the following constraint:
(80)    (COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9])≥4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))∧(U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥))

We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(81)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(84)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)

For Pair COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1, x3, x4, x5) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(-(x1, 1), 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1)) which results in the following constraint:
(85)    (COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10])≥2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))∧(U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥))

We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(86)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

We simplified constraint (86) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(87)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

We simplified constraint (87) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(88)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥)∧[1 + (-1)bso_53] ≥ 0)

We simplified constraint (88) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(89)    ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 0)

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

2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2, 1), <(x2, x0)), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])), ≥)∧[bni_32] = 0∧0 = 0∧[(-1)Bound*bni_32] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)
COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5), x3)
- ((U^Increasing(2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_35] ≥ 0)
2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2), x4) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4, 0), >(x2, 0)), >(x1, 0)), <(0, -(x4, 1))), 2738_0_random_IntArithmetic(x2), x4)
- (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)
- (x4[2] ≥ 0∧x1[2] + [-1] ≥ 0∧[2] + x4[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x4[2] ≥ 0∧[(-1)bso_37] ≥ 0)
COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2), x4) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x4, 1), 1)), x4, x1, 0, -(x4, 1))
- ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)
COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2), x4) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x4, 1), 1))
- ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0), x1, x3, x4, x0) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4, 0), >(x3, +(x4, 1))), >=(x1, 0)), <(0, -(x1, 1))), 2555_0_createTree_Return(x0), x1, x3, x4, x0)
- (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)
- (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[bni_42 + (-1)Bound*bni_42] + [bni_42]x1[5] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0), x1, x3, x4, x0) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x1, 1), 1)), x1, x3, +(x4, 1), -(x1, 1))
- ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0), x1, x3, x4, x0) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), -(-(x1, 1), 1))
- ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_47] ≥ 0)
4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1, x3, x4, x5) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4, 0), >(x3, +(x4, 1))), >=(x1, 0)), <(0, -(x1, 1))), 4367_0_createTree_Return, x1, x3, x4, x5)
- (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
- (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[bni_48 + (-1)Bound*bni_48] + [bni_48]x1[8] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1, x3, x4, x5) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(-(x1, 1), 1)), x1, x3, +(x4, 1), -(x1, 1))
- ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)
COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1, x3, x4, x5) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(-(x1, 1), 1))
- ((U^Increasing(2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_53] ≥ 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(4386_1_createTree_InvokeMethod(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(3215_0_createTree_InvokeMethod(x₁)) = [-1]
POL(4425_0_createTree_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(3344_0_createTree_InvokeMethod(x₁)) = [-1]
POL(2696_1_CREATETREE_INVOKEMETHOD(x₁, x₂)) = [-1] + x₂ + [-1]x₁
POL(2696_0_random_ArrayAccess(x₁, x₂)) = [-1]
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_2696_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(1) = [1]
POL(<(x₁, x₂)) = [-1]
POL(2738_1_CREATETREE_INVOKEMETHOD(x₁, x₂)) = [-1] + x₂
POL(2738_0_random_IntArithmetic(x₁)) = x₁
POL(COND_2738_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃
POL(0) = 0
POL(>(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(4386_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₂
POL(2696_1_createTree_InvokeMethod(x₁, x₂)) = x₂
POL(2555_0_createTree_Return(x₁)) = x₁
POL(COND_4386_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + x₃
POL(+(x₁, x₂)) = x₁ + x₂
POL(4367_0_createTree_Return) = [-1]
POL(COND_4386_1_CREATETREE_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + x₃

The following pairs are in P_>:

COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1]) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])
COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), -(-(x4[4], 1), 1))
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), -(-(x1[7], 1), 1))
COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), -(-(x1[10], 1), 1))

The following pairs are in P_bound:

2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])
4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])

The following pairs are in P_≥:

2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]) → COND_2696_1_CREATETREE_INVOKEMETHOD(&&(>=(x2[0], 1), <(x2[0], x0[0])), 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])
2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[2], 0), >(x2[2], 0)), >(x1[2], 0)), <(0, -(x4[2], 1))), 2738_0_random_IntArithmetic(x2[2]), x4[2])
COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), -(-(x4[3], 1), 1)), x4[3], x1[3], 0, -(x4[3], 1))
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))
4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))

There are no usable rules.

(18) Complex Obligation (AND)

(19) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
4386_1_createTree_InvokeMethod(3215_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(3344_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(4425_0_createTree_InvokeMethod(x1, x3, x4), x5, x7, x8, x9) → 4425_0_createTree_InvokeMethod(x5, x7, x8)

The integer pair graph contains the following rules and edges:
(0): 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]) → COND_2696_1_CREATETREE_INVOKEMETHOD(x2[0] >= 1 && x2[0] < x0[0], 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])
(2): 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x2[2]), x4[2]) → COND_2738_1_CREATETREE_INVOKEMETHOD(x4[2] >= 0 && x2[2] > 0 && x1[2] > 0 && 0 < x4[2] - 1, 2738_0_random_IntArithmetic(x2[2]), x4[2])
(3): COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), x4[3] - 1 - 1), x4[3], x1[3], 0, x4[3] - 1)
(5): 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(x4[5] >= 0 && x3[5] > x4[5] + 1 && x1[5] >= 0 && 0 < x1[5] - 1, 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])
(6): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1), x1[6], x3[6], x4[6] + 1, x1[6] - 1)
(8): 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1, 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
(9): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1), x1[9], x3[9], x4[9] + 1, x1[9] - 1)

(2) -> (3), if ((x4[2] >= 0 && x2[2] > 0 && x1[2] > 0 && 0 < x4[2] - 1 →^* TRUE)∧(2738_0_random_IntArithmetic(x2[2]) →^* 2738_0_random_IntArithmetic(x2[3]))∧(x4[2] →^* x4[3]))

(8) -> (9), if ((x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1 →^* TRUE)∧(x1[8] →^* x1[9])∧(x3[8] →^* x3[9])∧(x4[8] →^* x4[9])∧(x5[8] →^* x5[9]))

(20) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(21) Obligation:

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

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

The following domains are used:

Integer, Boolean

(8) -> (9), if ((x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1 →^* TRUE)∧(x1[8] →^* x1[9])∧(x3[8] →^* x3[9])∧(x4[8] →^* x4[9])∧(x5[8] →^* x5[9]))

(22) 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.

(23) Obligation:

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

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(9): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1), x1[9], x3[9], x4[9] + 1, x1[9] - 1)
(8): 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1, 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
(6): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1), x1[6], x3[6], x4[6] + 1, x1[6] - 1)
(5): 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(x4[5] >= 0 && x3[5] > x4[5] + 1 && x1[5] >= 0 && 0 < x1[5] - 1, 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])

(8) -> (9), if ((x4[8] >= 0 && x3[8] > x4[8] + 1 && x1[8] >= 0 && 0 < x1[8] - 1 →^* TRUE)∧(x1[8] →^* x1[9])∧(x3[8] →^* x3[9])∧(x4[8] →^* x4[9])∧(x5[8] →^* x5[9]))

(24) 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 COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1)) which results in the following constraint:
(1)    (COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9])≥4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))∧(U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥))

We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(2)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_17] ≥ 0)

We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(3)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_17] ≥ 0)

We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(4)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧[(-1)bso_17] ≥ 0)

We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(5)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_17] ≥ 0)

For Pair 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) the following chains were created:

We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]), COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1)) which results in the following constraint:
(6)    (&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1)))=TRUE∧x1[8]=x1[9]∧x3[8]=x3[9]∧x4[8]=x4[9]∧x5[8]=x5[9] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (6) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(7)    (<(0, -(x1[8], 1))=TRUE∧>=(x1[8], 0)=TRUE∧>=(x4[8], 0)=TRUE∧>(x3[8], +(x4[8], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])≥COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [(-1)bni_18]x4[8] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [(-1)bni_18]x4[8] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧[(2)bni_18 + (-1)Bound*bni_18] + [(-1)bni_18]x4[8] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    (x1[8] + [-2] ≥ 0∧x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(2)bni_18 + (-1)Bound*bni_18] + [(-1)bni_18]x4[8] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(12)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] + [-2] + [-1]x4[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(6)bni_18 + (-1)Bound*bni_18] + [(-1)bni_18]x4[8] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(8)bni_18 + (-1)Bound*bni_18] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

For Pair COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1)) the following chains were created:

We consider the chain COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1)) which results in the following constraint:
(14)    (COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6])≥NonInfC∧COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6])≥4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))∧(U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

For Pair 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) the following chains were created:

We consider the chain 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]), COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1)) which results in the following constraint:
(19)    (&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1)))=TRUE∧2555_0_createTree_Return(x0[5])=2555_0_createTree_Return(x0[6])∧x1[5]=x1[6]∧x3[5]=x3[6]∧x4[5]=x4[6]∧x0[5]=x0[6] ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (19) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(20)    (<(0, -(x1[5], 1))=TRUE∧>=(x1[5], 0)=TRUE∧>=(x4[5], 0)=TRUE∧>(x3[5], +(x4[5], 1))=TRUE ⇒ 4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥NonInfC∧4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])≥COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])∧(U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(2)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x4[5] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(2)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x4[5] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧[(2)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x4[5] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    (x1[5] + [-2] ≥ 0∧x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(2)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x4[5] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(25)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] + [-2] + [-1]x4[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(6)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x4[5] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(26)    (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(8)bni_22 + (-1)Bound*bni_22] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

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

COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))
- ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_17] ≥ 0)
4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
- (x1[8] ≥ 0∧[2] + x1[8] ≥ 0∧x4[8] ≥ 0∧x3[8] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])), ≥)∧0 = 0∧[(8)bni_18 + (-1)Bound*bni_18] + [bni_18]x3[8] + [(2)bni_18]x1[8] ≥ 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))
- ((U^Increasing(4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])
- (x1[5] ≥ 0∧[2] + x1[5] ≥ 0∧x4[5] ≥ 0∧x3[5] ≥ 0 ⇒ (U^Increasing(COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])), ≥)∧0 = 0∧[(8)bni_22 + (-1)Bound*bni_22] + [bni_22]x3[5] + [(2)bni_22]x1[5] ≥ 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(COND_4386_1_CREATETREE_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅, x₆)) = [1] + [-1]x₅ + x₄ + [2]x₃
POL(4367_0_createTree_Return) = [-1]
POL(4386_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [2] + [-1]x₄ + x₃ + [2]x₂
POL(2696_1_createTree_InvokeMethod(x₁, x₂)) = x₂
POL(2696_0_random_ArrayAccess(x₁, x₂)) = [-1]
POL(java.lang.Object(x₁)) = [-1]
POL(ARRAY(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(>(x₁, x₂)) = [-1]
POL(<(x₁, x₂)) = [-1]
POL(COND_4386_1_CREATETREE_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅, x₆)) = [1] + x₄ + [2]x₃ + [-1]x₅
POL(2555_0_createTree_Return(x₁)) = x₁

The following pairs are in P_>:

4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])

The following pairs are in P_bound:

4386_1_CREATETREE_INVOKEMETHOD(4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8]) → COND_4386_1_CREATETREE_INVOKEMETHOD1(&&(&&(&&(>=(x4[8], 0), >(x3[8], +(x4[8], 1))), >=(x1[8], 0)), <(0, -(x1[8], 1))), 4367_0_createTree_Return, x1[8], x3[8], x4[8], x5[8])
4386_1_CREATETREE_INVOKEMETHOD(2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5]) → COND_4386_1_CREATETREE_INVOKEMETHOD(&&(&&(&&(>=(x4[5], 0), >(x3[5], +(x4[5], 1))), >=(x1[5], 0)), <(0, -(x1[5], 1))), 2555_0_createTree_Return(x0[5]), x1[5], x3[5], x4[5], x0[5])

The following pairs are in P_≥:

COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), -(-(x1[9], 1), 1)), x1[9], x3[9], +(x4[9], 1), -(x1[9], 1))
COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), -(-(x1[6], 1), 1)), x1[6], x3[6], +(x4[6], 1), -(x1[6], 1))

There are no usable rules.

(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

R is empty.

The integer pair graph contains the following rules and edges:
(9): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1), x1[9], x3[9], x4[9] + 1, x1[9] - 1)
(6): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1), x1[6], x3[6], x4[6] + 1, x1[6] - 1)

The set Q consists of the following terms:
4386_1_createTree_InvokeMethod(3215_0_createTree_InvokeMethod(x0), x1, x2, x3, x4)
4386_1_createTree_InvokeMethod(3344_0_createTree_InvokeMethod(x0), x1, x2, x3, x4)
4386_1_createTree_InvokeMethod(4425_0_createTree_InvokeMethod(x0, x1, x2), x3, x4, x5, x6)

(26) IDependencyGraphProof (EQUIVALENT transformation)

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

(27) TRUE

(28) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
4386_1_createTree_InvokeMethod(3215_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(3344_0_createTree_InvokeMethod(x0), x1, x3, x4, x5) → 4425_0_createTree_InvokeMethod(x1, x3, x4)
4386_1_createTree_InvokeMethod(4425_0_createTree_InvokeMethod(x1, x3, x4), x5, x7, x8, x9) → 4425_0_createTree_InvokeMethod(x5, x7, x8)

The integer pair graph contains the following rules and edges:
(0): 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0]) → COND_2696_1_CREATETREE_INVOKEMETHOD(x2[0] >= 1 && x2[0] < x0[0], 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0])
(1): COND_2696_1_CREATETREE_INVOKEMETHOD(TRUE, 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1]) → 2738_1_CREATETREE_INVOKEMETHOD(2738_0_random_IntArithmetic(x5[1]), x3[1])
(3): COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[3]), x4[3]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[3], x6[3])), x7[3]), x4[3] - 1 - 1), x4[3], x1[3], 0, x4[3] - 1)
(4): COND_2738_1_CREATETREE_INVOKEMETHOD(TRUE, 2738_0_random_IntArithmetic(x2[4]), x4[4]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]), x4[4] - 1 - 1)
(6): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[6]), x1[6], x3[6], x4[6], x0[6]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[6], x6[6])), x7[6]), x1[6] - 1 - 1), x1[6], x3[6], x4[6] + 1, x1[6] - 1)
(7): COND_4386_1_CREATETREE_INVOKEMETHOD(TRUE, 2555_0_createTree_Return(x0[7]), x1[7], x3[7], x4[7], x0[7]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x1[7] - 1 - 1)
(9): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[9], x3[9], x4[9], x5[9]) → 4386_1_CREATETREE_INVOKEMETHOD(2696_1_createTree_InvokeMethod(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x1[9] - 1 - 1), x1[9], x3[9], x4[9] + 1, x1[9] - 1)
(10): COND_4386_1_CREATETREE_INVOKEMETHOD1(TRUE, 4367_0_createTree_Return, x1[10], x3[10], x4[10], x5[10]) → 2696_1_CREATETREE_INVOKEMETHOD(2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[10], x7[10])), x8[10]), x1[10] - 1 - 1)

(4) -> (0), if ((2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[4], x6[4])), x7[4]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x4[4] - 1 - 1 →^* x3[0]))

(7) -> (0), if ((2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]) →^* 2696_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x1[7] - 1 - 1 →^* x3[0]))

(29) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) IDPtoQDPProof (SOUND transformation)

(7) Obligation:

(8) DependencyGraphProof (EQUIVALENT transformation)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) QReductionProof (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) IDPNonInfProof (SOUND transformation)

(18) Complex Obligation (AND)

(19) Obligation:

(20) IDependencyGraphProof (EQUIVALENT transformation)

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) IDPNonInfProof (SOUND transformation)

(25) Obligation:

(26) IDependencyGraphProof (EQUIVALENT transformation)

(27) TRUE

(28) Obligation:

(29) IDependencyGraphProof (EQUIVALENT transformation)

(30) TRUE