Termination proof of /tmp/tmpm1v8K5/IntListDupRec.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 AND

    ↳5 IDP

        ↳6 IDPNonInfProof (⇒)

        ↳7 IDP

        ↳8 IDependencyGraphProof (⇔)

        ↳9 IDP

        ↳10 UsableRulesProof (⇔)

        ↳11 IDP

        ↳12 IDPtoQDPProof (⇒)

        ↳13 QDP

        ↳14 DependencyGraphProof (⇔)

        ↳15 TRUE

    ↳16 IDP

        ↳17 IDPNonInfProof (⇒)

        ↳18 AND

            ↳19 IDP

                ↳20 IDependencyGraphProof (⇔)

                ↳21 TRUE

            ↳22 IDP

                ↳23 IDependencyGraphProof (⇔)

                ↳24 TRUE

(0) Obligation:

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

package IntListDupRec;

public class IntListDupRec {
	public static void main(String[] args) {
		Random.args = args;
		List l = List.createList(Random.random());

		l.dupList();
	}
}

class List {
	boolean dupped;
	List next;

	public List(boolean d, List n) {
		this.dupped = d;
		this.next = n;
	}

	public void dupList() {
		if (this.next == null) {
			new List(false, this);
		} else if (this.dupped == false) {
			List next = this.next;
			this.next = new List(true, next);
		}
		this.next.dupList();
		this.dupped = false;
	}

	public static List createList(int l) {
		if (l < 0) {
			return null;
		} else {
			return new List(false, createList(l - 1));
		}
	}
}

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

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
IntListDupRec.IntListDupRec.main([Ljava/lang/String;)V: Graph of 97 nodes with 0 SCCs.

IntListDupRec.List.createList(I)LIntListDupRec/List;: Graph of 44 nodes with 0 SCCs.

IntListDupRec.List.dupList()V: Graph of 95 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 42 rules for P and 54 rules for R.

Combined rules. Obtained 2 rules for P and 5 rules for R.

Filtered ground terms:

IntListDupRec.List(x1, x2, x3) → IntListDupRec.List(x2, x3)
765_0_dupList_FieldAccess(x1, x2, x3) → 765_0_dupList_FieldAccess(x2, x3)
Cond_765_0_dupList_FieldAccess(x1, x2, x3, x4) → Cond_765_0_dupList_FieldAccess(x1, x3, x4)
1169_0_dupList_InvokeMethod(x1, x2, x3, x4) → 1169_0_dupList_InvokeMethod(x3, x4)
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
1107_0_dupList_InvokeMethod(x1, x2, x3, x4) → 1107_0_dupList_InvokeMethod(x3, x4)
950_0_dupList_InvokeMethod(x1, x2, x3, x4) → 950_0_dupList_InvokeMethod(x3)

Filtered duplicate args:

765_0_dupList_FieldAccess(x1, x2) → 765_0_dupList_FieldAccess(x2)
Cond_765_0_dupList_FieldAccess(x1, x2, x3) → Cond_765_0_dupList_FieldAccess(x1, x3)

Combined rules. Obtained 2 rules for P and 5 rules for R.

Finished conversion. Obtained 2 rules for P and 5 rules for R. System has predefined symbols.

Log for SCC 1:

Generated 12 rules for P and 30 rules for R.

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

Filtered ground terms:

243_0_createList_GE(x1, x2, x3) → 243_0_createList_GE(x2, x3)
Cond_243_0_createList_GE(x1, x2, x3, x4) → Cond_243_0_createList_GE(x1, x3, x4)
562_0_createList_Return(x1) → 562_0_createList_Return
316_0_createList_Return(x1) → 316_0_createList_Return
262_0_createList_Return(x1, x2) → 262_0_createList_Return

Filtered duplicate args:

243_0_createList_GE(x1, x2) → 243_0_createList_GE(x2)
Cond_243_0_createList_GE(x1, x2, x3) → Cond_243_0_createList_GE(x1, x3)

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

Finished conversion. Obtained 1 rules for P and 4 rules for R. System has predefined symbols.

(4) Complex Obligation (AND)

(5) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
807_1_dupList_InvokeMethod(950_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(NULL, x0))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0))) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0)))
807_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), x4)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
807_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), x5)), java.lang.Object(x4)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), x5)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))
916_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
916_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))

The integer pair graph contains the following rules and edges:
(0): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(x1[0] = 0), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))
(1): COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))
(2): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))

(0) -> (1), if ((!(x1[0] = 0) →^* TRUE)∧(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))))

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

(1) -> (2), if ((java.lang.Object(x0[1]) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))))

(2) -> (0), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))))

(2) -> (2), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]'), 0))))

The set Q consists of the following terms:
807_1_dupList_InvokeMethod(950_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(NULL, x0))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0)))
807_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3))
807_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3))
916_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)))
916_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)))

(6) IDPNonInfProof (SOUND transformation)

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

For Pair 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1, 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1))) the following chains were created:

We consider the chain 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))), COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1])) which results in the following constraint:
(1)    (!(=(x1[0], 0))=TRUE∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1])) ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))≥COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))∧(U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥))

We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
(2)    (!(=(x1[0], 0))=TRUE ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))≥COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))∧(U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (0 ≥ 0 ⇒ (U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥)∧[(5)bni_28 + (-1)Bound*bni_28] + [(4)bni_28]x0[0] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (0 ≥ 0 ⇒ (U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥)∧[(5)bni_28 + (-1)Bound*bni_28] + [(4)bni_28]x0[0] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (0 ≥ 0 ⇒ (U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥)∧[(5)bni_28 + (-1)Bound*bni_28] + [(4)bni_28]x0[0] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (0 ≥ 0 ⇒ (U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥)∧0 ≥ 0∧[(4)bni_28] ≥ 0∧[(5)bni_28 + (-1)Bound*bni_28] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_29] ≥ 0)

For Pair COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0)) the following chains were created:

We consider the chain 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))), COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1])), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) which results in the following constraint:
(7)    (!(=(x1[0], 0))=TRUE∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))∧java.lang.Object(x0[1])=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]1), x1[0]1)) ⇒ COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1])))≥NonInfC∧COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1])))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥))

We simplified constraint (7) using rules (I), (II), (III) which results in the following new constraint:
(8)    (!(=(x1[0], 0))=TRUE ⇒ COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]1), x1[0]1)), x1[0])))≥NonInfC∧COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]1), x1[0]1)), x1[0])))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]1), x1[0]1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[0]1 ≥ 0∧[8 + (-1)bso_31] + [4]x0[0]1 ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[0]1 ≥ 0∧[8 + (-1)bso_31] + [4]x0[0]1 ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[0]1 ≥ 0∧[8 + (-1)bso_31] + [4]x0[0]1 ≥ 0)

We simplified constraint (11) using rules (IDP_UNRESTRICTED_VARS), (IDP_POLY_GCD) which results in the following new constraint:
(12)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(8)bni_30] ≥ 0∧[(13)bni_30 + (-1)Bound*bni_30] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[8 + (-1)bso_31] ≥ 0∧[1] ≥ 0)
We consider the chain 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))), COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1])), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))) which results in the following constraint:
(13)    (!(=(x1[0], 0))=TRUE∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))∧java.lang.Object(x0[1])=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)) ⇒ COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1])))≥NonInfC∧COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1])))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥))

We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
(14)    (!(=(x1[0], 0))=TRUE ⇒ COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)), x1[0])))≥NonInfC∧COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)), x1[0])))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[2] ≥ 0∧[8 + (-1)bso_31] + [4]x0[2] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[2] ≥ 0∧[8 + (-1)bso_31] + [4]x0[2] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧[(13)bni_30 + (-1)Bound*bni_30] + [(8)bni_30]x0[2] ≥ 0∧[8 + (-1)bso_31] + [4]x0[2] ≥ 0)

We simplified constraint (17) using rules (IDP_UNRESTRICTED_VARS), (IDP_POLY_GCD) which results in the following new constraint:
(18)    (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧0 ≥ 0∧[(8)bni_30] ≥ 0∧[(13)bni_30 + (-1)Bound*bni_30] ≥ 0∧0 ≥ 0∧[8 + (-1)bso_31] ≥ 0∧[1] ≥ 0)

For Pair 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), 1))) the following chains were created:

We consider the chain COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1])), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) which results in the following constraint:
(19)    (java.lang.Object(x0[1])=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])) ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥))

We simplified constraint (19) using rules (I), (II), (III), (IV) which results in the following new constraint:
(20)    (765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    ((U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    ((U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    ((U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    ((U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥)∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
We consider the chain 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) which results in the following constraint:
(25) (java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0))∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])) ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0)))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0)))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1)))), ≥))

We solved constraint (25) using rules (I), (II).
We consider the chain COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1])), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))) which results in the following constraint:
(26) (java.lang.Object(x0[1])=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0)) ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0)))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥))

We solved constraint (26) using rules (I), (II).
We consider the chain 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))), 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))) which results in the following constraint:
(27) (java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0))∧java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1))=java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]2), 0)) ⇒ 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0)))≥NonInfC∧765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 0)))≥765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1)))∧(U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]1), 1)))), ≥))

We solved constraint (27) using rules (I), (II).

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

765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1, 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1)))
- (0 ≥ 0 ⇒ (U^Increasing(COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))), ≥)∧0 ≥ 0∧[(4)bni_28] ≥ 0∧[(5)bni_28 + (-1)Bound*bni_28] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_29] ≥ 0)
COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0), x1))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0))
- (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(8)bni_30] ≥ 0∧[(13)bni_30 + (-1)Bound*bni_30] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[8 + (-1)bso_31] ≥ 0∧[1] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))), ≥)∧0 ≥ 0∧[(8)bni_30] ≥ 0∧[(13)bni_30 + (-1)Bound*bni_30] ≥ 0∧0 ≥ 0∧[8 + (-1)bso_31] ≥ 0∧[1] ≥ 0)
765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0), 1)))
- ((U^Increasing(765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))), ≥)∧0 ≥ 0∧[(-1)bso_33] ≥ 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 with natural coefficients for non-tuple symbols [NONINF][POLO]:

POL(TRUE) = 0
POL(FALSE) = 0
POL(807_1_dupList_InvokeMethod(x₁, x₂, x₃)) = 0
POL(950_0_dupList_InvokeMethod(x₁)) = 0
POL(java.lang.Object(x₁)) = [2] + [2]x₁
POL(IntListDupRec.List(x₁, x₂)) = x₁
POL(NULL) = 0
POL(1107_0_dupList_InvokeMethod(x₁, x₂)) = 0
POL(1169_0_dupList_InvokeMethod(x₁, x₂)) = 0
POL(0) = 0
POL(916_1_dupList_InvokeMethod(x₁, x₂, x₃)) = 0
POL(1) = 0
POL(765_0_DUPLIST_FIELDACCESS(x₁)) = [-1] + x₁
POL(COND_765_0_DUPLIST_FIELDACCESS(x₁, x₂)) = [-1] + x₂ + x₁
POL(!(x₁)) = 0
POL(=(x₁, x₂)) = 0

The following pairs are in P_>:

COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))

The following pairs are in P_bound:

765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))
COND_765_0_DUPLIST_FIELDACCESS(TRUE, java.lang.Object(IntListDupRec.List(java.lang.Object(x0[1]), x1[1]))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(x0[1]))

The following pairs are in P_≥:

765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(=(x1[0], 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))
765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))

At least the following rules have been oriented under context sensitive arithmetic replacement:

!(TRUE)¹ ↔ FALSE¹
!(FALSE)¹ ↔ TRUE¹

(7) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
807_1_dupList_InvokeMethod(950_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(NULL, x0))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0))) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0)))
807_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), x4)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
807_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), x5)), java.lang.Object(x4)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), x5)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))
916_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
916_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))

The integer pair graph contains the following rules and edges:
(0): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))) → COND_765_0_DUPLIST_FIELDACCESS(!(x1[0] = 0), java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0])))
(2): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))

(2) -> (0), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[0]), x1[0]))))

(2) -> (2), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]'), 0))))

(8) IDependencyGraphProof (EQUIVALENT transformation)

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

(9) 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:
807_1_dupList_InvokeMethod(950_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(NULL, x0))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0))) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0)))
807_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), x4)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
807_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), x5)), java.lang.Object(x4)) → 1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), x5)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))
916_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)))
916_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(x4), 1))) → 1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)), 0)), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), 0)))

The integer pair graph contains the following rules and edges:
(2): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))

(2) -> (2), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]'), 0))))

(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:

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

R is empty.

The integer pair graph contains the following rules and edges:
(2): 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 0))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)))

(2) -> (2), if ((java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), 1)) →^* java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]'), 0))))

(12) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(13) Obligation:

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

765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), pos(01)))) → 765_0_DUPLIST_FIELDACCESS(java.lang.Object(IntListDupRec.List(java.lang.Object(x0[2]), pos(s(01)))))

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

807_1_dupList_InvokeMethod(950_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(NULL, x0))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(NULL, x0)), x1)), java.lang.Object(IntListDupRec.List(NULL, x0)))
807_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3))
807_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), pos(01))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), x4)), java.lang.Object(x3))
916_1_dupList_InvokeMethod(1107_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), java.lang.Object(IntListDupRec.List(x0, x1))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), pos(s(01)))), pos(01))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), pos(s(01)))))
916_1_dupList_InvokeMethod(1169_0_dupList_InvokeMethod(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2)), pos(01))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(x0, x1)), x2))), java.lang.Object(IntListDupRec.List(java.lang.Object(IntListDupRec.List(java.lang.Object(x3), pos(s(01)))), pos(01))), java.lang.Object(IntListDupRec.List(java.lang.Object(x3), pos(s(01)))))

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

(14) DependencyGraphProof (EQUIVALENT transformation)

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

(15) TRUE

(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:

Integer

The ITRS R consists of the following rules:
243_0_createList_GE(-1) → Cond_243_0_createList_GE(0 > -1, -1)
Cond_243_0_createList_GE(TRUE, -1) → 262_0_createList_Return
290_1_createList_InvokeMethod(262_0_createList_Return, -1) → 316_0_createList_Return
290_1_createList_InvokeMethod(316_0_createList_Return, x0) → 562_0_createList_Return
290_1_createList_InvokeMethod(562_0_createList_Return, x0) → 562_0_createList_Return

The integer pair graph contains the following rules and edges:
(0): 243_0_CREATELIST_GE(x0[0]) → COND_243_0_CREATELIST_GE(x0[0] >= 0, x0[0])
(1): COND_243_0_CREATELIST_GE(TRUE, x0[1]) → 243_0_CREATELIST_GE(x0[1] - 1)

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

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

The set Q consists of the following terms:
243_0_createList_GE(-1)
Cond_243_0_createList_GE(TRUE, -1)
290_1_createList_InvokeMethod(262_0_createList_Return, -1)
290_1_createList_InvokeMethod(316_0_createList_Return, x0)
290_1_createList_InvokeMethod(562_0_createList_Return, x0)

(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 243_0_CREATELIST_GE(x0) → COND_243_0_CREATELIST_GE(>=(x0, 0), x0) the following chains were created:

We consider the chain 243_0_CREATELIST_GE(x0[0]) → COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0]), COND_243_0_CREATELIST_GE(TRUE, x0[1]) → 243_0_CREATELIST_GE(-(x0[1], 1)) which results in the following constraint:
(1)    (>=(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 243_0_CREATELIST_GE(x0[0])≥NonInfC∧243_0_CREATELIST_GE(x0[0])≥COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])∧(U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>=(x0[0], 0)=TRUE ⇒ 243_0_CREATELIST_GE(x0[0])≥NonInfC∧243_0_CREATELIST_GE(x0[0])≥COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])∧(U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_15] + [(2)bni_15]x0[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_15] + [(2)bni_15]x0[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_15] + [(2)bni_15]x0[0] ≥ 0∧[(-1)bso_16] ≥ 0)

For Pair COND_243_0_CREATELIST_GE(TRUE, x0) → 243_0_CREATELIST_GE(-(x0, 1)) the following chains were created:

We consider the chain COND_243_0_CREATELIST_GE(TRUE, x0[1]) → 243_0_CREATELIST_GE(-(x0[1], 1)) which results in the following constraint:
(6)    (COND_243_0_CREATELIST_GE(TRUE, x0[1])≥NonInfC∧COND_243_0_CREATELIST_GE(TRUE, x0[1])≥243_0_CREATELIST_GE(-(x0[1], 1))∧(U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥))

We simplified constraint (6) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(7)    ((U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_18] ≥ 0)

We simplified constraint (7) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(8)    ((U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_18] ≥ 0)

We simplified constraint (8) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(9)    ((U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_18] ≥ 0)

We simplified constraint (9) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(10)    ((U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥)∧0 = 0∧[2 + (-1)bso_18] ≥ 0)

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

243_0_CREATELIST_GE(x0) → COND_243_0_CREATELIST_GE(>=(x0, 0), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_15] + [(2)bni_15]x0[0] ≥ 0∧[(-1)bso_16] ≥ 0)
COND_243_0_CREATELIST_GE(TRUE, x0) → 243_0_CREATELIST_GE(-(x0, 1))
- ((U^Increasing(243_0_CREATELIST_GE(-(x0[1], 1))), ≥)∧0 = 0∧[2 + (-1)bso_18] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(243_0_createList_GE(x₁)) = [-1]
POL(-1) = [-1]
POL(Cond_243_0_createList_GE(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(262_0_createList_Return) = [-1]
POL(290_1_createList_InvokeMethod(x₁, x₂)) = [-1]
POL(316_0_createList_Return) = [-1]
POL(562_0_createList_Return) = [-1]
POL(243_0_CREATELIST_GE(x₁)) = [2]x₁
POL(COND_243_0_CREATELIST_GE(x₁, x₂)) = [2]x₂
POL(>=(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]

The following pairs are in P_>:

COND_243_0_CREATELIST_GE(TRUE, x0[1]) → 243_0_CREATELIST_GE(-(x0[1], 1))

The following pairs are in P_bound:

243_0_CREATELIST_GE(x0[0]) → COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])

The following pairs are in P_≥:

243_0_CREATELIST_GE(x0[0]) → COND_243_0_CREATELIST_GE(>=(x0[0], 0), x0[0])

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:

Integer

The ITRS R consists of the following rules:
243_0_createList_GE(-1) → Cond_243_0_createList_GE(0 > -1, -1)
Cond_243_0_createList_GE(TRUE, -1) → 262_0_createList_Return
290_1_createList_InvokeMethod(262_0_createList_Return, -1) → 316_0_createList_Return
290_1_createList_InvokeMethod(316_0_createList_Return, x0) → 562_0_createList_Return
290_1_createList_InvokeMethod(562_0_createList_Return, x0) → 562_0_createList_Return

The integer pair graph contains the following rules and edges:
(0): 243_0_CREATELIST_GE(x0[0]) → COND_243_0_CREATELIST_GE(x0[0] >= 0, x0[0])

The set Q consists of the following terms:
243_0_createList_GE(-1)
Cond_243_0_createList_GE(TRUE, -1)
290_1_createList_InvokeMethod(262_0_createList_Return, -1)
290_1_createList_InvokeMethod(316_0_createList_Return, x0)
290_1_createList_InvokeMethod(562_0_createList_Return, x0)

(20) IDependencyGraphProof (EQUIVALENT transformation)

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

(21) TRUE

(22) Obligation:

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

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

The following domains are used:

Integer

The ITRS R consists of the following rules:
243_0_createList_GE(-1) → Cond_243_0_createList_GE(0 > -1, -1)
Cond_243_0_createList_GE(TRUE, -1) → 262_0_createList_Return
290_1_createList_InvokeMethod(262_0_createList_Return, -1) → 316_0_createList_Return
290_1_createList_InvokeMethod(316_0_createList_Return, x0) → 562_0_createList_Return
290_1_createList_InvokeMethod(562_0_createList_Return, x0) → 562_0_createList_Return

The integer pair graph contains the following rules and edges:
(1): COND_243_0_CREATELIST_GE(TRUE, x0[1]) → 243_0_CREATELIST_GE(x0[1] - 1)

The set Q consists of the following terms:
243_0_createList_GE(-1)
Cond_243_0_createList_GE(TRUE, -1)
290_1_createList_InvokeMethod(262_0_createList_Return, -1)
290_1_createList_InvokeMethod(316_0_createList_Return, x0)
290_1_createList_InvokeMethod(562_0_createList_Return, x0)

(23) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) IDPNonInfProof (SOUND transformation)

(7) Obligation:

(8) IDependencyGraphProof (EQUIVALENT transformation)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) IDPtoQDPProof (SOUND transformation)

(13) Obligation:

(14) DependencyGraphProof (EQUIVALENT transformation)

(15) TRUE

(16) Obligation:

(17) IDPNonInfProof (SOUND transformation)

(18) Complex Obligation (AND)

(19) Obligation:

(20) IDependencyGraphProof (EQUIVALENT transformation)

(21) TRUE

(22) Obligation:

(23) IDependencyGraphProof (EQUIVALENT transformation)

(24) TRUE