Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: ListContent

public class ListContent{

  public static void main(String[] args) {
    Random.args = args;
    IntList l = IntList.createIntList();

    while (l.value > 0) l.value--;
  }

}

class IntList {
  int value;
  IntList next;

  public IntList(int value, IntList next) {
    this.value = value;
    this.next = next;
  }

  public static IntList createIntList() {

    int i = Random.random();
    IntList l = null;

    while (i > 0) {
      l = new IntList(Random.random(), l);
      i--;
    }

    return l;
  }
}


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

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

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
ListContent.main([Ljava/lang/String;)V: Graph of 89 nodes with 1 SCC.

IntList.createIntList()LIntList;: Graph of 163 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 2 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: IntList.createIntList()LIntList;
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 38 rules for P and 0 rules for R.

P rules:
1325_0_createIntList_LE(EOS(STATIC_1325), i383, i383) → 1327_0_createIntList_LE(EOS(STATIC_1327), i383, i383)
1327_0_createIntList_LE(EOS(STATIC_1327), i383, i383) → 1330_0_createIntList_New(EOS(STATIC_1330), i383) | >(i383, 0)
1330_0_createIntList_New(EOS(STATIC_1330), i383) → 1334_0_createIntList_Duplicate(EOS(STATIC_1334), i383)
1334_0_createIntList_Duplicate(EOS(STATIC_1334), i383) → 1337_0_createIntList_InvokeMethod(EOS(STATIC_1337), i383)
1337_0_createIntList_InvokeMethod(EOS(STATIC_1337), i383) → 1340_0_random_FieldAccess(EOS(STATIC_1340), i383)
1340_0_random_FieldAccess(EOS(STATIC_1340), i383) → 1344_0_random_FieldAccess(EOS(STATIC_1344), i383)
1344_0_random_FieldAccess(EOS(STATIC_1344), i383) → 1347_0_random_ArrayAccess(EOS(STATIC_1347), i383)
1347_0_random_ArrayAccess(EOS(STATIC_1347), i383) → 1348_0_random_ArrayAccess(EOS(STATIC_1348), i383)
1348_0_random_ArrayAccess(EOS(STATIC_1348), i383) → 1351_0_random_Store(EOS(STATIC_1351), i383, o553)
1351_0_random_Store(EOS(STATIC_1351), i383, o553) → 1355_0_random_FieldAccess(EOS(STATIC_1355), i383, o553)
1355_0_random_FieldAccess(EOS(STATIC_1355), i383, o553) → 1357_0_random_ConstantStackPush(EOS(STATIC_1357), i383, o553)
1357_0_random_ConstantStackPush(EOS(STATIC_1357), i383, o553) → 1361_0_random_IntArithmetic(EOS(STATIC_1361), i383, o553)
1361_0_random_IntArithmetic(EOS(STATIC_1361), i383, o553) → 1364_0_random_FieldAccess(EOS(STATIC_1364), i383, o553)
1364_0_random_FieldAccess(EOS(STATIC_1364), i383, o553) → 1366_0_random_Load(EOS(STATIC_1366), i383, o553)
1366_0_random_Load(EOS(STATIC_1366), i383, o553) → 1371_0_random_InvokeMethod(EOS(STATIC_1371), i383, o553)
1371_0_random_InvokeMethod(EOS(STATIC_1371), i383, java.lang.Object(o570sub)) → 1374_0_random_InvokeMethod(EOS(STATIC_1374), i383, java.lang.Object(o570sub))
1374_0_random_InvokeMethod(EOS(STATIC_1374), i383, java.lang.Object(o570sub)) → 1377_0_length_Load(EOS(STATIC_1377), i383, java.lang.Object(o570sub), java.lang.Object(o570sub))
1377_0_length_Load(EOS(STATIC_1377), i383, java.lang.Object(o570sub), java.lang.Object(o570sub)) → 1386_0_length_FieldAccess(EOS(STATIC_1386), i383, java.lang.Object(o570sub), java.lang.Object(o570sub))
1386_0_length_FieldAccess(EOS(STATIC_1386), i383, java.lang.Object(java.lang.String(o578sub, i415)), java.lang.Object(java.lang.String(o578sub, i415))) → 1388_0_length_FieldAccess(EOS(STATIC_1388), i383, java.lang.Object(java.lang.String(o578sub, i415)), java.lang.Object(java.lang.String(o578sub, i415))) | &&(>=(i415, 0), >=(i416, 0))
1388_0_length_FieldAccess(EOS(STATIC_1388), i383, java.lang.Object(java.lang.String(o578sub, i415)), java.lang.Object(java.lang.String(o578sub, i415))) → 1394_0_length_Return(EOS(STATIC_1394), i383, java.lang.Object(java.lang.String(o578sub, i415)))
1394_0_length_Return(EOS(STATIC_1394), i383, java.lang.Object(java.lang.String(o578sub, i415))) → 1399_0_random_Return(EOS(STATIC_1399), i383)
1399_0_random_Return(EOS(STATIC_1399), i383) → 1401_0_createIntList_Load(EOS(STATIC_1401), i383)
1401_0_createIntList_Load(EOS(STATIC_1401), i383) → 1407_0_createIntList_InvokeMethod(EOS(STATIC_1407), i383)
1407_0_createIntList_InvokeMethod(EOS(STATIC_1407), i383) → 1412_0_<init>_Load(EOS(STATIC_1412), i383)
1412_0_<init>_Load(EOS(STATIC_1412), i383) → 1422_0_<init>_InvokeMethod(EOS(STATIC_1422), i383)
1422_0_<init>_InvokeMethod(EOS(STATIC_1422), i383) → 1429_0_<init>_Load(EOS(STATIC_1429), i383)
1429_0_<init>_Load(EOS(STATIC_1429), i383) → 1433_0_<init>_Load(EOS(STATIC_1433), i383)
1433_0_<init>_Load(EOS(STATIC_1433), i383) → 1441_0_<init>_FieldAccess(EOS(STATIC_1441), i383)
1441_0_<init>_FieldAccess(EOS(STATIC_1441), i383) → 1448_0_<init>_Load(EOS(STATIC_1448), i383)
1448_0_<init>_Load(EOS(STATIC_1448), i383) → 1454_0_<init>_Load(EOS(STATIC_1454), i383)
1454_0_<init>_Load(EOS(STATIC_1454), i383) → 1461_0_<init>_FieldAccess(EOS(STATIC_1461), i383)
1461_0_<init>_FieldAccess(EOS(STATIC_1461), i383) → 1469_0_<init>_Return(EOS(STATIC_1469), i383)
1469_0_<init>_Return(EOS(STATIC_1469), i383) → 1476_0_createIntList_Store(EOS(STATIC_1476), i383)
1476_0_createIntList_Store(EOS(STATIC_1476), i383) → 1484_0_createIntList_Inc(EOS(STATIC_1484), i383)
1484_0_createIntList_Inc(EOS(STATIC_1484), i383) → 1491_0_createIntList_JMP(EOS(STATIC_1491), +(i383, -1)) | >(i383, 0)
1491_0_createIntList_JMP(EOS(STATIC_1491), i460) → 1497_0_createIntList_Load(EOS(STATIC_1497), i460)
1497_0_createIntList_Load(EOS(STATIC_1497), i460) → 1321_0_createIntList_Load(EOS(STATIC_1321), i460)
1321_0_createIntList_Load(EOS(STATIC_1321), i379) → 1325_0_createIntList_LE(EOS(STATIC_1325), i379, i379)
R rules:

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1325_0_createIntList_LE(EOS(STATIC_1325), x0, x0) → 1325_0_createIntList_LE(EOS(STATIC_1325), +(x0, -1), +(x0, -1)) | >(x0, 0)
R rules:

Filtered ground terms:

1325_0_createIntList_LE(x1, x2, x3) → 1325_0_createIntList_LE(x2, x3)
EOS(x1) → EOS
Cond_1325_0_createIntList_LE(x1, x2, x3, x4) → Cond_1325_0_createIntList_LE(x1, x3, x4)

Filtered duplicate args:

1325_0_createIntList_LE(x1, x2) → 1325_0_createIntList_LE(x2)
Cond_1325_0_createIntList_LE(x1, x2, x3) → Cond_1325_0_createIntList_LE(x1, x3)

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1325_0_createIntList_LE(x0) → 1325_0_createIntList_LE(+(x0, -1)) | >(x0, 0)
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.

P rules:
1325_0_CREATEINTLIST_LE(x0) → COND_1325_0_CREATEINTLIST_LE(>(x0, 0), x0)
COND_1325_0_CREATEINTLIST_LE(TRUE, x0) → 1325_0_CREATEINTLIST_LE(+(x0, -1))
R rules:

(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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1325_0_CREATEINTLIST_LE(x0[0]) → COND_1325_0_CREATEINTLIST_LE(x0[0] > 0, x0[0])
(1): COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1325_0_CREATEINTLIST_LE(x0[1] + -1)

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

(1) -> (0), if (x0[1] + -1 →^* x0[0])

The set Q is empty.

(8) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpCand1ShapeHeuristic@6143c610 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 0 Max Right Steps: 0

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 1325_0_CREATEINTLIST_LE(x0) → COND_1325_0_CREATEINTLIST_LE(>(x0, 0), x0) the following chains were created:

• We consider the chain 1325_0_CREATEINTLIST_LE(x0[0]) → COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0]), COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1325_0_CREATEINTLIST_LE(+(x0[1], -1)) which results in the following constraint:
  

  (1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 1325_0_CREATEINTLIST_LE(x0[0])≥NonInfC∧1325_0_CREATEINTLIST_LE(x0[0])≥COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥))

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

  (2)    (>(x0[0], 0)=TRUE ⇒ 1325_0_CREATEINTLIST_LE(x0[0])≥NonInfC∧1325_0_CREATEINTLIST_LE(x0[0])≥COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥))

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

  (3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

  
  
  

For Pair COND_1325_0_CREATEINTLIST_LE(TRUE, x0) → 1325_0_CREATEINTLIST_LE(+(x0, -1)) the following chains were created:

• We consider the chain COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1325_0_CREATEINTLIST_LE(+(x0[1], -1)) which results in the following constraint:
  

  (7)    (COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1])≥NonInfC∧COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1])≥1325_0_CREATEINTLIST_LE(+(x0[1], -1))∧(U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥))

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

  (8)    ((U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (9)    ((U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (10)    ((U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (11)    ((U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

  
  
  

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

• 1325_0_CREATEINTLIST_LE(x0) → COND_1325_0_CREATEINTLIST_LE(>(x0, 0), x0)
  
  • (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
    
  
  
• COND_1325_0_CREATEINTLIST_LE(TRUE, x0) → 1325_0_CREATEINTLIST_LE(+(x0, -1))
  
  • ((U^Increasing(1325_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 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(1325_0_CREATEINTLIST_LE(x₁)) = [2]x₁   
POL(COND_1325_0_CREATEINTLIST_LE(x₁, x₂)) = [2]x₂   
POL(>(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(-1) = [-1]   

The following pairs are in P_>:

COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1325_0_CREATEINTLIST_LE(+(x0[1], -1))

The following pairs are in P_bound:

1325_0_CREATEINTLIST_LE(x0[0]) → COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])

The following pairs are in P_≥:

1325_0_CREATEINTLIST_LE(x0[0]) → COND_1325_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])

There are no usable rules.

(9) Complex Obligation (AND)

(10) 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:
(0): 1325_0_CREATEINTLIST_LE(x0[0]) → COND_1325_0_CREATEINTLIST_LE(x0[0] > 0, x0[0])


The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

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

(12) TRUE

(13) 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:
(1): COND_1325_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1325_0_CREATEINTLIST_LE(x0[1] + -1)


The set Q is empty.

(14) IDependencyGraphProof (EQUIVALENT transformation)

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

(15) TRUE

(16) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: ListContent.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(17) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 14 rules for P and 0 rules for R.

P rules:
1116_0_main_FieldAccess(EOS(STATIC_1116), java.lang.Object(o434sub), java.lang.Object(o434sub)) → 1119_0_main_FieldAccess(EOS(STATIC_1119), java.lang.Object(o434sub), java.lang.Object(o434sub))
1119_0_main_FieldAccess(EOS(STATIC_1119), java.lang.Object(IntList(EOC, i295)), java.lang.Object(IntList(EOC, i295))) → 1125_0_main_FieldAccess(EOS(STATIC_1125), java.lang.Object(IntList(EOC, i295)), java.lang.Object(IntList(EOC, i295)))
1125_0_main_FieldAccess(EOS(STATIC_1125), java.lang.Object(IntList(EOC, i295)), java.lang.Object(IntList(EOC, i295))) → 1130_0_main_LE(EOS(STATIC_1130), java.lang.Object(IntList(EOC, i295)), i295)
1130_0_main_LE(EOS(STATIC_1130), java.lang.Object(IntList(EOC, i301)), i301) → 1138_0_main_LE(EOS(STATIC_1138), java.lang.Object(IntList(EOC, i301)), i301)
1138_0_main_LE(EOS(STATIC_1138), java.lang.Object(IntList(EOC, i301)), i301) → 1143_0_main_Load(EOS(STATIC_1143), java.lang.Object(IntList(EOC, i301))) | >(i301, 0)
1143_0_main_Load(EOS(STATIC_1143), java.lang.Object(IntList(EOC, i301))) → 1150_0_main_Duplicate(EOS(STATIC_1150), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)))
1150_0_main_Duplicate(EOS(STATIC_1150), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301))) → 1156_0_main_FieldAccess(EOS(STATIC_1156), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)))
1156_0_main_FieldAccess(EOS(STATIC_1156), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301))) → 1162_0_main_ConstantStackPush(EOS(STATIC_1162), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), i301)
1162_0_main_ConstantStackPush(EOS(STATIC_1162), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), i301) → 1168_0_main_IntArithmetic(EOS(STATIC_1168), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), i301, 1)
1168_0_main_IntArithmetic(EOS(STATIC_1168), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), i301, matching1) → 1176_0_main_FieldAccess(EOS(STATIC_1176), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), -(i301, 1)) | &&(>(i301, 0), =(matching1, 1))
1176_0_main_FieldAccess(EOS(STATIC_1176), java.lang.Object(IntList(EOC, i301)), java.lang.Object(IntList(EOC, i301)), i316) → 1180_0_main_JMP(EOS(STATIC_1180), java.lang.Object(IntList(EOC, i316)))
1180_0_main_JMP(EOS(STATIC_1180), java.lang.Object(IntList(EOC, i316))) → 1186_0_main_Load(EOS(STATIC_1186), java.lang.Object(IntList(EOC, i316)))
1186_0_main_Load(EOS(STATIC_1186), java.lang.Object(IntList(EOC, i316))) → 1111_0_main_Load(EOS(STATIC_1111), java.lang.Object(IntList(EOC, i316)))
1111_0_main_Load(EOS(STATIC_1111), o424) → 1116_0_main_FieldAccess(EOS(STATIC_1116), o424, o424)
R rules:

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1116_0_main_FieldAccess(EOS(STATIC_1116), java.lang.Object(IntList(EOC, x0)), java.lang.Object(IntList(EOC, x0))) → 1116_0_main_FieldAccess(EOS(STATIC_1116), java.lang.Object(IntList(EOC, -(x0, 1))), java.lang.Object(IntList(EOC, -(x0, 1)))) | >(x0, 0)
R rules:

Filtered ground terms:

1116_0_main_FieldAccess(x1, x2, x3) → 1116_0_main_FieldAccess(x2, x3)
IntList(x1, x2) → IntList(x2)
EOS(x1) → EOS
Cond_1116_0_main_FieldAccess(x1, x2, x3, x4) → Cond_1116_0_main_FieldAccess(x1, x3, x4)

Filtered duplicate args:

1116_0_main_FieldAccess(x1, x2) → 1116_0_main_FieldAccess(x2)
Cond_1116_0_main_FieldAccess(x1, x2, x3) → Cond_1116_0_main_FieldAccess(x1, x3)

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1116_0_main_FieldAccess(java.lang.Object(IntList(x0))) → 1116_0_main_FieldAccess(java.lang.Object(IntList(-(x0, 1)))) | >(x0, 0)
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.

P rules:
1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0))) → COND_1116_0_MAIN_FIELDACCESS(>(x0, 0), java.lang.Object(IntList(x0)))
COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0, 1))))
R rules:

(18) 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:
(0): 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0]))) → COND_1116_0_MAIN_FIELDACCESS(x0[0] > 0, java.lang.Object(IntList(x0[0])))
(1): COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1]))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[1] - 1)))

(0) -> (1), if (x0[0] > 0 ∧java.lang.Object(IntList(x0[0])) →^* java.lang.Object(IntList(x0[1])))

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

The set Q is empty.

(19) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpCand1ShapeHeuristic@6143c610 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 0 Max Right Steps: 0

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 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0))) → COND_1116_0_MAIN_FIELDACCESS(>(x0, 0), java.lang.Object(IntList(x0))) the following chains were created:

• We consider the chain 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0]))) → COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0]))), COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1]))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1)))) which results in the following constraint:
  

  (1)    (>(x0[0], 0)=TRUE∧java.lang.Object(IntList(x0[0]))=java.lang.Object(IntList(x0[1])) ⇒ 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0])))≥NonInfC∧1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0])))≥COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))∧(U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥))

  
  
  We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
  

  (2)    (>(x0[0], 0)=TRUE ⇒ 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0])))≥NonInfC∧1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0])))≥COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))∧(U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥))

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

  (3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

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

  (6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

  
  
  

For Pair COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0, 1)))) the following chains were created:

• We consider the chain COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1]))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1)))) which results in the following constraint:
  

  (7)    (COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1])))≥NonInfC∧COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1])))≥1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))∧(U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥))

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

  (8)    ((U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (9)    ((U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (10)    ((U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

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

  (11)    ((U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

  
  
  

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

• 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0))) → COND_1116_0_MAIN_FIELDACCESS(>(x0, 0), java.lang.Object(IntList(x0)))
  
  • (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
    
  
  
• COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0, 1))))
  
  • ((U^Increasing(1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 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(1116_0_MAIN_FIELDACCESS(x₁)) = [2]x₁   
POL(java.lang.Object(x₁)) = x₁   
POL(IntList(x₁)) = x₁   
POL(COND_1116_0_MAIN_FIELDACCESS(x₁, x₂)) = [2]x₂   
POL(>(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(-(x₁, x₂)) = x₁ + [-1]x₂   
POL(1) = [1]   

The following pairs are in P_>:

COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1]))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(-(x0[1], 1))))

The following pairs are in P_bound:

1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0]))) → COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))

The following pairs are in P_≥:

1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0]))) → COND_1116_0_MAIN_FIELDACCESS(>(x0[0], 0), java.lang.Object(IntList(x0[0])))

There are no usable rules.

(20) Complex Obligation (AND)

(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

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[0]))) → COND_1116_0_MAIN_FIELDACCESS(x0[0] > 0, java.lang.Object(IntList(x0[0])))


The set Q is empty.

(22) IDependencyGraphProof (EQUIVALENT transformation)

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

(23) TRUE

(24) 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:
(1): COND_1116_0_MAIN_FIELDACCESS(TRUE, java.lang.Object(IntList(x0[1]))) → 1116_0_MAIN_FIELDACCESS(java.lang.Object(IntList(x0[1] - 1)))


The set Q is empty.

(25) IDependencyGraphProof (EQUIVALENT transformation)

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

(26) TRUE