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: StupidArray

public class StupidArray {
  public static void main(String[] args) {
    int i = 0;
    while (true) {
      i = args.length + 1;
      args[i] = new String();
    }
  }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
StupidArray.main([Ljava/lang/String;)V: Graph of 78 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

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

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 28 rules for P and 0 rules for R.

P rules:
142_0_main_ArrayLength(EOS(STATIC_142), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1))) → 144_0_main_ConstantStackPush(EOS(STATIC_144), java.lang.Object(ARRAY(i1)), i1) | >=(i1, 0)
144_0_main_ConstantStackPush(EOS(STATIC_144), java.lang.Object(ARRAY(i1)), i1) → 146_0_main_IntArithmetic(EOS(STATIC_146), java.lang.Object(ARRAY(i1)), i1, 1)
146_0_main_IntArithmetic(EOS(STATIC_146), java.lang.Object(ARRAY(i1)), i1, matching1) → 148_0_main_Store(EOS(STATIC_148), java.lang.Object(ARRAY(i1)), +(i1, 1)) | &&(>=(i1, 0), =(matching1, 1))
148_0_main_Store(EOS(STATIC_148), java.lang.Object(ARRAY(i1)), i5) → 150_0_main_Load(EOS(STATIC_150), java.lang.Object(ARRAY(i1)), i5)
150_0_main_Load(EOS(STATIC_150), java.lang.Object(ARRAY(i1)), i5) → 152_0_main_Load(EOS(STATIC_152), java.lang.Object(ARRAY(i1)), i5, java.lang.Object(ARRAY(i1)))
152_0_main_Load(EOS(STATIC_152), java.lang.Object(ARRAY(i1)), i5, java.lang.Object(ARRAY(i1))) → 154_0_main_New(EOS(STATIC_154), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
154_0_main_New(EOS(STATIC_154), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 157_0_main_Duplicate(EOS(STATIC_157), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
157_0_main_Duplicate(EOS(STATIC_157), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 159_0_main_InvokeMethod(EOS(STATIC_159), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
159_0_main_InvokeMethod(EOS(STATIC_159), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 161_0_<init>_Load(EOS(STATIC_161), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
161_0_<init>_Load(EOS(STATIC_161), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 163_0_<init>_InvokeMethod(EOS(STATIC_163), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
163_0_<init>_InvokeMethod(EOS(STATIC_163), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 166_0_<init>_Load(EOS(STATIC_166), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
166_0_<init>_Load(EOS(STATIC_166), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 168_0_<init>_ConstantStackPush(EOS(STATIC_168), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
168_0_<init>_ConstantStackPush(EOS(STATIC_168), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 171_0_<init>_FieldAccess(EOS(STATIC_171), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
171_0_<init>_FieldAccess(EOS(STATIC_171), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 174_0_<init>_Load(EOS(STATIC_174), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
174_0_<init>_Load(EOS(STATIC_174), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 175_0_<init>_ConstantStackPush(EOS(STATIC_175), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
175_0_<init>_ConstantStackPush(EOS(STATIC_175), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 178_0_<init>_FieldAccess(EOS(STATIC_178), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
178_0_<init>_FieldAccess(EOS(STATIC_178), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 181_0_<init>_Load(EOS(STATIC_181), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
181_0_<init>_Load(EOS(STATIC_181), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 183_0_<init>_ConstantStackPush(EOS(STATIC_183), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
183_0_<init>_ConstantStackPush(EOS(STATIC_183), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 186_0_<init>_ArrayCreate(EOS(STATIC_186), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
186_0_<init>_ArrayCreate(EOS(STATIC_186), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 189_0_<init>_FieldAccess(EOS(STATIC_189), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
189_0_<init>_FieldAccess(EOS(STATIC_189), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 194_0_<init>_Return(EOS(STATIC_194), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
194_0_<init>_Return(EOS(STATIC_194), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 197_0_main_ArrayAccess(EOS(STATIC_197), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
197_0_main_ArrayAccess(EOS(STATIC_197), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 199_0_main_ArrayAccess(EOS(STATIC_199), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
199_0_main_ArrayAccess(EOS(STATIC_199), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 202_0_main_ArrayAccess(EOS(STATIC_202), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
202_0_main_ArrayAccess(EOS(STATIC_202), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 209_0_main_JMP(EOS(STATIC_209), java.lang.Object(ARRAY(i1))) | <(i5, i1)
209_0_main_JMP(EOS(STATIC_209), java.lang.Object(ARRAY(i1))) → 216_0_main_Load(EOS(STATIC_216), java.lang.Object(ARRAY(i1)))
216_0_main_Load(EOS(STATIC_216), java.lang.Object(ARRAY(i1))) → 139_0_main_Load(EOS(STATIC_139), java.lang.Object(ARRAY(i1)))
139_0_main_Load(EOS(STATIC_139), java.lang.Object(ARRAY(i1))) → 142_0_main_ArrayLength(EOS(STATIC_142), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)))
R rules:

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

P rules:
142_0_main_ArrayLength(EOS(STATIC_142), java.lang.Object(ARRAY(x0)), java.lang.Object(ARRAY(x0))) → 142_0_main_ArrayLength(EOS(STATIC_142), java.lang.Object(ARRAY(x0)), java.lang.Object(ARRAY(x0))) | &&(>(+(x0, 1), 0), >(x0, +(x0, 1)))
R rules:

Filtered ground terms:

142_0_main_ArrayLength(x1, x2, x3) → 142_0_main_ArrayLength(x2, x3)
EOS(x1) → EOS
Cond_142_0_main_ArrayLength(x1, x2, x3, x4) → Cond_142_0_main_ArrayLength(x1, x3, x4)

Filtered duplicate args:

142_0_main_ArrayLength(x1, x2) → 142_0_main_ArrayLength(x2)
Cond_142_0_main_ArrayLength(x1, x2, x3) → Cond_142_0_main_ArrayLength(x1, x3)

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

P rules:
142_0_main_ArrayLength(java.lang.Object(ARRAY(x0))) → 142_0_main_ArrayLength(java.lang.Object(ARRAY(x0))) | &&(>(x0, -1), >(x0, +(x0, 1)))
R rules:

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

P rules:
142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0)))
COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0)))
R rules:

(6) 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

R is empty.

The integer pair graph contains the following rules and edges:
(0): 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(x0[0] > -1 && x0[0] > x0[0] + 1, java.lang.Object(ARRAY(x0[0])))
(1): COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))

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

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

The set Q is empty.

(7) 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.IdpDefaultShapeHeuristic@b53b098 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

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 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0))) the following chains were created:

• We consider the chain COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1]))), 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0]))), COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1]))) which results in the following constraint:
  

  (1)    (java.lang.Object(ARRAY(x0[1]))=java.lang.Object(ARRAY(x0[0]))∧&&(>(x0[0], -1), >(x0[0], +(x0[0], 1)))=TRUE∧java.lang.Object(ARRAY(x0[0]))=java.lang.Object(ARRAY(x0[1]1)) ⇒ 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥NonInfC∧142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))∧(U^Increasing(COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))), ≥))

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

  (2)    (>(x0[0], -1)=TRUE∧>(x0[0], +(x0[0], 1))=TRUE ⇒ 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥NonInfC∧142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))∧(U^Increasing(COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))), ≥))

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

  (3)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[0] ≥ 0∧[-1 + (-1)bso_15] ≥ 0)

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

  (4)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[0] ≥ 0∧[-1 + (-1)bso_15] ≥ 0)

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

  (5)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[0] ≥ 0∧[-1 + (-1)bso_15] ≥ 0)

  
  
  We solved constraint (5) using rule (IDP_SMT_SPLIT).

For Pair COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) the following chains were created:

• We consider the chain 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0]))), COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1]))), 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0]))) which results in the following constraint:
  

  (6)    (&&(>(x0[0], -1), >(x0[0], +(x0[0], 1)))=TRUE∧java.lang.Object(ARRAY(x0[0]))=java.lang.Object(ARRAY(x0[1]))∧java.lang.Object(ARRAY(x0[1]))=java.lang.Object(ARRAY(x0[0]1)) ⇒ COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1])))≥NonInfC∧COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1])))≥142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))∧(U^Increasing(142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))), ≥))

  
  
  We simplified constraint (6) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (7)    (>(x0[0], -1)=TRUE∧>(x0[0], +(x0[0], 1))=TRUE ⇒ COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[0])))≥NonInfC∧COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[0])))≥142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))∧(U^Increasing(142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))), ≥))

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

  (8)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[0] ≥ 0∧[(-1)bso_17] ≥ 0)

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

  (9)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[0] ≥ 0∧[(-1)bso_17] ≥ 0)

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

  (10)    (x0[0] ≥ 0∧[-2] ≥ 0 ⇒ (U^Increasing(142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[0] ≥ 0∧[(-1)bso_17] ≥ 0)

  
  
  We solved constraint (10) using rule (IDP_SMT_SPLIT).

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

• 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0)))
  
  
• COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0)))
  
  

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(142_0_MAIN_ARRAYLENGTH(x₁)) = [-1] + [-1]x₁   
POL(java.lang.Object(x₁)) = [-1] + [-1]x₁   
POL(ARRAY(x₁)) = [-1] + [-1]x₁   
POL(COND_142_0_MAIN_ARRAYLENGTH(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁   
POL(&&(x₁, x₂)) = [-1]   
POL(>(x₁, x₂)) = [-1]   
POL(-1) = [-1]   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   

The following pairs are in P_>:

142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))
COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))

The following pairs are in P_bound:

142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_142_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))
COND_142_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 142_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))

The following pairs are in P_≥:
none

There are no usable rules.

(8) 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 is empty.

The set Q is empty.

(9) IDependencyGraphProof (EQUIVALENT transformation)

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

(10) TRUE