Termination of the given JBC could be proven:

0 JBC
↳1 JBCToGraph (⇒, 120 ms)
↳2 JBCTerminationGraph
↳3 TerminationGraphToSCCProof (⇒, 0 ms)
↳4 JBCTerminationSCC
↳5 SCCToIDPv1Proof (⇒, 100 ms)
↳6 IDP
↳7 IDPNonInfProof (⇒, 10 ms)
↳8 IDP
↳9 IDependencyGraphProof (⇔, 0 ms)
↳10 TRUE

(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:
126_0_main_ArrayLength(EOS(STATIC_126), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1))) → 128_0_main_ConstantStackPush(EOS(STATIC_128), java.lang.Object(ARRAY(i1)), i1) | >=(i1, 0)
128_0_main_ConstantStackPush(EOS(STATIC_128), java.lang.Object(ARRAY(i1)), i1) → 129_0_main_IntArithmetic(EOS(STATIC_129), java.lang.Object(ARRAY(i1)), i1, 1)
129_0_main_IntArithmetic(EOS(STATIC_129), java.lang.Object(ARRAY(i1)), i1, matching1) → 131_0_main_Store(EOS(STATIC_131), java.lang.Object(ARRAY(i1)), +(i1, 1)) | &&(>=(i1, 0), =(matching1, 1))
131_0_main_Store(EOS(STATIC_131), java.lang.Object(ARRAY(i1)), i5) → 133_0_main_Load(EOS(STATIC_133), java.lang.Object(ARRAY(i1)), i5)
133_0_main_Load(EOS(STATIC_133), java.lang.Object(ARRAY(i1)), i5) → 134_0_main_Load(EOS(STATIC_134), java.lang.Object(ARRAY(i1)), i5, java.lang.Object(ARRAY(i1)))
134_0_main_Load(EOS(STATIC_134), java.lang.Object(ARRAY(i1)), i5, java.lang.Object(ARRAY(i1))) → 136_0_main_New(EOS(STATIC_136), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
136_0_main_New(EOS(STATIC_136), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 138_0_main_Duplicate(EOS(STATIC_138), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
138_0_main_Duplicate(EOS(STATIC_138), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 139_0_main_InvokeMethod(EOS(STATIC_139), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
139_0_main_InvokeMethod(EOS(STATIC_139), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 140_0_<init>_Load(EOS(STATIC_140), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
140_0_<init>_Load(EOS(STATIC_140), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 142_0_<init>_InvokeMethod(EOS(STATIC_142), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
142_0_<init>_InvokeMethod(EOS(STATIC_142), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 144_0_<init>_Load(EOS(STATIC_144), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
144_0_<init>_Load(EOS(STATIC_144), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 145_0_<init>_ConstantStackPush(EOS(STATIC_145), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
145_0_<init>_ConstantStackPush(EOS(STATIC_145), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 147_0_<init>_FieldAccess(EOS(STATIC_147), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
147_0_<init>_FieldAccess(EOS(STATIC_147), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 149_0_<init>_Load(EOS(STATIC_149), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
149_0_<init>_Load(EOS(STATIC_149), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 151_0_<init>_ConstantStackPush(EOS(STATIC_151), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
151_0_<init>_ConstantStackPush(EOS(STATIC_151), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 152_0_<init>_FieldAccess(EOS(STATIC_152), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
152_0_<init>_FieldAccess(EOS(STATIC_152), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 154_0_<init>_Load(EOS(STATIC_154), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
154_0_<init>_Load(EOS(STATIC_154), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 156_0_<init>_ConstantStackPush(EOS(STATIC_156), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
156_0_<init>_ConstantStackPush(EOS(STATIC_156), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 158_0_<init>_ArrayCreate(EOS(STATIC_158), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
158_0_<init>_ArrayCreate(EOS(STATIC_158), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 160_0_<init>_FieldAccess(EOS(STATIC_160), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
160_0_<init>_FieldAccess(EOS(STATIC_160), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 163_0_<init>_Return(EOS(STATIC_163), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
163_0_<init>_Return(EOS(STATIC_163), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 164_0_main_ArrayAccess(EOS(STATIC_164), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
164_0_main_ArrayAccess(EOS(STATIC_164), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 165_0_main_ArrayAccess(EOS(STATIC_165), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
165_0_main_ArrayAccess(EOS(STATIC_165), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 166_0_main_ArrayAccess(EOS(STATIC_166), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5)
166_0_main_ArrayAccess(EOS(STATIC_166), java.lang.Object(ARRAY(i1)), java.lang.Object(ARRAY(i1)), i5) → 168_0_main_JMP(EOS(STATIC_168), java.lang.Object(ARRAY(i1))) | <(i5, i1)
168_0_main_JMP(EOS(STATIC_168), java.lang.Object(ARRAY(i1))) → 180_0_main_Load(EOS(STATIC_180), java.lang.Object(ARRAY(i1)))
180_0_main_Load(EOS(STATIC_180), java.lang.Object(ARRAY(i1))) → 123_0_main_Load(EOS(STATIC_123), java.lang.Object(ARRAY(i1)))
123_0_main_Load(EOS(STATIC_123), java.lang.Object(ARRAY(i1))) → 126_0_main_ArrayLength(EOS(STATIC_126), 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:
126_0_main_ArrayLength(EOS(STATIC_126), java.lang.Object(ARRAY(x0)), java.lang.Object(ARRAY(x0))) → 126_0_main_ArrayLength(EOS(STATIC_126), java.lang.Object(ARRAY(x0)), java.lang.Object(ARRAY(x0))) | &&(>(+(x0, 1), 0), >(x0, +(x0, 1)))
R rules:

Filtered ground terms:



126_0_main_ArrayLength(x1, x2, x3) → 126_0_main_ArrayLength(x2, x3)
EOS(x1) → EOS
Cond_126_0_main_ArrayLength(x1, x2, x3, x4) → Cond_126_0_main_ArrayLength(x1, x3, x4)

Filtered duplicate args:



126_0_main_ArrayLength(x1, x2) → 126_0_main_ArrayLength(x2)
Cond_126_0_main_ArrayLength(x1, x2, x3) → Cond_126_0_main_ArrayLength(x1, x3)

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


P rules:
126_0_main_ArrayLength(java.lang.Object(ARRAY(x0))) → 126_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:
126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0)))
COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 126_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): 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_0_MAIN_ARRAYLENGTH(x0[0] > -1 && x0[0] > x0[0] + 1, java.lang.Object(ARRAY(x0[0])))
(1): COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_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@2c5a1e6b 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 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0))) the following chains were created:
  • We consider the chain COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1]))), 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0]))), COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_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)) ⇒ 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥NonInfC∧126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))∧(UIncreasing(COND_126_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 ⇒ 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥NonInfC∧126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))≥COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))∧(UIncreasing(COND_126_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 ⇒ (UIncreasing(COND_126_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 ⇒ (UIncreasing(COND_126_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 ⇒ (UIncreasing(COND_126_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_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) the following chains were created:
  • We consider the chain 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0]))), COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1]))), 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_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_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1])))≥NonInfC∧COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1])))≥126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))∧(UIncreasing(126_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_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[0])))≥NonInfC∧COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[0])))≥126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0])))∧(UIncreasing(126_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 ⇒ (UIncreasing(126_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 ⇒ (UIncreasing(126_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 ⇒ (UIncreasing(126_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.
  • 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0, -1), >(x0, +(x0, 1))), java.lang.Object(ARRAY(x0)))

  • COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0))) → 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0)))




The constraints for P> respective Pbound 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 Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(126_0_MAIN_ARRAYLENGTH(x1)) = [-1] + [-1]x1   
POL(java.lang.Object(x1)) = [-1] + [-1]x1   
POL(ARRAY(x1)) = [-1] + [-1]x1   
POL(COND_126_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>:

126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))
COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[1])))

The following pairs are in Pbound:

126_0_MAIN_ARRAYLENGTH(java.lang.Object(ARRAY(x0[0]))) → COND_126_0_MAIN_ARRAYLENGTH(&&(>(x0[0], -1), >(x0[0], +(x0[0], 1))), java.lang.Object(ARRAY(x0[0])))
COND_126_0_MAIN_ARRAYLENGTH(TRUE, java.lang.Object(ARRAY(x0[1]))) → 126_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