Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇐)
↳2 FIGraph
↳3 FIGtoITRSProof (⇐)
↳4 ITRS
↳5 ITRStoIDPProof (⇔)
↳6 IDP
↳7 UsableRulesProof (⇔)
↳8 IDP
↳9 ItpfGraphProof (⇔)
↳10 IDP
↳11 IDPNonInfProof (⇐)
↳12 AND
    ↳13 IDP
        ↳14 IDependencyGraphProof (⇔)
        ↳15 TRUE
    ↳16 IDP
        ↳17 IDependencyGraphProof (⇔)
        ↳18 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
No human-readable program information known.

Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: Loop1

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 36 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

(4) Obligation:

ITRS 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 TRS R consists of the following rules:
Load113(java.lang.Object(ARRAY(i4, a6data)), i5) → Cond_Load113(i5 >= 0 && i5 < i4 && i5 + 1 > 0, java.lang.Object(ARRAY(i4, a6data)), i5)
Cond_Load113(TRUE, java.lang.Object(ARRAY(i4, a6data)), i5) → Load113(java.lang.Object(ARRAY(i4, a6data)), i5 + 1)
The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(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


The ITRS R consists of the following rules:
Load113(java.lang.Object(ARRAY(i4, a6data)), i5) → Cond_Load113(i5 >= 0 && i5 < i4 && i5 + 1 > 0, java.lang.Object(ARRAY(i4, a6data)), i5)
Cond_Load113(TRUE, java.lang.Object(ARRAY(i4, a6data)), i5) → Load113(java.lang.Object(ARRAY(i4, a6data)), i5 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0, java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])
(1): COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1] + 1)

(0) -> (1), if ((i5[0] →* i5[1])∧(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0 →* TRUE)∧(java.lang.Object(ARRAY(i4[0], a6data[0])) →* java.lang.Object(ARRAY(i4[1], a6data[1]))))


(1) -> (0), if ((java.lang.Object(ARRAY(i4[1], a6data[1])) →* java.lang.Object(ARRAY(i4[0], a6data[0])))∧(i5[1] + 1 →* i5[0]))



The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(7) 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.

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0, java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])
(1): COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1] + 1)

(0) -> (1), if ((i5[0] →* i5[1])∧(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0 →* TRUE)∧(java.lang.Object(ARRAY(i4[0], a6data[0])) →* java.lang.Object(ARRAY(i4[1], a6data[1]))))


(1) -> (0), if ((java.lang.Object(ARRAY(i4[1], a6data[1])) →* java.lang.Object(ARRAY(i4[0], a6data[0])))∧(i5[1] + 1 →* i5[0]))



The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(9) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0, java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])
(1): COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1] + 1)

(0) -> (1), if ((i5[0] →* i5[1])∧(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0 →* TRUE)∧((i4[0] →* i4[1])∧(a6data[0] →* a6data[1])))


(1) -> (0), if (((i4[1] →* i4[0])∧(a6data[1] →* a6data[0]))∧(i5[1] + 1 →* i5[0]))



The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(11) 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 LOAD113(java.lang.Object(ARRAY(i4, a6data)), i5) → COND_LOAD113(&&(&&(>=(i5, 0), <(i5, i4)), >(+(i5, 1), 0)), java.lang.Object(ARRAY(i4, a6data)), i5) the following chains were created:
  • We consider the chain LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]), COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1)) which results in the following constraint:

    (1)    (i5[0]=i5[1]∧&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0))=TRUE∧i4[0]=i4[1]∧a6data[0]=a6data[1] ⇒ LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])≥NonInfC∧LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])≥COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])∧(UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥))



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

    (2)    (>(+(i5[0], 1), 0)=TRUE∧>=(i5[0], 0)=TRUE∧<(i5[0], i4[0])=TRUE ⇒ LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])≥NonInfC∧LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])≥COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])∧(UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥))



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

    (3)    (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] + [-1] + [-1]i5[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]i5[0] + [bni_14]i4[0] ≥ 0∧[(-1)bso_15] ≥ 0)



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

    (4)    (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] + [-1] + [-1]i5[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]i5[0] + [bni_14]i4[0] ≥ 0∧[(-1)bso_15] ≥ 0)



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

    (5)    (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] + [-1] + [-1]i5[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]i5[0] + [bni_14]i4[0] ≥ 0∧[(-1)bso_15] ≥ 0)



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

    (6)    (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] + [-1] + [-1]i5[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧0 = 0∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]i5[0] + [bni_14]i4[0] ≥ 0∧0 = 0∧[(-1)bso_15] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧0 = 0∧[(-1)Bound*bni_14] + [bni_14]i4[0] ≥ 0∧0 = 0∧[(-1)bso_15] ≥ 0)







For Pair COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4, a6data)), i5) → LOAD113(java.lang.Object(ARRAY(i4, a6data)), +(i5, 1)) the following chains were created:
  • We consider the chain COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1)) which results in the following constraint:

    (8)    (COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1])≥NonInfC∧COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1])≥LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))∧(UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥))



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

    (9)    ((UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥)∧[1 + (-1)bso_17] ≥ 0)



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

    (10)    ((UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥)∧[1 + (-1)bso_17] ≥ 0)



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

    (11)    ((UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥)∧[1 + (-1)bso_17] ≥ 0)



    We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (12)    ((UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_17] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD113(java.lang.Object(ARRAY(i4, a6data)), i5) → COND_LOAD113(&&(&&(>=(i5, 0), <(i5, i4)), >(+(i5, 1), 0)), java.lang.Object(ARRAY(i4, a6data)), i5)
    • (i5[0] ≥ 0∧i5[0] ≥ 0∧i4[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])), ≥)∧0 = 0∧[(-1)Bound*bni_14] + [bni_14]i4[0] ≥ 0∧0 = 0∧[(-1)bso_15] ≥ 0)

  • COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4, a6data)), i5) → LOAD113(java.lang.Object(ARRAY(i4, a6data)), +(i5, 1))
    • ((UIncreasing(LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_17] ≥ 0)




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(LOAD113(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(java.lang.Object(x1)) = x1   
POL(ARRAY(x1, x2)) = [-1]x1   
POL(COND_LOAD113(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(<(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   

The following pairs are in P>:

COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), +(i5[1], 1))

The following pairs are in Pbound:

LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])

The following pairs are in P≥:

LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(&&(&&(>=(i5[0], 0), <(i5[0], i4[0])), >(+(i5[0], 1), 0)), java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])

There are no usable rules.

(12) Complex Obligation (AND)

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD113(java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0]) → COND_LOAD113(i5[0] >= 0 && i5[0] < i4[0] && i5[0] + 1 > 0, java.lang.Object(ARRAY(i4[0], a6data[0])), i5[0])


The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(14) IDependencyGraphProof (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


R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_LOAD113(TRUE, java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1]) → LOAD113(java.lang.Object(ARRAY(i4[1], a6data[1])), i5[1] + 1)


The set Q consists of the following terms:
Load113(java.lang.Object(ARRAY(x0, x1)), x2)
Cond_Load113(TRUE, java.lang.Object(ARRAY(x0, x1)), x2)

(17) IDependencyGraphProof (EQUIVALENT transformation)

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

(18) TRUE