Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:

No human-readable program information known.

Manifest-Version: 1.0 Created-By: 1.6.0_20 (Sun Microsystems Inc.) Main-Class: NestedLoop

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 313 nodes with 3 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

(4) Complex Obligation (AND)

(5) 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:
Load876(i103, i76) → Cond_Load876(i103 >= 0 && i103 < i76 - 1 && i103 + 1 > 0, i103, i76)
Cond_Load876(TRUE, i103, i76) → Load876(i103 + 1, i76)
The set Q consists of the following terms:
Load876(x0, x1)
Cond_Load876(TRUE, x0, x1)

(6) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(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:
Load876(i103, i76) → Cond_Load876(i103 >= 0 && i103 < i76 - 1 && i103 + 1 > 0, i103, i76)
Cond_Load876(TRUE, i103, i76) → Load876(i103 + 1, i76)

The integer pair graph contains the following rules and edges:
(0): LOAD876(i103[0], i76[0]) → COND_LOAD876(i103[0] >= 0 && i103[0] < i76[0] - 1 && i103[0] + 1 > 0, i103[0], i76[0])
(1): COND_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(i103[1] + 1, i76[1])

(0) -> (1), if ((i76[0] →^* i76[1])∧(i103[0] >= 0 && i103[0] < i76[0] - 1 && i103[0] + 1 > 0 →^* TRUE)∧(i103[0] →^* i103[1]))

(1) -> (0), if ((i103[1] + 1 →^* i103[0])∧(i76[1] →^* i76[0]))

The set Q consists of the following terms:
Load876(x0, x1)
Cond_Load876(TRUE, x0, x1)

(8) 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.

(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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD876(i103[0], i76[0]) → COND_LOAD876(i103[0] >= 0 && i103[0] < i76[0] - 1 && i103[0] + 1 > 0, i103[0], i76[0])
(1): COND_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(i103[1] + 1, i76[1])

(0) -> (1), if ((i76[0] →^* i76[1])∧(i103[0] >= 0 && i103[0] < i76[0] - 1 && i103[0] + 1 > 0 →^* TRUE)∧(i103[0] →^* i103[1]))

(1) -> (0), if ((i103[1] + 1 →^* i103[0])∧(i76[1] →^* i76[0]))

The set Q consists of the following terms:
Load876(x0, x1)
Cond_Load876(TRUE, x0, x1)

(10) 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 LOAD876(i103, i76) → COND_LOAD876(&&(&&(>=(i103, 0), <(i103, -(i76, 1))), >(+(i103, 1), 0)), i103, i76) the following chains were created:

• We consider the chain LOAD876(i103[0], i76[0]) → COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0]), COND_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(+(i103[1], 1), i76[1]) which results in the following constraint:
  

  (1)    (i76[0]=i76[1]∧&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0))=TRUE∧i103[0]=i103[1] ⇒ LOAD876(i103[0], i76[0])≥NonInfC∧LOAD876(i103[0], i76[0])≥COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])∧(U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥))

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

  (2)    (>(+(i103[0], 1), 0)=TRUE∧>=(i103[0], 0)=TRUE∧<(i103[0], -(i76[0], 1))=TRUE ⇒ LOAD876(i103[0], i76[0])≥NonInfC∧LOAD876(i103[0], i76[0])≥COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])∧(U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥))

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

  (3)    (i103[0] ≥ 0∧i103[0] ≥ 0∧i76[0] + [-2] + [-1]i103[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]i76[0] + [(-1)bni_11]i103[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

  (4)    (i103[0] ≥ 0∧i103[0] ≥ 0∧i76[0] + [-2] + [-1]i103[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]i76[0] + [(-1)bni_11]i103[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

  (5)    (i103[0] ≥ 0∧i103[0] ≥ 0∧i76[0] + [-2] + [-1]i103[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]i76[0] + [(-1)bni_11]i103[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

  (6)    (i103[0] ≥ 0∧i103[0] ≥ 0∧i76[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [bni_11]i76[0] ≥ 0∧[(-1)bso_12] ≥ 0)

  
  
  

For Pair COND_LOAD876(TRUE, i103, i76) → LOAD876(+(i103, 1), i76) the following chains were created:

• We consider the chain COND_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(+(i103[1], 1), i76[1]) which results in the following constraint:
  

  (7)    (COND_LOAD876(TRUE, i103[1], i76[1])≥NonInfC∧COND_LOAD876(TRUE, i103[1], i76[1])≥LOAD876(+(i103[1], 1), i76[1])∧(U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥))

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

  (8)    ((U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

  (9)    ((U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

  (10)    ((U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

  (11)    ((U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

  
  
  

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

• LOAD876(i103, i76) → COND_LOAD876(&&(&&(>=(i103, 0), <(i103, -(i76, 1))), >(+(i103, 1), 0)), i103, i76)
  
  • (i103[0] ≥ 0∧i103[0] ≥ 0∧i76[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [bni_11]i76[0] ≥ 0∧[(-1)bso_12] ≥ 0)
    
  
  
• COND_LOAD876(TRUE, i103, i76) → LOAD876(+(i103, 1), i76)
  
  • ((U^Increasing(LOAD876(+(i103[1], 1), i76[1])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 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(LOAD876(x₁, x₂)) = [-1] + x₂ + [-1]x₁   
POL(COND_LOAD876(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂   
POL(&&(x₁, x₂)) = [-1]   
POL(>=(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(<(x₁, x₂)) = [-1]   
POL(-(x₁, x₂)) = x₁ + [-1]x₂   
POL(1) = [1]   
POL(>(x₁, x₂)) = [-1]   
POL(+(x₁, x₂)) = x₁ + x₂   

The following pairs are in P_>:

COND_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(+(i103[1], 1), i76[1])

The following pairs are in P_bound:

LOAD876(i103[0], i76[0]) → COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])

The following pairs are in P_≥:

LOAD876(i103[0], i76[0]) → COND_LOAD876(&&(&&(>=(i103[0], 0), <(i103[0], -(i76[0], 1))), >(+(i103[0], 1), 0)), i103[0], i76[0])

There are no usable rules.

(11) Complex Obligation (AND)

(12) 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): LOAD876(i103[0], i76[0]) → COND_LOAD876(i103[0] >= 0 && i103[0] < i76[0] - 1 && i103[0] + 1 > 0, i103[0], i76[0])


The set Q consists of the following terms:
Load876(x0, x1)
Cond_Load876(TRUE, x0, x1)

(13) IDependencyGraphProof (EQUIVALENT transformation)

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

(14) TRUE

(15) 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_LOAD876(TRUE, i103[1], i76[1]) → LOAD876(i103[1] + 1, i76[1])


The set Q consists of the following terms:
Load876(x0, x1)
Cond_Load876(TRUE, x0, x1)

(16) IDependencyGraphProof (EQUIVALENT transformation)

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

(17) TRUE

(18) 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:
Inc1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775(i75, i94 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Load775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Cond_Load775ARR1(i105 >= i112 && i94 > 0 && i94 < i76 && i75 >= 0 && i75 < i76 && i94 + 1 > 0, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Cond_Load775ARR1(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Load775(i75, i94 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Load560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Cond_Load560ARR2(i105 >= i112 && i75 + 1 > 0 && i75 + 1 < i76 && i75 >= 0 && i75 < i76 && i75 < i76 - 1 && i75 + 1 + 1 > 0, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Cond_Load560ARR2(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Load775(i75, i75 + 1 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Load775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Cond_Load775ARR3(i94 > 0 && i94 < i76 && i75 >= 0 && i75 < i76 && i105 < i112, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Cond_Load775ARR3(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Inc1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52dataNew)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Load560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Cond_Load560ARR4(i75 + 1 > 0 && i75 + 1 < i76 && i75 >= 0 && i75 < i76 && i105 < i112 && i75 < i76 - 1, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Cond_Load560ARR4(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Inc1031(i75, i75 + 1, i76, java.lang.Object(ARRAY(i76, a52dataNew)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Cond_Load775(i94 > 0 && i76 >= 0 && i94 >= i76 && i75 + 1 > 0, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)))
Cond_Load775(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560(i75 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Cond_Load560(i75 + 1 > 0 && i76 >= 0 && i75 + 1 >= i76 && i75 < i76 - 1 && i75 + 1 > 0, i75, i76, java.lang.Object(ARRAY(i76, a52data)))
Cond_Load560(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560(i75 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(19) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(20) 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, Boolean

The ITRS R consists of the following rules:
Inc1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775(i75, i94 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Load775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Cond_Load775ARR1(i105 >= i112 && i94 > 0 && i94 < i76 && i75 >= 0 && i75 < i76 && i94 + 1 > 0, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Cond_Load775ARR1(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Load775(i75, i94 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Load560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Cond_Load560ARR2(i105 >= i112 && i75 + 1 > 0 && i75 + 1 < i76 && i75 >= 0 && i75 < i76 && i75 < i76 - 1 && i75 + 1 + 1 > 0, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
Cond_Load560ARR2(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → Load775(i75, i75 + 1 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Load775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Cond_Load775ARR3(i94 > 0 && i94 < i76 && i75 >= 0 && i75 < i76 && i105 < i112, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Cond_Load775ARR3(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Inc1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52dataNew)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Load560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Cond_Load560ARR4(i75 + 1 > 0 && i75 + 1 < i76 && i75 >= 0 && i75 < i76 && i105 < i112 && i75 < i76 - 1, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
Cond_Load560ARR4(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → Inc1031(i75, i75 + 1, i76, java.lang.Object(ARRAY(i76, a52dataNew)))
Load775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Cond_Load775(i94 > 0 && i76 >= 0 && i94 >= i76 && i75 + 1 > 0, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)))
Cond_Load775(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560(i75 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))
Load560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Cond_Load560(i75 + 1 > 0 && i76 >= 0 && i75 + 1 >= i76 && i75 < i76 - 1 && i75 + 1 > 0, i75, i76, java.lang.Object(ARRAY(i76, a52data)))
Cond_Load560(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data))) → Load560(i75 + 1, i76, java.lang.Object(ARRAY(i76, a52data)))

The integer pair graph contains the following rules and edges:
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(15): LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0, i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))
(16): COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(i75[16] + 1, i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))

(0) -> (1), if ((java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧(java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[7], a52data[7]))))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧(java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i75[0] →^* i75[13]))

(1) -> (2), if ((java.lang.Object(ARRAY(i76[1], a52data[1])) →^* java.lang.Object(ARRAY(i76[2], a52data[2])))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧(java.lang.Object(ARRAY(i76[2], a52data[2])) →^* java.lang.Object(ARRAY(i76[3], a52data[3])))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧(java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i76[3] →^* i76[1]))

(3) -> (7), if ((java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[7], a52data[7])))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(3) -> (13), if ((java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(4) -> (5), if ((java.lang.Object(ARRAY(i76[4], a52data[4])) →^* java.lang.Object(ARRAY(i76[5], a52data[5])))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧(java.lang.Object(ARRAY(i76[5], a52data[5])) →^* java.lang.Object(ARRAY(i76[6], a52data[6]))))

(6) -> (1), if ((i76[6] →^* i76[1])∧(java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(6) -> (7), if ((i75[6] →^* i75[7])∧(java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[7], a52data[7])))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(6) -> (13), if ((java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(7) -> (8), if ((i112[7] →^* i112[8])∧(java.lang.Object(ARRAY(i76[7], a52data[7])) →^* java.lang.Object(ARRAY(i76[8], a52data[8])))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧(java.lang.Object(ARRAY(i76[8], a52data[8])) →^* java.lang.Object(ARRAY(i76[9], a52data[9])))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(9) -> (0), if ((java.lang.Object(ARRAY(i76[9], a52dataNew[9])) →^* java.lang.Object(ARRAY(i76[0], a52data[0])))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(10) -> (11), if ((java.lang.Object(ARRAY(i76[10], a52data[10])) →^* java.lang.Object(ARRAY(i76[11], a52data[11])))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧(java.lang.Object(ARRAY(i76[11], a52data[11])) →^* java.lang.Object(ARRAY(i76[12], a52data[12])))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(12) -> (0), if ((java.lang.Object(ARRAY(i76[12], a52dataNew[12])) →^* java.lang.Object(ARRAY(i76[0], a52data[0])))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(13) -> (14), if ((java.lang.Object(ARRAY(i76[13], a52data[13])) →^* java.lang.Object(ARRAY(i76[14], a52data[14])))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[4], a52data[4])))∧(i76[14] →^* i76[4]))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[10], a52data[10])))∧(i76[14] →^* i76[10]))

(14) -> (15), if ((i75[14] + 1 →^* i75[15])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[15], a52data[15])))∧(i76[14] →^* i76[15]))

(15) -> (16), if ((java.lang.Object(ARRAY(i76[15], a52data[15])) →^* java.lang.Object(ARRAY(i76[16], a52data[16])))∧(i75[15] →^* i75[16])∧(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0 →^* TRUE)∧(i76[15] →^* i76[16]))

(16) -> (4), if ((i75[16] + 1 →^* i75[4])∧(i76[16] →^* i76[4])∧(java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[4], a52data[4]))))

(16) -> (10), if ((i76[16] →^* i76[10])∧(i75[16] + 1 →^* i75[10])∧(java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[10], a52data[10]))))

(16) -> (15), if ((java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[15], a52data[15])))∧(i75[16] + 1 →^* i75[15])∧(i76[16] →^* i76[15]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(21) 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.

(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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(15): LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0, i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))
(16): COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(i75[16] + 1, i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))

(0) -> (1), if ((java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧(java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[7], a52data[7]))))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧(java.lang.Object(ARRAY(i76[0], a52data[0])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i75[0] →^* i75[13]))

(1) -> (2), if ((java.lang.Object(ARRAY(i76[1], a52data[1])) →^* java.lang.Object(ARRAY(i76[2], a52data[2])))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧(java.lang.Object(ARRAY(i76[2], a52data[2])) →^* java.lang.Object(ARRAY(i76[3], a52data[3])))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧(java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i76[3] →^* i76[1]))

(3) -> (7), if ((java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[7], a52data[7])))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(3) -> (13), if ((java.lang.Object(ARRAY(i76[3], a52data[3])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(4) -> (5), if ((java.lang.Object(ARRAY(i76[4], a52data[4])) →^* java.lang.Object(ARRAY(i76[5], a52data[5])))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧(java.lang.Object(ARRAY(i76[5], a52data[5])) →^* java.lang.Object(ARRAY(i76[6], a52data[6]))))

(6) -> (1), if ((i76[6] →^* i76[1])∧(java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[1], a52data[1])))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(6) -> (7), if ((i75[6] →^* i75[7])∧(java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[7], a52data[7])))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(6) -> (13), if ((java.lang.Object(ARRAY(i76[6], a52data[6])) →^* java.lang.Object(ARRAY(i76[13], a52data[13])))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(7) -> (8), if ((i112[7] →^* i112[8])∧(java.lang.Object(ARRAY(i76[7], a52data[7])) →^* java.lang.Object(ARRAY(i76[8], a52data[8])))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧(java.lang.Object(ARRAY(i76[8], a52data[8])) →^* java.lang.Object(ARRAY(i76[9], a52data[9])))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(9) -> (0), if ((java.lang.Object(ARRAY(i76[9], a52dataNew[9])) →^* java.lang.Object(ARRAY(i76[0], a52data[0])))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(10) -> (11), if ((java.lang.Object(ARRAY(i76[10], a52data[10])) →^* java.lang.Object(ARRAY(i76[11], a52data[11])))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧(java.lang.Object(ARRAY(i76[11], a52data[11])) →^* java.lang.Object(ARRAY(i76[12], a52data[12])))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(12) -> (0), if ((java.lang.Object(ARRAY(i76[12], a52dataNew[12])) →^* java.lang.Object(ARRAY(i76[0], a52data[0])))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(13) -> (14), if ((java.lang.Object(ARRAY(i76[13], a52data[13])) →^* java.lang.Object(ARRAY(i76[14], a52data[14])))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[4], a52data[4])))∧(i76[14] →^* i76[4]))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[10], a52data[10])))∧(i76[14] →^* i76[10]))

(14) -> (15), if ((i75[14] + 1 →^* i75[15])∧(java.lang.Object(ARRAY(i76[14], a52data[14])) →^* java.lang.Object(ARRAY(i76[15], a52data[15])))∧(i76[14] →^* i76[15]))

(15) -> (16), if ((java.lang.Object(ARRAY(i76[15], a52data[15])) →^* java.lang.Object(ARRAY(i76[16], a52data[16])))∧(i75[15] →^* i75[16])∧(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0 →^* TRUE)∧(i76[15] →^* i76[16]))

(16) -> (4), if ((i75[16] + 1 →^* i75[4])∧(i76[16] →^* i76[4])∧(java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[4], a52data[4]))))

(16) -> (10), if ((i76[16] →^* i76[10])∧(i75[16] + 1 →^* i75[10])∧(java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[10], a52data[10]))))

(16) -> (15), if ((java.lang.Object(ARRAY(i76[16], a52data[16])) →^* java.lang.Object(ARRAY(i76[15], a52data[15])))∧(i75[16] + 1 →^* i75[15])∧(i76[16] →^* i76[15]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(23) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

(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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(15): LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0, i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))
(16): COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(i75[16] + 1, i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(4) -> (5), if (((i76[4] →^* i76[5])∧(a52data[4] →^* a52data[5]))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧((i76[5] →^* i76[6])∧(a52data[5] →^* a52data[6])))

(6) -> (1), if ((i76[6] →^* i76[1])∧((i76[6] →^* i76[1])∧(a52data[6] →^* a52data[1]))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(6) -> (7), if ((i75[6] →^* i75[7])∧((i76[6] →^* i76[7])∧(a52data[6] →^* a52data[7]))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(6) -> (13), if (((i76[6] →^* i76[13])∧(a52data[6] →^* a52data[13]))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(10) -> (11), if (((i76[10] →^* i76[11])∧(a52data[10] →^* a52data[11]))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧((i76[11] →^* i76[12])∧(a52data[11] →^* a52data[12]))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(13) -> (14), if (((i76[13] →^* i76[14])∧(a52data[13] →^* a52data[14]))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧((i76[14] →^* i76[4])∧(a52data[14] →^* a52data[4]))∧(i76[14] →^* i76[4]))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧((i76[14] →^* i76[10])∧(a52data[14] →^* a52data[10]))∧(i76[14] →^* i76[10]))

(14) -> (15), if ((i75[14] + 1 →^* i75[15])∧((i76[14] →^* i76[15])∧(a52data[14] →^* a52data[15]))∧(i76[14] →^* i76[15]))

(15) -> (16), if (((i76[15] →^* i76[16])∧(a52data[15] →^* a52data[16]))∧(i75[15] →^* i75[16])∧(i75[15] + 1 > 0 && i76[15] >= 0 && i75[15] + 1 >= i76[15] && i75[15] < i76[15] - 1 && i75[15] + 1 > 0 →^* TRUE)∧(i76[15] →^* i76[16]))

(16) -> (4), if ((i75[16] + 1 →^* i75[4])∧(i76[16] →^* i76[4])∧((i76[16] →^* i76[4])∧(a52data[16] →^* a52data[4])))

(16) -> (10), if ((i76[16] →^* i76[10])∧(i75[16] + 1 →^* i75[10])∧((i76[16] →^* i76[10])∧(a52data[16] →^* a52data[10])))

(16) -> (15), if (((i76[16] →^* i76[15])∧(a52data[16] →^* a52data[15]))∧(i75[16] + 1 →^* i75[15])∧(i76[16] →^* i76[15]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(25) 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 INC1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775(i75, +(i94, 1), i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) which results in the following constraint:
  

  (1)    (INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥NonInfC∧INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))∧(U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥))

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

  (2)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_34] ≥ 0)

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

  (3)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_34] ≥ 0)

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

  (4)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_34] ≥ 0)

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

  (5)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

  
  
  

For Pair LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) the following chains were created:

• We consider the chain LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) which results in the following constraint:
  

  (6)    (LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥NonInfC∧LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])∧(U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥))

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

  (7)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

  (8)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

  (9)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

  (10)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

  
  
  

For Pair LOAD775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105, i112), >(i94, 0)), <(i94, i76)), >=(i75, 0)), <(i75, i76)), >(+(i94, 1), 0)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) the following chains were created:

• We consider the chain LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]), COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (11)    (&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0))=TRUE∧i112[2]=i112[3]∧i94[2]=i94[3]∧i76[2]=i76[3]∧a52data[2]=a52data[3]∧i105[2]=i105[3]∧i75[2]=i75[3] ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (11) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (12)    (>(+(i94[2], 1), 0)=TRUE∧<(i75[2], i76[2])=TRUE∧>=(i75[2], 0)=TRUE∧<(i94[2], i76[2])=TRUE∧>=(i105[2], i112[2])=TRUE∧>(i94[2], 0)=TRUE ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (12) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (13)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (13) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (14)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (14) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (15)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (15) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (16)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (17)    ([1] + i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (18)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (19)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  
  We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (20)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  

  (21)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR1(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → LOAD775(i75, +(i94, 1), i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (22)    (COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥NonInfC∧COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))∧(U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥))

  
  
  We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (23)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_40] ≥ 0)

  
  
  We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (24)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_40] ≥ 0)

  
  
  We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (25)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_40] ≥ 0)

  
  
  We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (26)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)

  
  
  

For Pair LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) the following chains were created:

• We consider the chain LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4]) which results in the following constraint:
  

  (27)    (LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])))≥NonInfC∧LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])))≥LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])∧(U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥))

  
  
  We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (28)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_42] ≥ 0)

  
  
  We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (29)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_42] ≥ 0)

  
  
  We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (30)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_42] ≥ 0)

  
  
  We simplified constraint (30) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (31)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)

  
  
  

For Pair LOAD560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105, i112), >(+(i75, 1), 0)), <(+(i75, 1), i76)), >=(i75, 0)), <(i75, i76)), <(i75, -(i76, 1))), >(+(+(i75, 1), 1), 0)), i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) the following chains were created:

• We consider the chain LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]), COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6]))) which results in the following constraint:
  

  (32)    (i76[5]=i76[6]∧&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0))=TRUE∧i105[5]=i105[6]∧i112[5]=i112[6]∧i75[5]=i75[6]∧a52data[5]=a52data[6] ⇒ LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥NonInfC∧LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])∧(U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥))

  
  
  We simplified constraint (32) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (33)    (>(+(+(i75[5], 1), 1), 0)=TRUE∧<(i75[5], -(i76[5], 1))=TRUE∧<(i75[5], i76[5])=TRUE∧>=(i75[5], 0)=TRUE∧<(+(i75[5], 1), i76[5])=TRUE∧>=(i105[5], i112[5])=TRUE∧>(+(i75[5], 1), 0)=TRUE ⇒ LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥NonInfC∧LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])∧(U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥))

  
  
  We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (34)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (34) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (35)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (35) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (36)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (36) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (37)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (38)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (39)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (40)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  
  

  (41)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

  
  
  

For Pair COND_LOAD560ARR2(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → LOAD775(i75, +(+(i75, 1), 1), i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6]))) which results in the following constraint:
  

  (42)    (COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6])≥NonInfC∧COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6])≥LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))∧(U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥))

  
  
  We simplified constraint (42) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (43)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[(-1)bso_46] ≥ 0)

  
  
  We simplified constraint (43) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (44)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[(-1)bso_46] ≥ 0)

  
  
  We simplified constraint (44) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (45)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[(-1)bso_46] ≥ 0)

  
  
  We simplified constraint (45) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (46)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)

  
  
  

For Pair LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) the following chains were created:

• We consider the chain LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) which results in the following constraint:
  

  (47)    (LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥NonInfC∧LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])∧(U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥))

  
  
  We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (48)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_48] ≥ 0)

  
  
  We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (49)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_48] ≥ 0)

  
  
  We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (50)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_48] ≥ 0)

  
  
  We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (51)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)

  
  
  

For Pair LOAD775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94, 0), <(i94, i76)), >=(i75, 0)), <(i75, i76)), <(i105, i112)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) the following chains were created:

• We consider the chain LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]), COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (52)    (i105[8]=i105[9]∧i94[8]=i94[9]∧i76[8]=i76[9]∧i112[8]=i112[9]∧i131[8]=i131[9]∧a52data[8]=a52data[9]∧i75[8]=i75[9]∧i152[8]=i152[9]∧&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8]))=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

  
  
  We simplified constraint (52) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (53)    (<(i105[8], i112[8])=TRUE∧<(i75[8], i76[8])=TRUE∧>=(i75[8], 0)=TRUE∧>(i94[8], 0)=TRUE∧<(i94[8], i76[8])=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

  
  
  We simplified constraint (53) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (54)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (54) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (55)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (55) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (56)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (56) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (57)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (57) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (58)    (i112[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (58) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (59)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (59) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (60)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  
  We simplified constraint (60) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (61)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  

  (62)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR3(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → INC1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52dataNew))) the following chains were created:

• We consider the chain COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (63)    (COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥NonInfC∧COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))∧(U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥))

  
  
  We simplified constraint (63) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (64)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_52] ≥ 0)

  
  
  We simplified constraint (64) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (65)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_52] ≥ 0)

  
  
  We simplified constraint (65) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (66)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_52] ≥ 0)

  
  
  We simplified constraint (66) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (67)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)

  
  
  

For Pair LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) the following chains were created:

• We consider the chain LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10]) which results in the following constraint:
  

  (68)    (LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])))≥NonInfC∧LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])))≥LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])∧(U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥))

  
  
  We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (69)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[(-1)bso_54] ≥ 0)

  
  
  We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (70)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[(-1)bso_54] ≥ 0)

  
  
  We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (71)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[(-1)bso_54] ≥ 0)

  
  
  We simplified constraint (71) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (72)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_54] ≥ 0)

  
  
  

For Pair LOAD560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75, 1), 0), <(+(i75, 1), i76)), >=(i75, 0)), <(i75, i76)), <(i105, i112)), <(i75, -(i76, 1))), i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) the following chains were created:

• We consider the chain LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]), COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12]))) which results in the following constraint:
  

  (73)    (i112[11]=i112[12]∧i105[11]=i105[12]∧i76[11]=i76[12]∧i75[11]=i75[12]∧&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1)))=TRUE∧a52data[11]=a52data[12]∧i131[11]=i131[12]∧i152[11]=i152[12] ⇒ LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥NonInfC∧LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])∧(U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥))

  
  
  We simplified constraint (73) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (74)    (<(i75[11], -(i76[11], 1))=TRUE∧<(i105[11], i112[11])=TRUE∧<(i75[11], i76[11])=TRUE∧>=(i75[11], 0)=TRUE∧>(+(i75[11], 1), 0)=TRUE∧<(+(i75[11], 1), i76[11])=TRUE ⇒ LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥NonInfC∧LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])∧(U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥))

  
  
  We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (75)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (76)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (77)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (77) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (78)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (78) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (79)    (i76[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (79) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (80)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  
  
  We simplified constraint (80) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (81)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  
  

  (82)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  
  
  

For Pair COND_LOAD560ARR4(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → INC1031(i75, +(i75, 1), i76, java.lang.Object(ARRAY(i76, a52dataNew))) the following chains were created:

• We consider the chain COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12]))) which results in the following constraint:
  

  (83)    (COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12])≥NonInfC∧COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12])≥INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))∧(U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥))

  
  
  We simplified constraint (83) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (84)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_58] ≥ 0)

  
  
  We simplified constraint (84) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (85)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_58] ≥ 0)

  
  
  We simplified constraint (85) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (86)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_58] ≥ 0)

  
  
  We simplified constraint (86) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (87)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

  
  
  

For Pair LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → COND_LOAD775(&&(&&(&&(>(i94, 0), >=(i76, 0)), >=(i94, i76)), >(+(i75, 1), 0)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))), COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) which results in the following constraint:
  

  (88)    (i76[13]=i76[14]∧a52data[13]=a52data[14]∧i75[13]=i75[14]∧&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0))=TRUE∧i94[13]=i94[14] ⇒ LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥NonInfC∧LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))∧(U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥))

  
  
  We simplified constraint (88) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (89)    (>(+(i75[13], 1), 0)=TRUE∧>=(i94[13], i76[13])=TRUE∧>(i94[13], 0)=TRUE∧>=(i76[13], 0)=TRUE ⇒ LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥NonInfC∧LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))∧(U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥))

  
  
  We simplified constraint (89) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (90)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧[(-1)bso_60] ≥ 0)

  
  
  We simplified constraint (90) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (91)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧[(-1)bso_60] ≥ 0)

  
  
  We simplified constraint (91) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (92)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧[(-1)bso_60] ≥ 0)

  
  
  We simplified constraint (92) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (93)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧0 = 0∧[(-1)bso_60] ≥ 0)

  
  
  We simplified constraint (93) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (94)    (i75[13] ≥ 0∧i94[13] ≥ 0∧i76[13] + [-1] + i94[13] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧0 = 0∧[(-1)bso_60] ≥ 0)

  
  
  

For Pair COND_LOAD775(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560(+(i75, 1), i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) which results in the following constraint:
  

  (95)    (COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))≥NonInfC∧COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))≥LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))∧(U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥))

  
  
  We simplified constraint (95) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (96)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[1 + (-1)bso_62] ≥ 0)

  
  
  We simplified constraint (96) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (97)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[1 + (-1)bso_62] ≥ 0)

  
  
  We simplified constraint (97) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (98)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[1 + (-1)bso_62] ≥ 0)

  
  
  We simplified constraint (98) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (99)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_62] ≥ 0)

  
  
  

For Pair LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → COND_LOAD560(&&(&&(&&(&&(>(+(i75, 1), 0), >=(i76, 0)), >=(+(i75, 1), i76)), <(i75, -(i76, 1))), >(+(i75, 1), 0)), i75, i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))), COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) which results in the following constraint:
  

  (100)    (i76[15]=i76[16]∧a52data[15]=a52data[16]∧i75[15]=i75[16]∧&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0))=TRUE ⇒ LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))≥NonInfC∧LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))≥COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))∧(U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥))

  
  
  We simplified constraint (100) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (101)    (>(+(i75[15], 1), 0)=TRUE∧<(i75[15], -(i76[15], 1))=TRUE∧>=(+(i75[15], 1), i76[15])=TRUE∧>=(i76[15], 0)=TRUE ⇒ LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))≥NonInfC∧LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))≥COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))∧(U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥))

  
  
  We simplified constraint (101) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (102)    (i75[15] ≥ 0∧i76[15] + [-2] + [-1]i75[15] ≥ 0∧i75[15] + [1] + [-1]i76[15] ≥ 0∧i76[15] ≥ 0 ⇒ (U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i75[15] ≥ 0∧[(-1)bso_64] ≥ 0)

  
  
  We simplified constraint (102) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (103)    (i75[15] ≥ 0∧i76[15] + [-2] + [-1]i75[15] ≥ 0∧i75[15] + [1] + [-1]i76[15] ≥ 0∧i76[15] ≥ 0 ⇒ (U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i75[15] ≥ 0∧[(-1)bso_64] ≥ 0)

  
  
  We simplified constraint (103) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (104)    (i75[15] ≥ 0∧i76[15] + [-2] + [-1]i75[15] ≥ 0∧i75[15] + [1] + [-1]i76[15] ≥ 0∧i76[15] ≥ 0 ⇒ (U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i75[15] ≥ 0∧[(-1)bso_64] ≥ 0)

  
  
  We simplified constraint (104) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (105)    (i75[15] ≥ 0∧i76[15] + [-2] + [-1]i75[15] ≥ 0∧i75[15] + [1] + [-1]i76[15] ≥ 0∧i76[15] ≥ 0 ⇒ (U^Increasing(COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))), ≥)∧0 = 0∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i75[15] ≥ 0∧0 = 0∧[(-1)bso_64] ≥ 0)

  
  
  We solved constraint (105) using rule (IDP_SMT_SPLIT).

For Pair COND_LOAD560(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560(+(i75, 1), i76, java.lang.Object(ARRAY(i76, a52data))) the following chains were created:

• We consider the chain COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) which results in the following constraint:
  

  (106)    (COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))≥NonInfC∧COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))≥LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))∧(U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥))

  
  
  We simplified constraint (106) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (107)    ((U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥)∧[1 + (-1)bso_66] ≥ 0)

  
  
  We simplified constraint (107) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (108)    ((U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥)∧[1 + (-1)bso_66] ≥ 0)

  
  
  We simplified constraint (108) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (109)    ((U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥)∧[1 + (-1)bso_66] ≥ 0)

  
  
  We simplified constraint (109) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (110)    ((U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_66] ≥ 0)

  
  
  

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

• INC1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775(i75, +(i94, 1), i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)
    
  
  
• LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
  
  • ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)
    
  
  
• LOAD775ARR1(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105, i112), >(i94, 0)), <(i94, i76)), >=(i75, 0)), <(i75, i76)), >(+(i94, 1), 0)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
  
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)
    
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i75[2] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)
    
  
  
• COND_LOAD775ARR1(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → LOAD775(i75, +(i94, 1), i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)
    
  
  
• LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
  
  • ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)
    
  
  
• LOAD560ARR2(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105, i112), >(+(i75, 1), 0)), <(+(i75, 1), i76)), >=(i75, 0)), <(i75, i76)), <(i75, -(i76, 1))), >(+(+(i75, 1), 1), 0)), i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105)
  
  • (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)
    
  • (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]i75[5] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)
    
  
  
• COND_LOAD560ARR2(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i112, i105) → LOAD775(i75, +(+(i75, 1), 1), i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)
    
  
  
• LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
  
  • ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)
    
  
  
• LOAD775ARR3(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94, 0), <(i94, i76)), >=(i75, 0)), <(i75, i76)), <(i105, i112)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
  
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)
    
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i75[8] ≥ 0∧0 = 0∧[(-1)bso_50] ≥ 0)
    
  
  
• COND_LOAD775ARR3(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → INC1031(i75, i94, i76, java.lang.Object(ARRAY(i76, a52dataNew)))
  
  • ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)
    
  
  
• LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
  
  • ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_54] ≥ 0)
    
  
  
• LOAD560ARR4(i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75, 1), 0), <(+(i75, 1), i76)), >=(i75, 0)), <(i75, i76)), <(i105, i112)), <(i75, -(i76, 1))), i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105)
  
  • (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)
    
  • (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]i75[11] ≥ 0∧0 = 0∧[(-1)bso_56] ≥ 0)
    
  
  
• COND_LOAD560ARR4(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data)), i152, i131, i112, i105) → INC1031(i75, +(i75, 1), i76, java.lang.Object(ARRAY(i76, a52dataNew)))
  
  • ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)
    
  
  
• LOAD775(i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → COND_LOAD775(&&(&&(&&(>(i94, 0), >=(i76, 0)), >=(i94, i76)), >(+(i75, 1), 0)), i75, i94, i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • (i75[13] ≥ 0∧i94[13] ≥ 0∧i76[13] + [-1] + i94[13] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-1)bni_59 + (-1)Bound*bni_59] + [(-1)bni_59]i75[13] ≥ 0∧0 = 0∧[(-1)bso_60] ≥ 0)
    
  
  
• COND_LOAD775(TRUE, i75, i94, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560(+(i75, 1), i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_62] ≥ 0)
    
  
  
• LOAD560(i75, i76, java.lang.Object(ARRAY(i76, a52data))) → COND_LOAD560(&&(&&(&&(&&(>(+(i75, 1), 0), >=(i76, 0)), >=(+(i75, 1), i76)), <(i75, -(i76, 1))), >(+(i75, 1), 0)), i75, i76, java.lang.Object(ARRAY(i76, a52data)))
  
  
• COND_LOAD560(TRUE, i75, i76, java.lang.Object(ARRAY(i76, a52data))) → LOAD560(+(i75, 1), i76, java.lang.Object(ARRAY(i76, a52data)))
  
  • ((U^Increasing(LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_66] ≥ 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(INC1031(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₁   
POL(java.lang.Object(x₁)) = x₁   
POL(ARRAY(x₁, x₂)) = [-1]x₁   
POL(LOAD775(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₁   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₁   
POL(COND_LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = [-1] + [-1]x₅ + [-1]x₄ + [-1]x₂   
POL(&&(x₁, x₂)) = [-1]   
POL(>=(x₁, x₂)) = [-1]   
POL(>(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(<(x₁, x₂)) = [-1]   
POL(LOAD560(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁   
POL(LOAD560ARR2(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁   
POL(COND_LOAD560ARR2(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂   
POL(-(x₁, x₂)) = x₁ + [-1]x₂   
POL(LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₁   
POL(COND_LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)) = [-1] + [-1]x₅ + [-1]x₄ + [-1]x₂   
POL(LOAD560ARR4(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁   
POL(COND_LOAD560ARR4(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂   
POL(COND_LOAD775(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₅ + [-1]x₄ + [-1]x₂   
POL(COND_LOAD560(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂   

The following pairs are in P_>:

COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))
COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(+(i75[16], 1), i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))

The following pairs are in P_bound:

LOAD560(i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15]))) → COND_LOAD560(&&(&&(&&(&&(>(+(i75[15], 1), 0), >=(i76[15], 0)), >=(+(i75[15], 1), i76[15])), <(i75[15], -(i76[15], 1))), >(+(i75[15], 1), 0)), i75[15], i76[15], java.lang.Object(ARRAY(i76[15], a52data[15])))

The following pairs are in P_≥:

INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))

There are no usable rules.

(26) Complex Obligation (AND)

(27) 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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(6) -> (1), if ((i76[6] →^* i76[1])∧((i76[6] →^* i76[1])∧(a52data[6] →^* a52data[1]))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(4) -> (5), if (((i76[4] →^* i76[5])∧(a52data[4] →^* a52data[5]))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧((i76[5] →^* i76[6])∧(a52data[5] →^* a52data[6])))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(6) -> (7), if ((i75[6] →^* i75[7])∧((i76[6] →^* i76[7])∧(a52data[6] →^* a52data[7]))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(10) -> (11), if (((i76[10] →^* i76[11])∧(a52data[10] →^* a52data[11]))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧((i76[11] →^* i76[12])∧(a52data[11] →^* a52data[12]))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(6) -> (13), if (((i76[6] →^* i76[13])∧(a52data[6] →^* a52data[13]))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(28) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes.

(29) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(30) 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 COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) the following chains were created:

• We consider the chain COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (1)    (COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥NonInfC∧COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))∧(U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥))

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

  (2)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (3)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (4)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (5)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)

  
  
  

For Pair LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) the following chains were created:

• We consider the chain LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]), COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (6)    (i105[8]=i105[9]∧i94[8]=i94[9]∧i76[8]=i76[9]∧i112[8]=i112[9]∧i131[8]=i131[9]∧a52data[8]=a52data[9]∧i75[8]=i75[9]∧i152[8]=i152[9]∧&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8]))=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

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

  (7)    (<(i105[8], i112[8])=TRUE∧<(i75[8], i76[8])=TRUE∧>=(i75[8], 0)=TRUE∧>(i94[8], 0)=TRUE∧<(i94[8], i76[8])=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

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

  (8)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i76[8] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (9)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i76[8] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (10)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i76[8] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (11)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

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

  (12)    (i112[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  
  We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (13)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  
  We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (14)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  
  We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (15)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  

  (16)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  
  

For Pair LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) the following chains were created:

• We consider the chain LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) which results in the following constraint:
  

  (17)    (LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥NonInfC∧LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])∧(U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥))

  
  
  We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (18)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (19)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (20)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (20) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (21)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_22] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) the following chains were created:

• We consider the chain COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (22)    (COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥NonInfC∧COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))∧(U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥))

  
  
  We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (23)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (24)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (25)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (26)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)

  
  
  

For Pair LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) the following chains were created:

• We consider the chain LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]), COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (27)    (&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0))=TRUE∧i112[2]=i112[3]∧i94[2]=i94[3]∧i76[2]=i76[3]∧a52data[2]=a52data[3]∧i105[2]=i105[3]∧i75[2]=i75[3] ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (27) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (28)    (>(+(i94[2], 1), 0)=TRUE∧<(i75[2], i76[2])=TRUE∧>=(i75[2], 0)=TRUE∧<(i94[2], i76[2])=TRUE∧>=(i105[2], i112[2])=TRUE∧>(i94[2], 0)=TRUE ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (29)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (30)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (31)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (32)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (33)    ([1] + i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-2)bni_25 + (-1)Bound*bni_25] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (34)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (35)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  
  We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (36)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  

  (37)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  
  
  

For Pair LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) the following chains were created:

• We consider the chain LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) which results in the following constraint:
  

  (38)    (LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥NonInfC∧LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])∧(U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥))

  
  
  We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (39)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_28] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (40)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_28] ≥ 0)

  
  
  We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (41)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_28] ≥ 0)

  
  
  We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (42)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)

  
  
  

For Pair INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) the following chains were created:

• We consider the chain INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) which results in the following constraint:
  

  (43)    (INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥NonInfC∧INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))∧(U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥))

  
  
  We simplified constraint (43) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (44)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[1 + (-1)bso_30] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (45)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[1 + (-1)bso_30] ≥ 0)

  
  
  We simplified constraint (45) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (46)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[1 + (-1)bso_30] ≥ 0)

  
  
  We simplified constraint (46) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (47)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

  
  
  

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

• COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
  
  • ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)
    
  
  
• LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
  
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)
    
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]i94[8] + [bni_19]i75[8] + [bni_19]i76[8] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)
    
  
  
• LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
  
  • ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_22] ≥ 0)
    
  
  
• COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
  
  • ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)
    
  
  
• LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
  
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)
    
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25 + (-1)bni_25] + [bni_25]i75[2] + [bni_25]i76[2] + [(-1)bni_25]i94[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)
    
  
  
• LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
  
  • ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)
    
  
  
• INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
  
  • ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_30] ≥ 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(COND_LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)) = [-1] + [-1]x₃ + x₄   
POL(java.lang.Object(x₁)) = x₁   
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁   
POL(INC1031(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + x₃   
POL(LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [-1]x₂ + x₃   
POL(&&(x₁, x₂)) = [-1]   
POL(>(x₁, x₂)) = 0   
POL(0) = 0   
POL(<(x₁, x₂)) = 0   
POL(>=(x₁, x₂)) = [-1]   
POL(LOAD775(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + x₃   
POL(COND_LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = [-1] + x₄ + [-1]x₃   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + x₃ + [-1]x₂   

The following pairs are in P_>:

COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

The following pairs are in P_bound:

LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])

The following pairs are in P_≥:

COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])

There are no usable rules.

(31) Complex Obligation (AND)

(32) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(33) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 5 less nodes.

(34) TRUE

(35) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(36) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 5 less nodes.

(37) TRUE

(38) 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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(16): COND_LOAD560(TRUE, i75[16], i76[16], java.lang.Object(ARRAY(i76[16], a52data[16]))) → LOAD560(i75[16] + 1, i76[16], java.lang.Object(ARRAY(i76[16], a52data[16])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(6) -> (1), if ((i76[6] →^* i76[1])∧((i76[6] →^* i76[1])∧(a52data[6] →^* a52data[1]))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧((i76[14] →^* i76[4])∧(a52data[14] →^* a52data[4]))∧(i76[14] →^* i76[4]))

(16) -> (4), if ((i75[16] + 1 →^* i75[4])∧(i76[16] →^* i76[4])∧((i76[16] →^* i76[4])∧(a52data[16] →^* a52data[4])))

(4) -> (5), if (((i76[4] →^* i76[5])∧(a52data[4] →^* a52data[5]))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧((i76[5] →^* i76[6])∧(a52data[5] →^* a52data[6])))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(6) -> (7), if ((i75[6] →^* i75[7])∧((i76[6] →^* i76[7])∧(a52data[6] →^* a52data[7]))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧((i76[14] →^* i76[10])∧(a52data[14] →^* a52data[10]))∧(i76[14] →^* i76[10]))

(16) -> (10), if ((i76[16] →^* i76[10])∧(i75[16] + 1 →^* i75[10])∧((i76[16] →^* i76[10])∧(a52data[16] →^* a52data[10])))

(10) -> (11), if (((i76[10] →^* i76[11])∧(a52data[10] →^* a52data[11]))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧((i76[11] →^* i76[12])∧(a52data[11] →^* a52data[12]))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(6) -> (13), if (((i76[6] →^* i76[13])∧(a52data[6] →^* a52data[13]))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(13) -> (14), if (((i76[13] →^* i76[14])∧(a52data[13] →^* a52data[14]))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(39) IDependencyGraphProof (EQUIVALENT transformation)

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

(40) 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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(6) -> (1), if ((i76[6] →^* i76[1])∧((i76[6] →^* i76[1])∧(a52data[6] →^* a52data[1]))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧((i76[14] →^* i76[4])∧(a52data[14] →^* a52data[4]))∧(i76[14] →^* i76[4]))

(4) -> (5), if (((i76[4] →^* i76[5])∧(a52data[4] →^* a52data[5]))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(5) -> (6), if ((i76[5] →^* i76[6])∧(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0 →^* TRUE)∧(i105[5] →^* i105[6])∧(i112[5] →^* i112[6])∧(i75[5] →^* i75[6])∧((i76[5] →^* i76[6])∧(a52data[5] →^* a52data[6])))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(6) -> (7), if ((i75[6] →^* i75[7])∧((i76[6] →^* i76[7])∧(a52data[6] →^* a52data[7]))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧((i76[14] →^* i76[10])∧(a52data[14] →^* a52data[10]))∧(i76[14] →^* i76[10]))

(10) -> (11), if (((i76[10] →^* i76[11])∧(a52data[10] →^* a52data[11]))∧(i112[10] →^* i112[11])∧(i76[10] →^* i76[11])∧(i75[10] →^* i75[11])∧(i131[10] →^* i131[11])∧(i105[10] →^* i105[11])∧(i152[10] →^* i152[11]))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧((i76[11] →^* i76[12])∧(a52data[11] →^* a52data[12]))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(6) -> (13), if (((i76[6] →^* i76[13])∧(a52data[6] →^* a52data[13]))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(13) -> (14), if (((i76[13] →^* i76[14])∧(a52data[13] →^* a52data[14]))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(41) 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 COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12]))) the following chains were created:

• We consider the chain COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12]))) which results in the following constraint:
  

  (1)    (COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12])≥NonInfC∧COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12])≥INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))∧(U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥))

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

  (2)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_21] ≥ 0)

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

  (3)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_21] ≥ 0)

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

  (4)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧[(-1)bso_21] ≥ 0)

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

  (5)    ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

  
  
  

For Pair LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) the following chains were created:

• We consider the chain LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]), COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12]))) which results in the following constraint:
  

  (6)    (i112[11]=i112[12]∧i105[11]=i105[12]∧i76[11]=i76[12]∧i75[11]=i75[12]∧&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1)))=TRUE∧a52data[11]=a52data[12]∧i131[11]=i131[12]∧i152[11]=i152[12] ⇒ LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥NonInfC∧LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])∧(U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥))

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

  (7)    (<(i75[11], -(i76[11], 1))=TRUE∧<(i105[11], i112[11])=TRUE∧<(i75[11], i76[11])=TRUE∧>=(i75[11], 0)=TRUE∧>(+(i75[11], 1), 0)=TRUE∧<(+(i75[11], 1), i76[11])=TRUE ⇒ LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥NonInfC∧LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])≥COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])∧(U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥))

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

  (8)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-3)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]i76[11] + [(-1)bni_22]i75[11] ≥ 0∧[(-1)bso_23] ≥ 0)

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

  (9)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-3)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]i76[11] + [(-1)bni_22]i75[11] ≥ 0∧[(-1)bso_23] ≥ 0)

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

  (10)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧[(-3)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]i76[11] + [(-1)bni_22]i75[11] ≥ 0∧[(-1)bso_23] ≥ 0)

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

  (11)    (i76[11] + [-2] + [-1]i75[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧i76[11] + [-1] + [-1]i75[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] + [-2] + [-1]i75[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(-3)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]i76[11] + [(-1)bni_22]i75[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

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

  (12)    (i76[11] ≥ 0∧i112[11] + [-1] + [-1]i105[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (13)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (14)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  

  (15)    (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  

For Pair LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10]) the following chains were created:

• We consider the chain LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10]) which results in the following constraint:
  

  (16)    (LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])))≥NonInfC∧LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])))≥LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])∧(U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥))

  
  
  We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (17)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[1 + (-1)bso_25] ≥ 0)

  
  
  We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (18)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[1 + (-1)bso_25] ≥ 0)

  
  
  We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (19)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧[1 + (-1)bso_25] ≥ 0)

  
  
  We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (20)    ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)

  
  
  

For Pair COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6]))) the following chains were created:

• We consider the chain COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6]))) which results in the following constraint:
  

  (21)    (COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6])≥NonInfC∧COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6])≥LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))∧(U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥))

  
  
  We simplified constraint (21) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (22)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[1 + (-1)bso_27] ≥ 0)

  
  
  We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (23)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[1 + (-1)bso_27] ≥ 0)

  
  
  We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (24)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧[1 + (-1)bso_27] ≥ 0)

  
  
  We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (25)    ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

  
  
  

For Pair LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) the following chains were created:

• We consider the chain LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]), COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6]))) which results in the following constraint:
  

  (26)    (i76[5]=i76[6]∧&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0))=TRUE∧i105[5]=i105[6]∧i112[5]=i112[6]∧i75[5]=i75[6]∧a52data[5]=a52data[6] ⇒ LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥NonInfC∧LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])∧(U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥))

  
  
  We simplified constraint (26) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (27)    (>(+(+(i75[5], 1), 1), 0)=TRUE∧<(i75[5], -(i76[5], 1))=TRUE∧<(i75[5], i76[5])=TRUE∧>=(i75[5], 0)=TRUE∧<(+(i75[5], 1), i76[5])=TRUE∧>=(i105[5], i112[5])=TRUE∧>(+(i75[5], 1), 0)=TRUE ⇒ LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥NonInfC∧LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])≥COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])∧(U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥))

  
  
  We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (28)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-2)bni_28 + (-1)Bound*bni_28] + [(3)bni_28]i76[5] + [(-1)bni_28]i75[5] ≥ 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (29)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-2)bni_28 + (-1)Bound*bni_28] + [(3)bni_28]i76[5] + [(-1)bni_28]i75[5] ≥ 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (30)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧[(-2)bni_28 + (-1)Bound*bni_28] + [(3)bni_28]i76[5] + [(-1)bni_28]i75[5] ≥ 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (30) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (31)    (i75[5] + [1] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i76[5] + [-1] + [-1]i75[5] ≥ 0∧i75[5] ≥ 0∧i76[5] + [-2] + [-1]i75[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(-2)bni_28 + (-1)Bound*bni_28] + [(3)bni_28]i76[5] + [(-1)bni_28]i75[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (32)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] + [-1]i112[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (33)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)

  
  
  We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (34)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)

  
  

  (35)    (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)

  
  
  

For Pair LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4]) the following chains were created:

• We consider the chain LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4]) which results in the following constraint:
  

  (36)    (LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])))≥NonInfC∧LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])))≥LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])∧(U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥))

  
  
  We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (37)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_31] ≥ 0)

  
  
  We simplified constraint (37) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (38)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_31] ≥ 0)

  
  
  We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (39)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧[(-1)bso_31] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (40)    ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)

  
  
  

For Pair COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) the following chains were created:

• We consider the chain COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) which results in the following constraint:
  

  (41)    (COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))≥NonInfC∧COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))≥LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))∧(U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥))

  
  
  We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (42)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[(-1)bso_33] ≥ 0)

  
  
  We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (43)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[(-1)bso_33] ≥ 0)

  
  
  We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (44)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧[(-1)bso_33] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (45)    ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)

  
  
  

For Pair LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) the following chains were created:

• We consider the chain LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))), COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) which results in the following constraint:
  

  (46)    (i76[13]=i76[14]∧a52data[13]=a52data[14]∧i75[13]=i75[14]∧&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0))=TRUE∧i94[13]=i94[14] ⇒ LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥NonInfC∧LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))∧(U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥))

  
  
  We simplified constraint (46) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (47)    (>(+(i75[13], 1), 0)=TRUE∧>=(i94[13], i76[13])=TRUE∧>(i94[13], 0)=TRUE∧>=(i76[13], 0)=TRUE ⇒ LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥NonInfC∧LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))≥COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))∧(U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥))

  
  
  We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (48)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧[(-1)bso_35] ≥ 0)

  
  
  We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (49)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧[(-1)bso_35] ≥ 0)

  
  
  We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (50)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧[(-1)bso_35] ≥ 0)

  
  
  We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (51)    (i75[13] ≥ 0∧i94[13] + [-1]i76[13] ≥ 0∧i94[13] + [-1] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

  
  
  We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (52)    (i75[13] ≥ 0∧i94[13] ≥ 0∧i76[13] + [-1] + i94[13] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) the following chains were created:

• We consider the chain COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (53)    (COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥NonInfC∧COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))∧(U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥))

  
  
  We simplified constraint (53) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (54)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_37] ≥ 0)

  
  
  We simplified constraint (54) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (55)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_37] ≥ 0)

  
  
  We simplified constraint (55) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (56)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_37] ≥ 0)

  
  
  We simplified constraint (56) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (57)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

  
  
  

For Pair LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) the following chains were created:

• We consider the chain LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]), COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (58)    (i105[8]=i105[9]∧i94[8]=i94[9]∧i76[8]=i76[9]∧i112[8]=i112[9]∧i131[8]=i131[9]∧a52data[8]=a52data[9]∧i75[8]=i75[9]∧i152[8]=i152[9]∧&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8]))=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

  
  
  We simplified constraint (58) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (59)    (<(i105[8], i112[8])=TRUE∧<(i75[8], i76[8])=TRUE∧>=(i75[8], 0)=TRUE∧>(i94[8], 0)=TRUE∧<(i94[8], i76[8])=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

  
  
  We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (60)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-3)bni_38 + (-1)Bound*bni_38] + [(3)bni_38]i76[8] + [(-1)bni_38]i75[8] ≥ 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (61)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-3)bni_38 + (-1)Bound*bni_38] + [(3)bni_38]i76[8] + [(-1)bni_38]i75[8] ≥ 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (62)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-3)bni_38 + (-1)Bound*bni_38] + [(3)bni_38]i76[8] + [(-1)bni_38]i75[8] ≥ 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (62) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (63)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-3)bni_38 + (-1)Bound*bni_38] + [(3)bni_38]i76[8] + [(-1)bni_38]i75[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (64)    (i112[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-3)bni_38 + (-1)Bound*bni_38] + [(3)bni_38]i76[8] + [(-1)bni_38]i75[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (65)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (65) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (66)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  
  We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (67)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  

  (68)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  
  
  

For Pair LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) the following chains were created:

• We consider the chain LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) which results in the following constraint:
  

  (69)    (LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥NonInfC∧LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])∧(U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥))

  
  
  We simplified constraint (69) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (70)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_41] ≥ 0)

  
  
  We simplified constraint (70) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (71)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_41] ≥ 0)

  
  
  We simplified constraint (71) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (72)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[(-1)bso_41] ≥ 0)

  
  
  We simplified constraint (72) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (73)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) the following chains were created:

• We consider the chain COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (74)    (COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥NonInfC∧COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))∧(U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥))

  
  
  We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (75)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_43] ≥ 0)

  
  
  We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (76)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_43] ≥ 0)

  
  
  We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (77)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[(-1)bso_43] ≥ 0)

  
  
  We simplified constraint (77) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (78)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

  
  
  

For Pair LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) the following chains were created:

• We consider the chain LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]), COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (79)    (&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0))=TRUE∧i112[2]=i112[3]∧i94[2]=i94[3]∧i76[2]=i76[3]∧a52data[2]=a52data[3]∧i105[2]=i105[3]∧i75[2]=i75[3] ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (79) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (80)    (>(+(i94[2], 1), 0)=TRUE∧<(i75[2], i76[2])=TRUE∧>=(i75[2], 0)=TRUE∧<(i94[2], i76[2])=TRUE∧>=(i105[2], i112[2])=TRUE∧>(i94[2], 0)=TRUE ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (81)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-3)bni_44 + (-1)Bound*bni_44] + [(3)bni_44]i76[2] + [(-1)bni_44]i75[2] ≥ 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (82)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-3)bni_44 + (-1)Bound*bni_44] + [(3)bni_44]i76[2] + [(-1)bni_44]i75[2] ≥ 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (83)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-3)bni_44 + (-1)Bound*bni_44] + [(3)bni_44]i76[2] + [(-1)bni_44]i75[2] ≥ 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (84)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-3)bni_44 + (-1)Bound*bni_44] + [(3)bni_44]i76[2] + [(-1)bni_44]i75[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (84) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (85)    ([1] + i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-3)bni_44 + (-1)Bound*bni_44] + [(3)bni_44]i76[2] + [(-1)bni_44]i75[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (85) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (86)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (86) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (87)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  
  We simplified constraint (87) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (88)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  

  (89)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  
  
  

For Pair LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) the following chains were created:

• We consider the chain LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) which results in the following constraint:
  

  (90)    (LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥NonInfC∧LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])∧(U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥))

  
  
  We simplified constraint (90) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (91)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_47] ≥ 0)

  
  
  We simplified constraint (91) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (92)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_47] ≥ 0)

  
  
  We simplified constraint (92) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (93)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_47] ≥ 0)

  
  
  We simplified constraint (93) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (94)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

  
  
  

For Pair INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) the following chains were created:

• We consider the chain INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) which results in the following constraint:
  

  (95)    (INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥NonInfC∧INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))∧(U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥))

  
  
  We simplified constraint (95) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (96)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_49] ≥ 0)

  
  
  We simplified constraint (96) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (97)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_49] ≥ 0)

  
  
  We simplified constraint (97) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (98)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_49] ≥ 0)

  
  
  We simplified constraint (98) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (99)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

  
  
  

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

• COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
  
  • ((U^Increasing(INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)
    
  
  
• LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
  
  • (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)
    
  • (i76[11] ≥ 0∧i112[11] ≥ 0∧[1] + i76[11] ≥ 0∧i75[11] ≥ 0∧i75[11] ≥ 0∧i76[11] ≥ 0∧i105[11] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])), ≥)∧0 = 0∧[(3)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i75[11] + [(3)bni_22]i76[11] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)
    
  
  
• LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
  
  • ((U^Increasing(LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)
    
  
  
• COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
  
  • ((U^Increasing(LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)
    
  
  
• LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
  
  • (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)
    
  • (i75[5] + [1] ≥ 0∧i76[5] ≥ 0∧[1] + i76[5] ≥ 0∧i75[5] ≥ 0∧i76[5] ≥ 0∧i105[5] ≥ 0∧i75[5] ≥ 0∧i112[5] ≥ 0 ⇒ (U^Increasing(COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])), ≥)∧0 = 0∧[(4)bni_28 + (-1)Bound*bni_28] + [(2)bni_28]i75[5] + [(3)bni_28]i76[5] ≥ 0∧0 = 0∧[(-1)bso_29] ≥ 0)
    
  
  
• LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
  
  • ((U^Increasing(LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)
    
  
  
• COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
  
  • ((U^Increasing(LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)
    
  
  
• LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
  
  • (i75[13] ≥ 0∧i94[13] ≥ 0∧i76[13] + [-1] + i94[13] ≥ 0∧i76[13] ≥ 0 ⇒ (U^Increasing(COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))), ≥)∧0 = 0∧[(-3)bni_34 + (-1)Bound*bni_34] + [(3)bni_34]i76[13] + [(-1)bni_34]i75[13] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)
    
  
  
• COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
  
  • ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
    
  
  
• LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
  
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)
    
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_38] + [(2)bni_38]i75[8] + [(3)bni_38]i76[8] ≥ 0∧0 = 0∧[(-1)bso_39] ≥ 0)
    
  
  
• LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
  
  • ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
    
  
  
• COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
  
  • ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
    
  
  
• LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
  
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)
    
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_44] + [(2)bni_44]i75[2] + [(3)bni_44]i76[2] ≥ 0∧0 = 0∧[(-1)bso_45] ≥ 0)
    
  
  
• LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
  
  • ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    
  
  
• INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
  
  • ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 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(COND_LOAD560ARR4(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [2]x₃ + [-1]x₂ + [-1]x₄   
POL(java.lang.Object(x₁)) = x₁   
POL(ARRAY(x₁, x₂)) = [2] + [-1]x₁   
POL(INC1031(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [2]x₃ + [-1]x₁   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(LOAD560ARR4(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = [-1] + [2]x₂ + [-1]x₁ + [-1]x₃   
POL(&&(x₁, x₂)) = 0   
POL(>(x₁, x₂)) = 0   
POL(0) = 0   
POL(<(x₁, x₂)) = [-1]   
POL(>=(x₁, x₂)) = [-1]   
POL(-(x₁, x₂)) = x₁ + [-1]x₂   
POL(LOAD560(x₁, x₂, x₃)) = [2]x₂ + [-1]x₁ + [-1]x₃   
POL(COND_LOAD560ARR2(x₁, x₂, x₃, x₄, x₅, x₆)) = [2]x₃ + [-1]x₂ + [-1]x₄   
POL(LOAD775(x₁, x₂, x₃, x₄)) = [-1] + [2]x₃ + [-1]x₁ + [-1]x₄   
POL(LOAD560ARR2(x₁, x₂, x₃, x₄, x₅)) = [2]x₂ + [-1]x₁ + [-1]x₃   
POL(COND_LOAD775(x₁, x₂, x₃, x₄, x₅)) = [-1] + [2]x₄ + [-1]x₂ + [-1]x₅   
POL(COND_LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)) = [-1] + [2]x₄ + [-1]x₂ + [-1]x₅   
POL(LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [2]x₃ + [-1]x₁ + [-1]x₄   
POL(COND_LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = [-1] + [2]x₄ + [-1]x₂ + [-1]x₅   
POL(LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [2]x₃ + [-1]x₁ + [-1]x₄   

The following pairs are in P_>:

LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], +(+(i75[6], 1), 1), i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))

The following pairs are in P_bound:

LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])

The following pairs are in P_≥:

COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], +(i75[12], 1), i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(&&(&&(&&(&&(&&(>(+(i75[11], 1), 0), <(+(i75[11], 1), i76[11])), >=(i75[11], 0)), <(i75[11], i76[11])), <(i105[11], i112[11])), <(i75[11], -(i76[11], 1))), i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(&&(&&(&&(&&(&&(&&(>=(i105[5], i112[5]), >(+(i75[5], 1), 0)), <(+(i75[5], 1), i76[5])), >=(i75[5], 0)), <(i75[5], i76[5])), <(i75[5], -(i76[5], 1))), >(+(+(i75[5], 1), 1), 0)), i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(+(i75[14], 1), i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(&&(&&(&&(>(i94[13], 0), >=(i76[13], 0)), >=(i94[13], i76[13])), >(+(i75[13], 1), 0)), i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

There are no usable rules.

(42) Complex Obligation (AND)

(43) 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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(11): LOAD560ARR4(i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11]) → COND_LOAD560ARR4(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1, i75[11], i76[11], java.lang.Object(ARRAY(i76[11], a52data[11])), i152[11], i131[11], i112[11], i105[11])
(5): LOAD560ARR2(i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5]) → COND_LOAD560ARR2(i105[5] >= i112[5] && i75[5] + 1 > 0 && i75[5] + 1 < i76[5] && i75[5] >= 0 && i75[5] < i76[5] && i75[5] < i76[5] - 1 && i75[5] + 1 + 1 > 0, i75[5], i76[5], java.lang.Object(ARRAY(i76[5], a52data[5])), i112[5], i105[5])
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧((i76[14] →^* i76[4])∧(a52data[14] →^* a52data[4]))∧(i76[14] →^* i76[4]))

(4) -> (5), if (((i76[4] →^* i76[5])∧(a52data[4] →^* a52data[5]))∧(i76[4] →^* i76[5])∧(i112[4] →^* i112[5])∧(i105[4] →^* i105[5])∧(i75[4] →^* i75[5]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

(11) -> (12), if ((i112[11] →^* i112[12])∧(i105[11] →^* i105[12])∧(i76[11] →^* i76[12])∧(i75[11] →^* i75[12])∧(i75[11] + 1 > 0 && i75[11] + 1 < i76[11] && i75[11] >= 0 && i75[11] < i76[11] && i105[11] < i112[11] && i75[11] < i76[11] - 1 →^* TRUE)∧((i76[11] →^* i76[12])∧(a52data[11] →^* a52data[12]))∧(i131[11] →^* i131[12])∧(i152[11] →^* i152[12]))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(13) -> (14), if (((i76[13] →^* i76[14])∧(a52data[13] →^* a52data[14]))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(44) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes.

(45) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(2) -> (3), if ((i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0 →^* TRUE)∧(i112[2] →^* i112[3])∧(i94[2] →^* i94[3])∧(i76[2] →^* i76[3])∧((i76[2] →^* i76[3])∧(a52data[2] →^* a52data[3]))∧(i105[2] →^* i105[3])∧(i75[2] →^* i75[3]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(7) -> (8), if ((i112[7] →^* i112[8])∧((i76[7] →^* i76[8])∧(a52data[7] →^* a52data[8]))∧(i94[7] →^* i94[8])∧(i105[7] →^* i105[8])∧(i131[7] →^* i131[8])∧(i76[7] →^* i76[8])∧(i152[7] →^* i152[8])∧(i75[7] →^* i75[8]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(46) 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 COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) the following chains were created:

• We consider the chain COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (1)    (COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥NonInfC∧COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9])≥INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))∧(U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥))

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

  (2)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_15] ≥ 0)

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

  (3)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_15] ≥ 0)

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

  (4)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧[(-1)bso_15] ≥ 0)

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

  (5)    ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_15] ≥ 0)

  
  
  

For Pair LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) the following chains were created:

• We consider the chain LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]), COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9]))) which results in the following constraint:
  

  (6)    (i105[8]=i105[9]∧i94[8]=i94[9]∧i76[8]=i76[9]∧i112[8]=i112[9]∧i131[8]=i131[9]∧a52data[8]=a52data[9]∧i75[8]=i75[9]∧i152[8]=i152[9]∧&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8]))=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

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

  (7)    (<(i105[8], i112[8])=TRUE∧<(i75[8], i76[8])=TRUE∧>=(i75[8], 0)=TRUE∧>(i94[8], 0)=TRUE∧<(i94[8], i76[8])=TRUE ⇒ LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥NonInfC∧LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])≥COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])∧(U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥))

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

  (8)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-2)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [(2)bni_16]i76[8] + [(-1)bni_16]i75[8] ≥ 0∧[(-1)bso_17] ≥ 0)

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

  (9)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-2)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [(2)bni_16]i76[8] + [(-1)bni_16]i75[8] ≥ 0∧[(-1)bso_17] ≥ 0)

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

  (10)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧[(-2)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [(2)bni_16]i76[8] + [(-1)bni_16]i75[8] ≥ 0∧[(-1)bso_17] ≥ 0)

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

  (11)    (i112[8] + [-1] + [-1]i105[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-2)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [(2)bni_16]i76[8] + [(-1)bni_16]i75[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

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

  (12)    (i112[8] ≥ 0∧i76[8] + [-1] + [-1]i75[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i76[8] + [-1] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-2)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [(2)bni_16]i76[8] + [(-1)bni_16]i75[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  
  
  We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (13)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] + [-1] ≥ 0∧i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  
  
  We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (14)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  
  
  We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (15)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  
  

  (16)    (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  
  
  

For Pair LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) the following chains were created:

• We consider the chain LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7]) which results in the following constraint:
  

  (17)    (LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥NonInfC∧LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])))≥LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])∧(U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥))

  
  
  We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (18)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[1 + (-1)bso_19] ≥ 0)

  
  
  We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (19)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[1 + (-1)bso_19] ≥ 0)

  
  
  We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (20)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧[1 + (-1)bso_19] ≥ 0)

  
  
  We simplified constraint (20) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (21)    ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

  
  
  

For Pair COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) the following chains were created:

• We consider the chain COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (22)    (COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥NonInfC∧COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3])≥LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))∧(U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥))

  
  
  We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (23)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_21] ≥ 0)

  
  
  We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (24)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_21] ≥ 0)

  
  
  We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (25)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧[1 + (-1)bso_21] ≥ 0)

  
  
  We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (26)    ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_21] ≥ 0)

  
  
  

For Pair LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) the following chains were created:

• We consider the chain LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]), COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3]))) which results in the following constraint:
  

  (27)    (&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0))=TRUE∧i112[2]=i112[3]∧i94[2]=i94[3]∧i76[2]=i76[3]∧a52data[2]=a52data[3]∧i105[2]=i105[3]∧i75[2]=i75[3] ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (27) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
  

  (28)    (>(+(i94[2], 1), 0)=TRUE∧<(i75[2], i76[2])=TRUE∧>=(i75[2], 0)=TRUE∧<(i94[2], i76[2])=TRUE∧>=(i105[2], i112[2])=TRUE∧>(i94[2], 0)=TRUE ⇒ LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥NonInfC∧LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])≥COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])∧(U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥))

  
  
  We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (29)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i76[2] + [(-1)bni_22]i75[2] + [(-1)bni_22]i94[2] ≥ 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (30)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i76[2] + [(-1)bni_22]i75[2] + [(-1)bni_22]i94[2] ≥ 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (31)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i76[2] + [(-1)bni_22]i75[2] + [(-1)bni_22]i94[2] ≥ 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (32)    (i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-1] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i76[2] + [(-1)bni_22]i75[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (33)    ([1] + i94[2] ≥ 0∧i76[2] + [-1] + [-1]i75[2] ≥ 0∧i75[2] ≥ 0∧i76[2] + [-2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-2)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]i76[2] + [(-1)bni_22]i75[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (34)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] + [-1]i112[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (35)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (36)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  

  (37)    ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  
  
  

For Pair LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) the following chains were created:

• We consider the chain LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1]) which results in the following constraint:
  

  (38)    (LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥NonInfC∧LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])))≥LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])∧(U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥))

  
  
  We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (39)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_25] ≥ 0)

  
  
  We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (40)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_25] ≥ 0)

  
  
  We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (41)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧[(-1)bso_25] ≥ 0)

  
  
  We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (42)    ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

  
  
  

For Pair INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) the following chains were created:

• We consider the chain INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) which results in the following constraint:
  

  (43)    (INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥NonInfC∧INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))≥LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))∧(U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥))

  
  
  We simplified constraint (43) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (44)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_27] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (45)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_27] ≥ 0)

  
  
  We simplified constraint (45) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (46)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧[(-1)bso_27] ≥ 0)

  
  
  We simplified constraint (46) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (47)    ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)

  
  
  

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

• COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
  
  • ((U^Increasing(INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_15] ≥ 0)
    
  
  
• LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
  
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)
    
  • (i112[8] ≥ 0∧i76[8] ≥ 0∧i75[8] ≥ 0∧i94[8] ≥ 0∧[-1] + i75[8] + i76[8] + [-1]i94[8] ≥ 0∧i105[8] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i94[8] + [bni_16]i75[8] + [(2)bni_16]i76[8] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)
    
  
  
• LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
  
  • ((U^Increasing(LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)
    
  
  
• COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
  
  • ((U^Increasing(LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_21] ≥ 0)
    
  
  
• LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
  
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)
    
  • ([1] + i94[2] ≥ 0∧i76[2] ≥ 0∧i75[2] ≥ 0∧[-1] + i75[2] + i76[2] + [-1]i94[2] ≥ 0∧i105[2] ≥ 0∧i94[2] ≥ 0∧i112[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])), ≥)∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i75[2] + [(2)bni_22]i76[2] + [(-1)bni_22]i94[2] ≥ 0∧0 = 0∧[(-1)bso_23] ≥ 0)
    
  
  
• LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
  
  • ((U^Increasing(LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)
    
  
  
• INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))
  
  • ((U^Increasing(LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 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(COND_LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)) = [-1] + [-1]x₃ + x₄ + [-1]x₂ + [-1]x₅   
POL(java.lang.Object(x₁)) = x₁   
POL(ARRAY(x₁, x₂)) = [1] + [-1]x₁   
POL(INC1031(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₂ + x₃ + [-1]x₁   
POL(LOAD775ARR3(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈)) = [-1] + [-1]x₂ + x₃ + [-1]x₁ + [-1]x₄   
POL(&&(x₁, x₂)) = [-1]   
POL(>(x₁, x₂)) = 0   
POL(0) = 0   
POL(<(x₁, x₂)) = [-1]   
POL(>=(x₁, x₂)) = [-1]   
POL(LOAD775(x₁, x₂, x₃, x₄)) = [-1]x₂ + x₃ + [-1]x₁ + [-1]x₄   
POL(COND_LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₄ + [-1]x₂ + [-1]x₃ + [-1]x₅   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(1) = [1]   
POL(LOAD775ARR1(x₁, x₂, x₃, x₄, x₅, x₆)) = x₃ + [-1]x₁ + [-1]x₂ + [-1]x₄   

The following pairs are in P_>:

LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], +(i94[3], 1), i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))

The following pairs are in P_bound:

LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])

The following pairs are in P_≥:

COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(&&(&&(&&(&&(>(i94[8], 0), <(i94[8], i76[8])), >=(i75[8], 0)), <(i75[8], i76[8])), <(i105[8], i112[8])), i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(&&(&&(&&(&&(&&(>=(i105[2], i112[2]), >(i94[2], 0)), <(i94[2], i76[2])), >=(i75[2], 0)), <(i75[2], i76[2])), >(+(i94[2], 1), 0)), i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], +(i94[0], 1), i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

There are no usable rules.

(47) Complex Obligation (AND)

(48) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(8): LOAD775ARR3(i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8]) → COND_LOAD775ARR3(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8], i75[8], i94[8], i76[8], java.lang.Object(ARRAY(i76[8], a52data[8])), i152[8], i131[8], i112[8], i105[8])
(2): LOAD775ARR1(i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2]) → COND_LOAD775ARR1(i105[2] >= i112[2] && i94[2] > 0 && i94[2] < i76[2] && i75[2] >= 0 && i75[2] < i76[2] && i94[2] + 1 > 0, i75[2], i94[2], i76[2], java.lang.Object(ARRAY(i76[2], a52data[2])), i112[2], i105[2])
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(1) -> (2), if (((i76[1] →^* i76[2])∧(a52data[1] →^* a52data[2]))∧(i76[1] →^* i76[2])∧(i75[1] →^* i75[2])∧(i94[1] →^* i94[2])∧(i105[1] →^* i105[2])∧(i112[1] →^* i112[2]))

(8) -> (9), if ((i105[8] →^* i105[9])∧(i94[8] →^* i94[9])∧(i76[8] →^* i76[9])∧(i112[8] →^* i112[9])∧(i131[8] →^* i131[9])∧((i76[8] →^* i76[9])∧(a52data[8] →^* a52data[9]))∧(i75[8] →^* i75[9])∧(i152[8] →^* i152[9])∧(i94[8] > 0 && i94[8] < i76[8] && i75[8] >= 0 && i75[8] < i76[8] && i105[8] < i112[8] →^* TRUE))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(49) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 5 less nodes.

(50) TRUE

(51) 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:
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(52) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 5 less nodes.

(53) TRUE

(54) 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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(12): COND_LOAD560ARR4(TRUE, i75[12], i76[12], java.lang.Object(ARRAY(i76[12], a52data[12])), i152[12], i131[12], i112[12], i105[12]) → INC1031(i75[12], i75[12] + 1, i76[12], java.lang.Object(ARRAY(i76[12], a52dataNew[12])))
(10): LOAD560(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10]))) → LOAD560ARR4(i75[10], i76[10], java.lang.Object(ARRAY(i76[10], a52data[10])), i152[10], i131[10], i112[10], i105[10])
(6): COND_LOAD560ARR2(TRUE, i75[6], i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])), i112[6], i105[6]) → LOAD775(i75[6], i75[6] + 1 + 1, i76[6], java.lang.Object(ARRAY(i76[6], a52data[6])))
(4): LOAD560(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4]))) → LOAD560ARR2(i75[4], i76[4], java.lang.Object(ARRAY(i76[4], a52data[4])), i112[4], i105[4])
(14): COND_LOAD775(TRUE, i75[14], i94[14], i76[14], java.lang.Object(ARRAY(i76[14], a52data[14]))) → LOAD560(i75[14] + 1, i76[14], java.lang.Object(ARRAY(i76[14], a52data[14])))
(13): LOAD775(i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13]))) → COND_LOAD775(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0, i75[13], i94[13], i76[13], java.lang.Object(ARRAY(i76[13], a52data[13])))
(9): COND_LOAD775ARR3(TRUE, i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52data[9])), i152[9], i131[9], i112[9], i105[9]) → INC1031(i75[9], i94[9], i76[9], java.lang.Object(ARRAY(i76[9], a52dataNew[9])))
(7): LOAD775(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7]))) → LOAD775ARR3(i75[7], i94[7], i76[7], java.lang.Object(ARRAY(i76[7], a52data[7])), i152[7], i131[7], i112[7], i105[7])
(3): COND_LOAD775ARR1(TRUE, i75[3], i94[3], i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])), i112[3], i105[3]) → LOAD775(i75[3], i94[3] + 1, i76[3], java.lang.Object(ARRAY(i76[3], a52data[3])))
(1): LOAD775(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1]))) → LOAD775ARR1(i75[1], i94[1], i76[1], java.lang.Object(ARRAY(i76[1], a52data[1])), i112[1], i105[1])
(0): INC1031(i75[0], i94[0], i76[0], java.lang.Object(ARRAY(i76[0], a52data[0]))) → LOAD775(i75[0], i94[0] + 1, i76[0], java.lang.Object(ARRAY(i76[0], a52data[0])))

(9) -> (0), if (((i76[9] →^* i76[0])∧(a52dataNew[9] →^* a52data[0]))∧(i76[9] →^* i76[0])∧(i75[9] →^* i75[0])∧(i94[9] →^* i94[0]))

(12) -> (0), if (((i76[12] →^* i76[0])∧(a52dataNew[12] →^* a52data[0]))∧(i75[12] →^* i75[0])∧(i75[12] + 1 →^* i94[0])∧(i76[12] →^* i76[0]))

(0) -> (1), if (((i76[0] →^* i76[1])∧(a52data[0] →^* a52data[1]))∧(i94[0] + 1 →^* i94[1])∧(i76[0] →^* i76[1])∧(i75[0] →^* i75[1]))

(3) -> (1), if ((i75[3] →^* i75[1])∧(i94[3] + 1 →^* i94[1])∧((i76[3] →^* i76[1])∧(a52data[3] →^* a52data[1]))∧(i76[3] →^* i76[1]))

(6) -> (1), if ((i76[6] →^* i76[1])∧((i76[6] →^* i76[1])∧(a52data[6] →^* a52data[1]))∧(i75[6] →^* i75[1])∧(i75[6] + 1 + 1 →^* i94[1]))

(14) -> (4), if ((i75[14] + 1 →^* i75[4])∧((i76[14] →^* i76[4])∧(a52data[14] →^* a52data[4]))∧(i76[14] →^* i76[4]))

(0) -> (7), if ((i94[0] + 1 →^* i94[7])∧(i76[0] →^* i76[7])∧(i75[0] →^* i75[7])∧((i76[0] →^* i76[7])∧(a52data[0] →^* a52data[7])))

(3) -> (7), if (((i76[3] →^* i76[7])∧(a52data[3] →^* a52data[7]))∧(i76[3] →^* i76[7])∧(i94[3] + 1 →^* i94[7])∧(i75[3] →^* i75[7]))

(6) -> (7), if ((i75[6] →^* i75[7])∧((i76[6] →^* i76[7])∧(a52data[6] →^* a52data[7]))∧(i76[6] →^* i76[7])∧(i75[6] + 1 + 1 →^* i94[7]))

(14) -> (10), if ((i75[14] + 1 →^* i75[10])∧((i76[14] →^* i76[10])∧(a52data[14] →^* a52data[10]))∧(i76[14] →^* i76[10]))

(0) -> (13), if ((i76[0] →^* i76[13])∧(i94[0] + 1 →^* i94[13])∧((i76[0] →^* i76[13])∧(a52data[0] →^* a52data[13]))∧(i75[0] →^* i75[13]))

(3) -> (13), if (((i76[3] →^* i76[13])∧(a52data[3] →^* a52data[13]))∧(i75[3] →^* i75[13])∧(i94[3] + 1 →^* i94[13])∧(i76[3] →^* i76[13]))

(6) -> (13), if (((i76[6] →^* i76[13])∧(a52data[6] →^* a52data[13]))∧(i76[6] →^* i76[13])∧(i75[6] + 1 + 1 →^* i94[13])∧(i75[6] →^* i75[13]))

(13) -> (14), if (((i76[13] →^* i76[14])∧(a52data[13] →^* a52data[14]))∧(i75[13] →^* i75[14])∧(i94[13] > 0 && i76[13] >= 0 && i94[13] >= i76[13] && i75[13] + 1 > 0 →^* TRUE)∧(i94[13] →^* i94[14])∧(i76[13] →^* i76[14]))

The set Q consists of the following terms:
Inc1031(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Load775ARR1(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Cond_Load775ARR1(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
Load560(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load560ARR2(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Cond_Load560ARR2(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4)
Load775ARR3(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Cond_Load775ARR3(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5, x6, x7)
Load560ARR4(x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load560ARR4(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5, x6)
Cond_Load775(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)))
Cond_Load560(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)))

(55) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 11 less nodes.

(56) TRUE

(57) 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:
Load270(i35, i34, java.lang.Object(ARRAY(i34, a21data))) → Load270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
Load270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → Cond_Load270ARR5(i35 >= 0 && i35 < i34 && i35 < i34 - 1 && i35 + 1 > 0, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
Cond_Load270ARR5(TRUE, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → Load270(i35 + 1, i34, java.lang.Object(ARRAY(i34, a21dataNew)))
The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(58) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(59) 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:
Load270(i35, i34, java.lang.Object(ARRAY(i34, a21data))) → Load270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
Load270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → Cond_Load270ARR5(i35 >= 0 && i35 < i34 && i35 < i34 - 1 && i35 + 1 > 0, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
Cond_Load270ARR5(TRUE, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → Load270(i35 + 1, i34, java.lang.Object(ARRAY(i34, a21dataNew)))

The integer pair graph contains the following rules and edges:
(0): LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
(1): LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0, i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))
(2): COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(i35[2] + 1, i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))

(0) -> (1), if ((i34[0] →^* i34[1])∧(java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])) →^* java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))∧(i35[0] →^* i35[1])∧(java.lang.Object(ARRAY(i34[0], a21data[0])) →^* java.lang.Object(ARRAY(i34[1], a21data[1]))))

(1) -> (2), if ((i35[1] →^* i35[2])∧(java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])) →^* java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2])))∧(i34[1] →^* i34[2])∧(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0 →^* TRUE)∧(java.lang.Object(ARRAY(i34[1], a21data[1])) →^* java.lang.Object(ARRAY(i34[2], a21data[2]))))

(2) -> (0), if ((java.lang.Object(ARRAY(i34[2], a21dataNew[2])) →^* java.lang.Object(ARRAY(i34[0], a21data[0])))∧(i35[2] + 1 →^* i35[0])∧(i34[2] →^* i34[0]))

The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(60) 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.

(61) 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): LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
(1): LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0, i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))
(2): COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(i35[2] + 1, i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))

(0) -> (1), if ((i34[0] →^* i34[1])∧(java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])) →^* java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))∧(i35[0] →^* i35[1])∧(java.lang.Object(ARRAY(i34[0], a21data[0])) →^* java.lang.Object(ARRAY(i34[1], a21data[1]))))

(1) -> (2), if ((i35[1] →^* i35[2])∧(java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])) →^* java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2])))∧(i34[1] →^* i34[2])∧(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0 →^* TRUE)∧(java.lang.Object(ARRAY(i34[1], a21data[1])) →^* java.lang.Object(ARRAY(i34[2], a21data[2]))))

(2) -> (0), if ((java.lang.Object(ARRAY(i34[2], a21dataNew[2])) →^* java.lang.Object(ARRAY(i34[0], a21data[0])))∧(i35[2] + 1 →^* i35[0])∧(i34[2] →^* i34[0]))

The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(62) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

(63) 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): LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
(1): LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0, i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))
(2): COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(i35[2] + 1, i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))

(0) -> (1), if ((i34[0] →^* i34[1])∧((i52[0] →^* i52[1])∧(i51[0] →^* i51[1])∧(i53[0] →^* i53[1])∧(a22[0] →^* a22[1]))∧(i35[0] →^* i35[1])∧((i34[0] →^* i34[1])∧(a21data[0] →^* a21data[1])))

(1) -> (2), if ((i35[1] →^* i35[2])∧((i52[1] →^* i52[2])∧(i51[1] →^* i51[2])∧(i53[1] →^* i53[2])∧(a22[1] →^* a22[2]))∧(i34[1] →^* i34[2])∧(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0 →^* TRUE)∧((i34[1] →^* i34[2])∧(a21data[1] →^* a21data[2])))

(2) -> (0), if (((i34[2] →^* i34[0])∧(a21dataNew[2] →^* a21data[0]))∧(i35[2] + 1 →^* i35[0])∧(i34[2] →^* i34[0]))

The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(64) 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 LOAD270(i35, i34, java.lang.Object(ARRAY(i34, a21data))) → LOAD270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) the following chains were created:

• We consider the chain LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0]))) which results in the following constraint:
  

  (1)    (LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])))≥NonInfC∧LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])))≥LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))∧(U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥))

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

  (2)    ((U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (3)    ((U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (4)    ((U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥)∧[(-1)bso_18] ≥ 0)

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

  (5)    ((U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)

  
  
  

For Pair LOAD270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → COND_LOAD270ARR5(&&(&&(&&(>=(i35, 0), <(i35, i34)), <(i35, -(i34, 1))), >(+(i35, 1), 0)), i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) the following chains were created:

• We consider the chain LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))), COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2]))) which results in the following constraint:
  

  (6)    (i35[1]=i35[2]∧i52[1]=i52[2]∧i51[1]=i51[2]∧i53[1]=i53[2]∧a22[1]=a22[2]∧i34[1]=i34[2]∧&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0))=TRUE∧a21data[1]=a21data[2] ⇒ LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))≥NonInfC∧LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))≥COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))∧(U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥))

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

  (7)    (>(+(i35[1], 1), 0)=TRUE∧<(i35[1], -(i34[1], 1))=TRUE∧>=(i35[1], 0)=TRUE∧<(i35[1], i34[1])=TRUE ⇒ LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))≥NonInfC∧LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))≥COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))∧(U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥))

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

  (8)    (i35[1] ≥ 0∧i34[1] + [-2] + [-1]i35[1] ≥ 0∧i35[1] ≥ 0∧i34[1] + [-1] + [-1]i35[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] + [(-1)bni_19]i35[1] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (9)    (i35[1] ≥ 0∧i34[1] + [-2] + [-1]i35[1] ≥ 0∧i35[1] ≥ 0∧i34[1] + [-1] + [-1]i35[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] + [(-1)bni_19]i35[1] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (10)    (i35[1] ≥ 0∧i34[1] + [-2] + [-1]i35[1] ≥ 0∧i35[1] ≥ 0∧i34[1] + [-1] + [-1]i35[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] + [(-1)bni_19]i35[1] ≥ 0∧[(-1)bso_20] ≥ 0)

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

  (11)    (i35[1] ≥ 0∧i34[1] + [-2] + [-1]i35[1] ≥ 0∧i35[1] ≥ 0∧i34[1] + [-1] + [-1]i35[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧0 = 0∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] + [(-1)bni_19]i35[1] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

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

  (12)    (i35[1] ≥ 0∧i34[1] ≥ 0∧i35[1] ≥ 0∧[1] + i34[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧0 = 0∧[bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)

  
  
  

For Pair COND_LOAD270ARR5(TRUE, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → LOAD270(+(i35, 1), i34, java.lang.Object(ARRAY(i34, a21dataNew))) the following chains were created:

• We consider the chain COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2]))) which results in the following constraint:
  

  (13)    (COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2])))≥NonInfC∧COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2])))≥LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))∧(U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥))

  
  
  We simplified constraint (13) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (14)    ((U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥)∧[1 + (-1)bso_22] ≥ 0)

  
  
  We simplified constraint (14) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (15)    ((U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥)∧[1 + (-1)bso_22] ≥ 0)

  
  
  We simplified constraint (15) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (16)    ((U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥)∧[1 + (-1)bso_22] ≥ 0)

  
  
  We simplified constraint (16) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (17)    ((U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_22] ≥ 0)

  
  
  

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

• LOAD270(i35, i34, java.lang.Object(ARRAY(i34, a21data))) → LOAD270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
  
  • ((U^Increasing(LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)
    
  
  
• LOAD270ARR5(i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → COND_LOAD270ARR5(&&(&&(&&(>=(i35, 0), <(i35, i34)), <(i35, -(i34, 1))), >(+(i35, 1), 0)), i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22)))
  
  • (i35[1] ≥ 0∧i34[1] ≥ 0∧i35[1] ≥ 0∧[1] + i34[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))), ≥)∧0 = 0∧[bni_19 + (-1)Bound*bni_19] + [bni_19]i34[1] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)
    
  
  
• COND_LOAD270ARR5(TRUE, i35, i34, java.lang.Object(ARRAY(i34, a21data)), java.lang.Object(java.lang.String(i52, i51, i53, a22))) → LOAD270(+(i35, 1), i34, java.lang.Object(ARRAY(i34, a21dataNew)))
  
  • ((U^Increasing(LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_22] ≥ 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(LOAD270(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₁   
POL(java.lang.Object(x₁)) = x₁   
POL(ARRAY(x₁, x₂)) = x₁   
POL(LOAD270ARR5(x₁, x₂, x₃, x₄)) = [-1] + x₂ + [-1]x₁   
POL(java.lang.String(x₁, x₂, x₃, x₄)) = [-1]   
POL(COND_LOAD270ARR5(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₃ + [-1]x₂   
POL(&&(x₁, x₂)) = [-1]   
POL(>=(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(<(x₁, x₂)) = [-1]   
POL(-(x₁, x₂)) = x₁ + [-1]x₂   
POL(1) = [1]   
POL(>(x₁, x₂)) = [-1]   
POL(+(x₁, x₂)) = x₁ + x₂   

The following pairs are in P_>:

COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(+(i35[2], 1), i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))

The following pairs are in P_bound:

LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))

The following pairs are in P_≥:

LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(&&(&&(&&(>=(i35[1], 0), <(i35[1], i34[1])), <(i35[1], -(i34[1], 1))), >(+(i35[1], 1), 0)), i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))

There are no usable rules.

(65) Complex Obligation (AND)

(66) 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): LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
(1): LOAD270ARR5(i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1]))) → COND_LOAD270ARR5(i35[1] >= 0 && i35[1] < i34[1] && i35[1] < i34[1] - 1 && i35[1] + 1 > 0, i35[1], i34[1], java.lang.Object(ARRAY(i34[1], a21data[1])), java.lang.Object(java.lang.String(i52[1], i51[1], i53[1], a22[1])))

(0) -> (1), if ((i34[0] →^* i34[1])∧((i52[0] →^* i52[1])∧(i51[0] →^* i51[1])∧(i53[0] →^* i53[1])∧(a22[0] →^* a22[1]))∧(i35[0] →^* i35[1])∧((i34[0] →^* i34[1])∧(a21data[0] →^* a21data[1])))

The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(67) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(68) TRUE

(69) 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): LOAD270(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0]))) → LOAD270ARR5(i35[0], i34[0], java.lang.Object(ARRAY(i34[0], a21data[0])), java.lang.Object(java.lang.String(i52[0], i51[0], i53[0], a22[0])))
(2): COND_LOAD270ARR5(TRUE, i35[2], i34[2], java.lang.Object(ARRAY(i34[2], a21data[2])), java.lang.Object(java.lang.String(i52[2], i51[2], i53[2], a22[2]))) → LOAD270(i35[2] + 1, i34[2], java.lang.Object(ARRAY(i34[2], a21dataNew[2])))

(2) -> (0), if (((i34[2] →^* i34[0])∧(a21dataNew[2] →^* a21data[0]))∧(i35[2] + 1 →^* i35[0])∧(i34[2] →^* i34[0]))

The set Q consists of the following terms:
Load270(x0, x1, java.lang.Object(ARRAY(x1, x2)))
Load270ARR5(x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))
Cond_Load270ARR5(TRUE, x0, x1, java.lang.Object(ARRAY(x1, x2)), java.lang.Object(java.lang.String(x3, x4, x5, x6)))

(70) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(71) TRUE