Termination of the given JBC could be proven:

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

(0) Obligation:

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

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 202 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

(4) Obligation:

ITRS problem:

The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean

The TRS R consists of the following rules:
Load671(i34, java.lang.Object(From(i35)), i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Cond_Load671(i36 >= 0 && i36 < i34 && i36 + 1 > 0 && i35 + 1 > 0, i34, java.lang.Object(From(i35)), i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36)
Cond_Load671(TRUE, i34, java.lang.Object(From(i35)), i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Load671(i34, java.lang.Object(From(i35 + 1)), i34, java.lang.Object(From(i35 + 1)), java.lang.Object(ARRAY(i34, a219dataNew)), i36 + 1)
The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

Some arguments are removed because they only appear as duplicates.
We removed arguments according to the following replacements:

Load671(x1, x2, x3, x4, x5, x6) → Load671(x3, x4, x5, x6)
Cond_Load671(x1, x2, x3, x4, x5, x6, x7) → Cond_Load671(x1, x4, x5, x6, x7)

(6) 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:
Load671(i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Cond_Load671(i36 >= 0 && i36 < i34 && i36 + 1 > 0 && i35 + 1 > 0, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36)
Cond_Load671(TRUE, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Load671(i34, java.lang.Object(From(i35 + 1)), java.lang.Object(ARRAY(i34, a219dataNew)), i36 + 1)
The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(7) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(8) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Boolean, Integer


The ITRS R consists of the following rules:
Load671(i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Cond_Load671(i36 >= 0 && i36 < i34 && i36 + 1 > 0 && i35 + 1 > 0, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36)
Cond_Load671(TRUE, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → Load671(i34, java.lang.Object(From(i35 + 1)), java.lang.Object(ARRAY(i34, a219dataNew)), i36 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0, i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])
(1): COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(i35[1] + 1)), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), i36[1] + 1)

(0) -> (1), if ((i34[0] →* i34[1])∧(java.lang.Object(ARRAY(i34[0], a219data[0])) →* java.lang.Object(ARRAY(i34[1], a219data[1])))∧(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0 →* TRUE)∧(i36[0] →* i36[1])∧(java.lang.Object(From(i35[0])) →* java.lang.Object(From(i35[1]))))


(1) -> (0), if ((i34[1] →* i34[0])∧(java.lang.Object(ARRAY(i34[1], a219dataNew[1])) →* java.lang.Object(ARRAY(i34[0], a219data[0])))∧(i36[1] + 1 →* i36[0])∧(java.lang.Object(From(i35[1] + 1)) →* java.lang.Object(From(i35[0]))))



The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(9) 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.

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0, i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])
(1): COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(i35[1] + 1)), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), i36[1] + 1)

(0) -> (1), if ((i34[0] →* i34[1])∧(java.lang.Object(ARRAY(i34[0], a219data[0])) →* java.lang.Object(ARRAY(i34[1], a219data[1])))∧(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0 →* TRUE)∧(i36[0] →* i36[1])∧(java.lang.Object(From(i35[0])) →* java.lang.Object(From(i35[1]))))


(1) -> (0), if ((i34[1] →* i34[0])∧(java.lang.Object(ARRAY(i34[1], a219dataNew[1])) →* java.lang.Object(ARRAY(i34[0], a219data[0])))∧(i36[1] + 1 →* i36[0])∧(java.lang.Object(From(i35[1] + 1)) →* java.lang.Object(From(i35[0]))))



The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(11) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

(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): LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0, i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])
(1): COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(i35[1] + 1)), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), i36[1] + 1)

(0) -> (1), if ((i34[0] →* i34[1])∧((i34[0] →* i34[1])∧(a219data[0] →* a219data[1]))∧(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0 →* TRUE)∧(i36[0] →* i36[1])∧((i35[0] →* i35[1])))


(1) -> (0), if ((i34[1] →* i34[0])∧((i34[1] →* i34[0])∧(a219dataNew[1] →* a219data[0]))∧(i36[1] + 1 →* i36[0])∧((i35[1] + 1 →* i35[0])))



The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(13) 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 LOAD671(i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → COND_LOAD671(&&(&&(&&(>=(i36, 0), <(i36, i34)), >(+(i36, 1), 0)), >(+(i35, 1), 0)), i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) the following chains were created:
  • We consider the chain LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]), COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1)) which results in the following constraint:

    (1)    (i34[0]=i34[1]∧a219data[0]=a219data[1]∧&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0))=TRUE∧i36[0]=i36[1]∧i35[0]=i35[1] ⇒ LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])≥NonInfC∧LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])≥COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])∧(UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥))



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

    (2)    (>(+(i35[0], 1), 0)=TRUE∧>(+(i36[0], 1), 0)=TRUE∧>=(i36[0], 0)=TRUE∧<(i36[0], i34[0])=TRUE ⇒ LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])≥NonInfC∧LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])≥COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])∧(UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥))



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

    (3)    (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] + [-1] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i36[0] + [bni_16]i34[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (4)    (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] + [-1] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i36[0] + [bni_16]i34[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (5)    (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] + [-1] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i36[0] + [bni_16]i34[0] ≥ 0∧[(-1)bso_17] ≥ 0)



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

    (6)    (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] + [-1] + [-1]i36[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧0 = 0∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]i36[0] + [bni_16]i34[0] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)



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

    (7)    (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧0 = 0∧[(-1)Bound*bni_16] + [bni_16]i34[0] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)







For Pair COND_LOAD671(TRUE, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → LOAD671(i34, java.lang.Object(From(+(i35, 1))), java.lang.Object(ARRAY(i34, a219dataNew)), +(i36, 1)) the following chains were created:
  • We consider the chain COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1)) which results in the following constraint:

    (8)    (COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1])≥NonInfC∧COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1])≥LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))∧(UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥))



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

    (9)    ((UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥)∧[1 + (-1)bso_19] ≥ 0)



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

    (10)    ((UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥)∧[1 + (-1)bso_19] ≥ 0)



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

    (11)    ((UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥)∧[1 + (-1)bso_19] ≥ 0)



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

    (12)    ((UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD671(i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → COND_LOAD671(&&(&&(&&(>=(i36, 0), <(i36, i34)), >(+(i36, 1), 0)), >(+(i35, 1), 0)), i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36)
    • (i35[0] ≥ 0∧i36[0] ≥ 0∧i36[0] ≥ 0∧i34[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])), ≥)∧0 = 0∧[(-1)Bound*bni_16] + [bni_16]i34[0] ≥ 0∧0 = 0∧[(-1)bso_17] ≥ 0)

  • COND_LOAD671(TRUE, i34, java.lang.Object(From(i35)), java.lang.Object(ARRAY(i34, a219data)), i36) → LOAD671(i34, java.lang.Object(From(+(i35, 1))), java.lang.Object(ARRAY(i34, a219dataNew)), +(i36, 1))
    • ((UIncreasing(LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(LOAD671(x1, x2, x3, x4)) = [-1] + [-1]x4 + x1   
POL(java.lang.Object(x1)) = x1   
POL(From(x1)) = x1   
POL(ARRAY(x1, x2)) = [-1] + [-1]x1   
POL(COND_LOAD671(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + x2   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(<(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   

The following pairs are in P>:

COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(+(i35[1], 1))), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), +(i36[1], 1))

The following pairs are in Pbound:

LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])

The following pairs are in P≥:

LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(&&(&&(&&(>=(i36[0], 0), <(i36[0], i34[0])), >(+(i36[0], 1), 0)), >(+(i35[0], 1), 0)), i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])

There are no usable rules.

(14) Complex Obligation (AND)

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD671(i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0]) → COND_LOAD671(i36[0] >= 0 && i36[0] < i34[0] && i36[0] + 1 > 0 && i35[0] + 1 > 0, i34[0], java.lang.Object(From(i35[0])), java.lang.Object(ARRAY(i34[0], a219data[0])), i36[0])


The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(16) IDependencyGraphProof (EQUIVALENT transformation)

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

(17) TRUE

(18) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Integer


R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_LOAD671(TRUE, i34[1], java.lang.Object(From(i35[1])), java.lang.Object(ARRAY(i34[1], a219data[1])), i36[1]) → LOAD671(i34[1], java.lang.Object(From(i35[1] + 1)), java.lang.Object(ARRAY(i34[1], a219dataNew[1])), i36[1] + 1)


The set Q consists of the following terms:
Load671(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)
Cond_Load671(TRUE, x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3)

(19) IDependencyGraphProof (EQUIVALENT transformation)

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

(20) TRUE