Termination of the given JBC could be proven:

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

(0) Obligation:

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

Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC10

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 296 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:
Load1414(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152) → Load1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
Load1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → Cond_Load1414ARR1(i150 + 1 > 0 && i150 + 1 < i3 && i150 > 0 && i150 < i3 && i151 - i152 >= 1 && i527 + 1 > 0 && i152 + i527 + 1 > 0 && i150 + 1 + 1 > 0, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → Load1414(java.lang.Object(ARRAY(i3, a2058data)), i150 + 1 + 1, i151 - i227, i152 + i527 + 1)
The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(6) Obligation:

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


The following domains are used:

Boolean, Integer


The ITRS R consists of the following rules:
Load1414(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152) → Load1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
Load1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → Cond_Load1414ARR1(i150 + 1 > 0 && i150 + 1 < i3 && i150 > 0 && i150 < i3 && i151 - i152 >= 1 && i527 + 1 > 0 && i152 + i527 + 1 > 0 && i150 + 1 + 1 > 0, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → Load1414(java.lang.Object(ARRAY(i3, a2058data)), i150 + 1 + 1, i151 - i227, i152 + i527 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))
(1): LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))
(2): COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2] + 1 + 1, i151[2] - i227[2], i152[2] + i527[2] + 1)

(0) -> (1), if ((java.lang.Object(ARRAY(i3[0], a2058data[0])) →* java.lang.Object(ARRAY(i3[1], a2058data[1])))∧(i152[0] →* i152[1])∧(i150[0] →* i150[1])∧(java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])) →* java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))∧(i151[0] →* i151[1])∧(java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])) →* java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1]))))


(1) -> (2), if ((i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0 →* TRUE)∧(java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])) →* java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2])))∧(java.lang.Object(ARRAY(i3[1], a2058data[1])) →* java.lang.Object(ARRAY(i3[2], a2058data[2])))∧(java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])) →* java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])))∧(i152[1] →* i152[2])∧(i151[1] →* i151[2])∧(i150[1] →* i150[2]))


(2) -> (0), if ((java.lang.Object(ARRAY(i3[2], a2058data[2])) →* java.lang.Object(ARRAY(i3[0], a2058data[0])))∧(i152[2] + i527[2] + 1 →* i152[0])∧(i150[2] + 1 + 1 →* i150[0])∧(i151[2] - i227[2] →* i151[0]))



The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(7) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(8) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))
(1): LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))
(2): COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2] + 1 + 1, i151[2] - i227[2], i152[2] + i527[2] + 1)

(0) -> (1), if ((java.lang.Object(ARRAY(i3[0], a2058data[0])) →* java.lang.Object(ARRAY(i3[1], a2058data[1])))∧(i152[0] →* i152[1])∧(i150[0] →* i150[1])∧(java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])) →* java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))∧(i151[0] →* i151[1])∧(java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])) →* java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1]))))


(1) -> (2), if ((i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0 →* TRUE)∧(java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])) →* java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2])))∧(java.lang.Object(ARRAY(i3[1], a2058data[1])) →* java.lang.Object(ARRAY(i3[2], a2058data[2])))∧(java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])) →* java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])))∧(i152[1] →* i152[2])∧(i151[1] →* i151[2])∧(i150[1] →* i150[2]))


(2) -> (0), if ((java.lang.Object(ARRAY(i3[2], a2058data[2])) →* java.lang.Object(ARRAY(i3[0], a2058data[0])))∧(i152[2] + i527[2] + 1 →* i152[0])∧(i150[2] + 1 + 1 →* i150[0])∧(i151[2] - i227[2] →* i151[0]))



The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(9) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

(10) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))
(1): LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))
(2): COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2] + 1 + 1, i151[2] - i227[2], i152[2] + i527[2] + 1)

(0) -> (1), if (((i3[0] →* i3[1])∧(a2058data[0] →* a2058data[1]))∧(i152[0] →* i152[1])∧(i150[0] →* i150[1])∧((i227[0] →* i227[1])∧(i226[0] →* i226[1])∧(i228[0] →* i228[1])∧(a2344[0] →* a2344[1]))∧(i151[0] →* i151[1])∧((i527[0] →* i527[1])∧(i526[0] →* i526[1])∧(i528[0] →* i528[1])∧(a3229[0] →* a3229[1])))


(1) -> (2), if ((i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0 →* TRUE)∧((i227[1] →* i227[2])∧(i226[1] →* i226[2])∧(i228[1] →* i228[2])∧(a2344[1] →* a2344[2]))∧((i3[1] →* i3[2])∧(a2058data[1] →* a2058data[2]))∧((i527[1] →* i527[2])∧(i526[1] →* i526[2])∧(i528[1] →* i528[2])∧(a3229[1] →* a3229[2]))∧(i152[1] →* i152[2])∧(i151[1] →* i151[2])∧(i150[1] →* i150[2]))


(2) -> (0), if (((i3[2] →* i3[0])∧(a2058data[2] →* a2058data[0]))∧(i152[2] + i527[2] + 1 →* i152[0])∧(i150[2] + 1 + 1 →* i150[0])∧(i151[2] - i227[2] →* i151[0]))



The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(11) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.


For Pair LOAD1414(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152) → LOAD1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) the following chains were created:
  • We consider the chain LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0]))) which results in the following constraint:

    (1)    (LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0])≥NonInfC∧LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0])≥LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))∧(UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥))



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

    (2)    ((UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥)∧[1 + (-1)bso_25] ≥ 0)



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

    (3)    ((UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥)∧[1 + (-1)bso_25] ≥ 0)



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

    (4)    ((UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥)∧[1 + (-1)bso_25] ≥ 0)



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

    (5)    ((UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)







For Pair LOAD1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150, 1), 0), <(+(i150, 1), i3)), >(i150, 0)), <(i150, i3)), >=(-(i151, i152), 1)), >(+(i527, 1), 0)), >(+(i152, +(i527, 1)), 0)), >(+(+(i150, 1), 1), 0)), java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) the following chains were created:
  • We consider the chain LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))), COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1))) which results in the following constraint:

    (6)    (&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0))=TRUE∧i227[1]=i227[2]∧i226[1]=i226[2]∧i228[1]=i228[2]∧a2344[1]=a2344[2]∧i3[1]=i3[2]∧a2058data[1]=a2058data[2]∧i527[1]=i527[2]∧i526[1]=i526[2]∧i528[1]=i528[2]∧a3229[1]=a3229[2]∧i152[1]=i152[2]∧i151[1]=i151[2]∧i150[1]=i150[2] ⇒ LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))≥NonInfC∧LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))≥COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))∧(UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥))



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

    (7)    (>(+(+(i150[1], 1), 1), 0)=TRUE∧>(+(i152[1], +(i527[1], 1)), 0)=TRUE∧>(+(i527[1], 1), 0)=TRUE∧>=(-(i151[1], i152[1]), 1)=TRUE∧<(i150[1], i3[1])=TRUE∧>(i150[1], 0)=TRUE∧>(+(i150[1], 1), 0)=TRUE∧<(+(i150[1], 1), i3[1])=TRUE ⇒ LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))≥NonInfC∧LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))≥COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))∧(UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥))



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

    (8)    (i150[1] + [1] ≥ 0∧i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] ≥ 0∧i3[1] + [-1] + [-1]i150[1] ≥ 0∧i150[1] + [-1] ≥ 0∧i150[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (9)    (i150[1] + [1] ≥ 0∧i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] ≥ 0∧i3[1] + [-1] + [-1]i150[1] ≥ 0∧i150[1] + [-1] ≥ 0∧i150[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (10)    (i150[1] + [1] ≥ 0∧i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] ≥ 0∧i3[1] + [-1] + [-1]i150[1] ≥ 0∧i150[1] + [-1] ≥ 0∧i150[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (11)    (i150[1] + [1] ≥ 0∧i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] ≥ 0∧i3[1] + [-1] + [-1]i150[1] ≥ 0∧i150[1] + [-1] ≥ 0∧i150[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (12)    ([2] + i150[1] ≥ 0∧i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] + [-3] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (13)    ([2] + i150[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧i3[1] + [-2] + [-1]i150[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] + [-3] + [-1]i150[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]i150[1] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (14)    ([2] + i150[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧[-1] + i3[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (15)    ([2] + i150[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (16)    ([2] + i150[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0∧i151[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)


    (17)    ([2] + i150[1] ≥ 0∧[-1]i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0∧i151[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)



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

    (18)    ([2] + i150[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [1] + i152[1] + i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0∧i151[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)







For Pair COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → LOAD1414(java.lang.Object(ARRAY(i3, a2058data)), +(+(i150, 1), 1), -(i151, i227), +(i152, +(i527, 1))) the following chains were created:
  • We consider the chain COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1))) which results in the following constraint:

    (19)    (COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2])))≥NonInfC∧COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2])))≥LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))∧(UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥))



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

    (20)    ((UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥)∧[1 + (-1)bso_29] ≥ 0)



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

    (21)    ((UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥)∧[1 + (-1)bso_29] ≥ 0)



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

    (22)    ((UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥)∧[1 + (-1)bso_29] ≥ 0)



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

    (23)    ((UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_29] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1414(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152) → LOAD1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
    • ((UIncreasing(LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)

  • LOAD1414ARR1(java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150, 1), 0), <(+(i150, 1), i3)), >(i150, 0)), <(i150, i3)), >=(-(i151, i152), 1)), >(+(i527, 1), 0)), >(+(i152, +(i527, 1)), 0)), >(+(+(i150, 1), 1), 0)), java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344)))
    • ([2] + i150[1] ≥ 0∧i151[1] + [-1] + [-1]i152[1] + i527[1] ≥ 0∧i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0∧i151[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)
    • ([2] + i150[1] ≥ 0∧i527[1] ≥ 0∧i151[1] + [1] + i152[1] + i527[1] ≥ 0∧i152[1] ≥ 0∧[1] + i3[1] ≥ 0∧i150[1] ≥ 0∧[1] + i150[1] ≥ 0∧i3[1] ≥ 0∧i151[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_26 + (-1)Bound*bni_26] + [bni_26]i3[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)

  • COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3, a2058data)), i150, i151, i152, java.lang.Object(java.lang.String(i527, i526, i528, a3229)), java.lang.Object(java.lang.String(i227, i226, i228, a2344))) → LOAD1414(java.lang.Object(ARRAY(i3, a2058data)), +(+(i150, 1), 1), -(i151, i227), +(i152, +(i527, 1)))
    • ((UIncreasing(LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_29] ≥ 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(LOAD1414(x1, x2, x3, x4)) = [2] + [-1]x2 + [-1]x1   
POL(java.lang.Object(x1)) = x1   
POL(ARRAY(x1, x2)) = [-1] + [-1]x1   
POL(LOAD1414ARR1(x1, x2, x3, x4, x5, x6)) = [-1]x5 + [-1]x2 + [-1]x1   
POL(java.lang.String(x1, x2, x3, x4)) = [-1]   
POL(COND_LOAD1414ARR1(x1, x2, x3, x4, x5, x6, x7)) = [-1] + [-1]x7 + [-1]x6 + [-1]x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(0) = 0   
POL(<(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(-(x1, x2)) = x1 + [-1]x2   

The following pairs are in P>:

LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))
COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), +(+(i150[2], 1), 1), -(i151[2], i227[2]), +(i152[2], +(i527[2], 1)))

The following pairs are in Pbound:

LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))

The following pairs are in P≥:

LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(&&(&&(&&(&&(&&(&&(&&(>(+(i150[1], 1), 0), <(+(i150[1], 1), i3[1])), >(i150[1], 0)), <(i150[1], i3[1])), >=(-(i151[1], i152[1]), 1)), >(+(i527[1], 1), 0)), >(+(i152[1], +(i527[1], 1)), 0)), >(+(+(i150[1], 1), 1), 0)), java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))

There are no usable rules.

(12) Complex Obligation (AND)

(13) Obligation:

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


The following domains are used:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(1): LOAD1414ARR1(java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1]))) → COND_LOAD1414ARR1(i150[1] + 1 > 0 && i150[1] + 1 < i3[1] && i150[1] > 0 && i150[1] < i3[1] && i151[1] - i152[1] >= 1 && i527[1] + 1 > 0 && i152[1] + i527[1] + 1 > 0 && i150[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i3[1], a2058data[1])), i150[1], i151[1], i152[1], java.lang.Object(java.lang.String(i527[1], i526[1], i528[1], a3229[1])), java.lang.Object(java.lang.String(i227[1], i226[1], i228[1], a2344[1])))


The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(14) IDependencyGraphProof (EQUIVALENT transformation)

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

(15) TRUE

(16) Obligation:

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


The following domains are used:

Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1414(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0]) → LOAD1414ARR1(java.lang.Object(ARRAY(i3[0], a2058data[0])), i150[0], i151[0], i152[0], java.lang.Object(java.lang.String(i527[0], i526[0], i528[0], a3229[0])), java.lang.Object(java.lang.String(i227[0], i226[0], i228[0], a2344[0])))
(2): COND_LOAD1414ARR1(TRUE, java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2], i151[2], i152[2], java.lang.Object(java.lang.String(i527[2], i526[2], i528[2], a3229[2])), java.lang.Object(java.lang.String(i227[2], i226[2], i228[2], a2344[2]))) → LOAD1414(java.lang.Object(ARRAY(i3[2], a2058data[2])), i150[2] + 1 + 1, i151[2] - i227[2], i152[2] + i527[2] + 1)

(2) -> (0), if (((i3[2] →* i3[0])∧(a2058data[2] →* a2058data[0]))∧(i152[2] + i527[2] + 1 →* i152[0])∧(i150[2] + 1 + 1 →* i150[0])∧(i151[2] - i227[2] →* i151[0]))



The set Q consists of the following terms:
Load1414(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1414ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))
Cond_Load1414ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5, x6, x7, x8)), java.lang.Object(java.lang.String(x9, x10, x11, x12)))

(17) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(18) TRUE