(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:
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)))

(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:
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:
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:
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))=TRUEi227[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])=TRUELOAD1414ARR1(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.

(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:
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.

(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: