### (0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC10
`/** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */public class PastaC10 {    public static void main(String[] args) {        Random.args = args;        int i = Random.random();        int j = Random.random();        while (i - j >= 1) {			i = i - Random.random();			int r = Random.random() + 1;			j = j + r;        }    } }public class Random {  static String[] args;  static int index = 0;  public static int random() {    String string = args[index];    index++;    return string.length();  }}`

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 319 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:
Load2257(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → Load2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201)))
Load2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → Cond_Load2257ARR1(i135 + 1 > 0 && i135 + 1 < i5 && i135 > 0 && i135 < i5 && i136 - i137 >= 1 && i135 + 1 + 1 > 0, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201)))
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → Load2257(java.lang.Object(ARRAY(i5, a5033data)), i135 + 1 + 1, i136 - i201, i137 + i476 + 1)
The set Q consists of the following terms:
Load2257ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (5) ITRSFilterProcessorProof (SOUND transformation)

We filter according the heuristic IdpCand1ShapeHeuristic
We removed arguments according to the following replacements:

### (6) Obligation:

ITRS problem:

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

The TRS R consists of the following rules:
Load2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → Cond_Load2257ARR1(i135 + 1 > 0 && i135 + 1 < i5 && i135 > 0 && i135 < i5 && i136 - i137 >= 1 && i135 + 1 + 1 > 0, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201)))
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → Load2257(java.lang.Object(ARRAY(i5, a5033data)), i135 + 1 + 1, i136 - i201, i137 + i476 + 1)
The set Q consists of the following terms:
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (8) Obligation:

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
Load2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → Cond_Load2257ARR1(i135 + 1 > 0 && i135 + 1 < i5 && i135 > 0 && i135 < i5 && i136 - i137 >= 1 && i135 + 1 + 1 > 0, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201)))
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → Load2257(java.lang.Object(ARRAY(i5, a5033data)), i135 + 1 + 1, i136 - i201, i137 + i476 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])
(1): LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
(2): COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2] + 1 + 1, i136[2] - i201[2], i137[2] + i476[2] + 1)

(0) -> (1), if ((i137[0]* i137[1])∧(i135[0]* i135[1])∧(java.lang.Object(ARRAY(i5[0], a5033data[0])) →* java.lang.Object(ARRAY(i5[1], a5033data[1])))∧(i136[0]* i136[1]))

(1) -> (2), if ((java.lang.Object(java.lang.String(i476[1])) →* java.lang.Object(java.lang.String(i476[2])))∧(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0* TRUE)∧(i137[1]* i137[2])∧(java.lang.Object(ARRAY(i5[1], a5033data[1])) →* java.lang.Object(ARRAY(i5[2], a5033data[2])))∧(java.lang.Object(java.lang.String(i201[1])) →* java.lang.Object(java.lang.String(i201[2])))∧(i135[1]* i135[2])∧(i136[1]* i136[2]))

(2) -> (0), if ((i135[2] + 1 + 1* i135[0])∧(java.lang.Object(ARRAY(i5[2], a5033data[2])) →* java.lang.Object(ARRAY(i5[0], a5033data[0])))∧(i137[2] + i476[2] + 1* i137[0])∧(i136[2] - i201[2]* i136[0]))

The set Q consists of the following terms:
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (9) UsableRulesProof (EQUIVALENT transformation)

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

### (10) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])
(1): LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
(2): COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2] + 1 + 1, i136[2] - i201[2], i137[2] + i476[2] + 1)

(0) -> (1), if ((i137[0]* i137[1])∧(i135[0]* i135[1])∧(java.lang.Object(ARRAY(i5[0], a5033data[0])) →* java.lang.Object(ARRAY(i5[1], a5033data[1])))∧(i136[0]* i136[1]))

(1) -> (2), if ((java.lang.Object(java.lang.String(i476[1])) →* java.lang.Object(java.lang.String(i476[2])))∧(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0* TRUE)∧(i137[1]* i137[2])∧(java.lang.Object(ARRAY(i5[1], a5033data[1])) →* java.lang.Object(ARRAY(i5[2], a5033data[2])))∧(java.lang.Object(java.lang.String(i201[1])) →* java.lang.Object(java.lang.String(i201[2])))∧(i135[1]* i135[2])∧(i136[1]* i136[2]))

(2) -> (0), if ((i135[2] + 1 + 1* i135[0])∧(java.lang.Object(ARRAY(i5[2], a5033data[2])) →* java.lang.Object(ARRAY(i5[0], a5033data[0])))∧(i137[2] + i476[2] + 1* i137[0])∧(i136[2] - i201[2]* i136[0]))

The set Q consists of the following terms:
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (11) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

### (12) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])
(1): LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
(2): COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2] + 1 + 1, i136[2] - i201[2], i137[2] + i476[2] + 1)

(0) -> (1), if ((i137[0]* i137[1])∧(i135[0]* i135[1])∧((i5[0]* i5[1])∧(a5033data[0]* a5033data[1]))∧(i136[0]* i136[1]))

(1) -> (2), if (((i476[1]* i476[2]))∧(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0* TRUE)∧(i137[1]* i137[2])∧((i5[1]* i5[2])∧(a5033data[1]* a5033data[2]))∧((i201[1]* i201[2]))∧(i135[1]* i135[2])∧(i136[1]* i136[2]))

(2) -> (0), if ((i135[2] + 1 + 1* i135[0])∧((i5[2]* i5[0])∧(a5033data[2]* a5033data[0]))∧(i137[2] + i476[2] + 1* i137[0])∧(i136[2] - i201[2]* i136[0]))

The set Q consists of the following terms:
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (13) IDPNonInfProof (SOUND transformation)

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

For Pair LOAD2257(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → LOAD2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) the following chains were created:
• We consider the chain LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]), LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1]))) which results in the following constraint:

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

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

(3)    ((UIncreasing(LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])), ≥)∧[1 + (-1)bso_33] ≥ 0)

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

(4)    ((UIncreasing(LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])), ≥)∧[1 + (-1)bso_33] ≥ 0)

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

(5)    ((UIncreasing(LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])), ≥)∧[1 + (-1)bso_33] ≥ 0)

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

(6)    ((UIncreasing(LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_33] ≥ 0)

For Pair LOAD2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135, 1), 0), <(+(i135, 1), i5)), >(i135, 0)), <(i135, i5)), >=(-(i136, i137), 1)), >(+(+(i135, 1), 1), 0)), java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) the following chains were created:
• We consider the chain LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]), LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1]))), COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1))) which results in the following constraint:

(7)    (i137[0]=i137[1]i135[0]=i135[1]i5[0]=i5[1]a5033data[0]=a5033data[1]i136[0]=i136[1]i476[1]=i476[2]&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0))=TRUEi137[1]=i137[2]i5[1]=i5[2]a5033data[1]=a5033data[2]i201[1]=i201[2]i135[1]=i135[2]i136[1]=i136[2]LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1])≥NonInfC∧LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1])≥COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))∧(UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥))

We simplified constraint (7) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(8)    (>(+(+(i135[1], 1), 1), 0)=TRUE>=(-(i136[1], i137[1]), 1)=TRUE<(i135[1], i5[1])=TRUE>(i135[1], 0)=TRUE>(+(i135[1], 1), 0)=TRUE<(+(i135[1], 1), i5[1])=TRUELOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[0])), i135[1], i136[1], i137[1])≥NonInfC∧LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[0])), i135[1], i136[1], i137[1])≥COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[0])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))∧(UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥))

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

(9)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧[(-1)bso_35] ≥ 0)

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

(10)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧[(-1)bso_35] ≥ 0)

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

(11)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧[(-1)bso_35] ≥ 0)

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

(12)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(3)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

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

(13)    ([2] + i135[1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] + [-3] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(2)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

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

(14)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] + [-3] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(2)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]i135[1] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

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

(15)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧[-1] + i5[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(4)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

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

(16)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(5)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

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

(17)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(5)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

(18)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(5)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

For Pair COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → LOAD2257(java.lang.Object(ARRAY(i5, a5033data)), +(+(i135, 1), 1), -(i136, i201), +(i137, +(i476, 1))) the following chains were created:
• We consider the chain LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1]))), COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1))), LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) which results in the following constraint:

(19)    (i476[1]=i476[2]&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0))=TRUEi137[1]=i137[2]i5[1]=i5[2]a5033data[1]=a5033data[2]i201[1]=i201[2]i135[1]=i135[2]i136[1]=i136[2]+(+(i135[2], 1), 1)=i135[0]i5[2]=i5[0]a5033data[2]=a5033data[0]+(i137[2], +(i476[2], 1))=i137[0]-(i136[2], i201[2])=i136[0]COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2])))≥NonInfC∧COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2])))≥LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))∧(UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥))

We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(20)    (>(+(+(i135[1], 1), 1), 0)=TRUE>=(-(i136[1], i137[1]), 1)=TRUE<(i135[1], i5[1])=TRUE>(i135[1], 0)=TRUE>(+(i135[1], 1), 0)=TRUE<(+(i135[1], 1), i5[1])=TRUECOND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))≥NonInfC∧COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))≥LOAD2257(java.lang.Object(ARRAY(i5[1], a5033data[1])), +(+(i135[1], 1), 1), -(i136[1], i201[1]), +(i137[1], +(i476[1], 1)))∧(UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥))

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

(21)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(22)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(23)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(24)    (i135[1] + [1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-1] + [-1]i135[1] ≥ 0∧i135[1] + [-1] ≥ 0∧i135[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(25)    ([2] + i135[1] ≥ 0∧i136[1] + [-1] + [-1]i137[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] + [-3] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(26)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧i5[1] + [-2] + [-1]i135[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] + [-3] + [-1]i135[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]i135[1] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(27)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧[-1] + i5[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(3)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(28)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(29)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

(30)    ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD2257(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → LOAD2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137)
• ((UIncreasing(LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_33] ≥ 0)

• LOAD2257ARR1(java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135, 1), 0), <(+(i135, 1), i5)), >(i135, 0)), <(i135, i5)), >=(-(i136, i137), 1)), >(+(+(i135, 1), 1), 0)), java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201)))
• ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(5)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)
• ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))), ≥)∧0 = 0∧[(5)bni_34 + (-1)Bound*bni_34] + [bni_34]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

• COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5, a5033data)), i135, i136, i137, java.lang.Object(java.lang.String(i476)), java.lang.Object(java.lang.String(i201))) → LOAD2257(java.lang.Object(ARRAY(i5, a5033data)), +(+(i135, 1), 1), -(i136, i201), +(i137, +(i476, 1)))
• ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
• ([2] + i135[1] ≥ 0∧i136[1] ≥ 0∧[1] + i5[1] ≥ 0∧i135[1] ≥ 0∧[1] + i135[1] ≥ 0∧i5[1] ≥ 0∧i137[1] ≥ 0 ⇒ (UIncreasing(LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]i5[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 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) = [2]
POL(LOAD2257(x1, x2, x3, x4)) = [1] + [-1]x2 + [-1]x1
POL(java.lang.Object(x1)) = [-1] + [-1]x1
POL(ARRAY(x1, x2)) = [2] + x1
POL(LOAD2257ARR1(x1, x2, x3, x4)) = [-1]x2 + [-1]x1
POL(COND_LOAD2257ARR1(x1, x2, x3, x4, x5, x6, x7)) = [-1] + [-1]x3 + [-1]x2 + [-1]x1
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
POL(java.lang.String(x1)) = [-1] + [-1]x1

The following pairs are in P>:

The following pairs are in Pbound:

LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))

The following pairs are in P:

LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(&&(&&(&&(&&(&&(>(+(i135[1], 1), 0), <(+(i135[1], 1), i5[1])), >(i135[1], 0)), <(i135[1], i5[1])), >=(-(i136[1], i137[1]), 1)), >(+(+(i135[1], 1), 1), 0)), java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), +(+(i135[2], 1), 1), -(i136[2], i201[2]), +(i137[2], +(i476[2], 1)))

At least the following rules have been oriented under context sensitive arithmetic replacement:

TRUE1&&(TRUE, TRUE)1
FALSE1&&(TRUE, FALSE)1
FALSE1&&(FALSE, TRUE)1
FALSE1&&(FALSE, FALSE)1

### (15) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): LOAD2257ARR1(java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1]) → COND_LOAD2257ARR1(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0, java.lang.Object(ARRAY(i5[1], a5033data[1])), i135[1], i136[1], i137[1], java.lang.Object(java.lang.String(i476[1])), java.lang.Object(java.lang.String(i201[1])))
(2): COND_LOAD2257ARR1(TRUE, java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2], i136[2], i137[2], java.lang.Object(java.lang.String(i476[2])), java.lang.Object(java.lang.String(i201[2]))) → LOAD2257(java.lang.Object(ARRAY(i5[2], a5033data[2])), i135[2] + 1 + 1, i136[2] - i201[2], i137[2] + i476[2] + 1)

(1) -> (2), if (((i476[1]* i476[2]))∧(i135[1] + 1 > 0 && i135[1] + 1 < i5[1] && i135[1] > 0 && i135[1] < i5[1] && i136[1] - i137[1] >= 1 && i135[1] + 1 + 1 > 0* TRUE)∧(i137[1]* i137[2])∧((i5[1]* i5[2])∧(a5033data[1]* a5033data[2]))∧((i201[1]* i201[2]))∧(i135[1]* i135[2])∧(i136[1]* i136[2]))

The set Q consists of the following terms:
Cond_Load2257ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

### (16) IDependencyGraphProof (EQUIVALENT transformation)

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

### (18) Obligation:

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

The following domains are used:
none

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD2257(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0]) → LOAD2257ARR1(java.lang.Object(ARRAY(i5[0], a5033data[0])), i135[0], i136[0], i137[0])

The set Q consists of the following terms: