(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC11
`/** * 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 PastaC11 {    public static void main(String[] args) {        Random.args = args;        int x = Random.random();        int y = Random.random();        while (true) {			if (x >= 0) {				x--;				y = Random.random();			} else if (y >= 0) {				y--;			} else {				break;			}        }    } }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 252 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:
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164, java.lang.Object(java.lang.String(i260)))
Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164, java.lang.Object(java.lang.String(i260))) → Cond_Load1423ARR1(i162 > 0 && i162 < i6 && i165 >= 0 && i162 + 1 > 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164, java.lang.Object(java.lang.String(i260)))
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164, java.lang.Object(java.lang.String(i260))) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162 + 1, i165 + -1, i260)
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Cond_Load1423(i175 >= 0 && i166 < 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175 + -1)
The set Q consists of the following terms:
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(5) ITRSFilterProcessorProof (SOUND transformation)

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

java.lang.String(x1) → java.lang.String
Cond_Load1423ARR1(x1, x2, x3, x4, x5, x6) → Cond_Load1423ARR1(x1, x2, x3, x4, x5)

(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:
Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Cond_Load1423ARR1(i162 > 0 && i162 < i6 && i165 >= 0 && i162 + 1 > 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162 + 1, i165 + -1, i260)
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Cond_Load1423(i175 >= 0 && i166 < 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175 + -1)
The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(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:
Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Cond_Load1423ARR1(i162 > 0 && i162 < i6 && i165 >= 0 && i162 + 1 > 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162 + 1, i165 + -1, i260)
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Cond_Load1423(i175 >= 0 && i166 < 0, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175 + -1)

The integer pair graph contains the following rules and edges:
(0): LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])
(1): LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
(2): COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2] + 1, i165[2] + -1, i260[2])
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

(0) -> (1), if ((i164[0]* i164[1])∧(java.lang.Object(ARRAY(i6[0], a2251data[0])) →* java.lang.Object(ARRAY(i6[1], a2251data[1])))∧(i165[0]* i165[1])∧(i162[0]* i162[1]))

(1) -> (2), if ((i165[1]* i165[2])∧(i162[1]* i162[2])∧(java.lang.Object(ARRAY(i6[1], a2251data[1])) →* java.lang.Object(ARRAY(i6[2], a2251data[2])))∧(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0* TRUE)∧(i164[1]* i164[2]))

(2) -> (0), if ((i165[2] + -1* i165[0])∧(java.lang.Object(ARRAY(i6[2], a2251data[2])) →* java.lang.Object(ARRAY(i6[0], a2251data[0])))∧(i162[2] + 1* i162[0])∧(i260[2]* i164[0]))

(2) -> (3), if ((i260[2]* i175[3])∧(java.lang.Object(ARRAY(i6[2], a2251data[2])) →* java.lang.Object(ARRAY(i6[3], a2251data[3])))∧(i165[2] + -1* i166[3])∧(i162[2] + 1* i162[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧(java.lang.Object(ARRAY(i6[3], a2251data[3])) →* java.lang.Object(ARRAY(i6[4], a2251data[4])))∧(i175[3]* i175[4]))

(4) -> (0), if ((i166[4]* i165[0])∧(i162[4]* i162[0])∧(i175[4] + -1* i164[0])∧(java.lang.Object(ARRAY(i6[4], a2251data[4])) →* java.lang.Object(ARRAY(i6[0], a2251data[0]))))

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧(java.lang.Object(ARRAY(i6[4], a2251data[4])) →* java.lang.Object(ARRAY(i6[3], a2251data[3])))∧(i166[4]* i166[3]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(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): LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])
(1): LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
(2): COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2] + 1, i165[2] + -1, i260[2])
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

(0) -> (1), if ((i164[0]* i164[1])∧(java.lang.Object(ARRAY(i6[0], a2251data[0])) →* java.lang.Object(ARRAY(i6[1], a2251data[1])))∧(i165[0]* i165[1])∧(i162[0]* i162[1]))

(1) -> (2), if ((i165[1]* i165[2])∧(i162[1]* i162[2])∧(java.lang.Object(ARRAY(i6[1], a2251data[1])) →* java.lang.Object(ARRAY(i6[2], a2251data[2])))∧(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0* TRUE)∧(i164[1]* i164[2]))

(2) -> (0), if ((i165[2] + -1* i165[0])∧(java.lang.Object(ARRAY(i6[2], a2251data[2])) →* java.lang.Object(ARRAY(i6[0], a2251data[0])))∧(i162[2] + 1* i162[0])∧(i260[2]* i164[0]))

(2) -> (3), if ((i260[2]* i175[3])∧(java.lang.Object(ARRAY(i6[2], a2251data[2])) →* java.lang.Object(ARRAY(i6[3], a2251data[3])))∧(i165[2] + -1* i166[3])∧(i162[2] + 1* i162[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧(java.lang.Object(ARRAY(i6[3], a2251data[3])) →* java.lang.Object(ARRAY(i6[4], a2251data[4])))∧(i175[3]* i175[4]))

(4) -> (0), if ((i166[4]* i165[0])∧(i162[4]* i162[0])∧(i175[4] + -1* i164[0])∧(java.lang.Object(ARRAY(i6[4], a2251data[4])) →* java.lang.Object(ARRAY(i6[0], a2251data[0]))))

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧(java.lang.Object(ARRAY(i6[4], a2251data[4])) →* java.lang.Object(ARRAY(i6[3], a2251data[3])))∧(i166[4]* i166[3]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(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): LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])
(1): LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
(2): COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2] + 1, i165[2] + -1, i260[2])
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

(0) -> (1), if ((i164[0]* i164[1])∧((i6[0]* i6[1])∧(a2251data[0]* a2251data[1]))∧(i165[0]* i165[1])∧(i162[0]* i162[1]))

(1) -> (2), if ((i165[1]* i165[2])∧(i162[1]* i162[2])∧((i6[1]* i6[2])∧(a2251data[1]* a2251data[2]))∧(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0* TRUE)∧(i164[1]* i164[2]))

(2) -> (0), if ((i165[2] + -1* i165[0])∧((i6[2]* i6[0])∧(a2251data[2]* a2251data[0]))∧(i162[2] + 1* i162[0])∧(i260[2]* i164[0]))

(2) -> (3), if ((i260[2]* i175[3])∧((i6[2]* i6[3])∧(a2251data[2]* a2251data[3]))∧(i165[2] + -1* i166[3])∧(i162[2] + 1* i162[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧((i6[3]* i6[4])∧(a2251data[3]* a2251data[4]))∧(i175[3]* i175[4]))

(4) -> (0), if ((i166[4]* i165[0])∧(i162[4]* i162[0])∧(i175[4] + -1* i164[0])∧((i6[4]* i6[0])∧(a2251data[4]* a2251data[0])))

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧((i6[4]* i6[3])∧(a2251data[4]* a2251data[3]))∧(i166[4]* i166[3]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(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 LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → LOAD1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]), LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[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(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥)∧[(-1)bso_35] ≥ 0)

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

(4)    ((UIncreasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥)∧[(-1)bso_35] ≥ 0)

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

(5)    ((UIncreasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥)∧[(-1)bso_35] ≥ 0)

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

(6)    ((UIncreasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

For Pair LOAD1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → COND_LOAD1423ARR1(&&(&&(&&(>(i162, 0), <(i162, i6)), >=(i165, 0)), >(+(i162, 1), 0)), java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) the following chains were created:
• We consider the chain LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]), COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2]) which results in the following constraint:

(7)    (i165[1]=i165[2]i162[1]=i162[2]i6[1]=i6[2]a2251data[1]=a2251data[2]&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0))=TRUEi164[1]=i164[2]LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥NonInfC∧LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])∧(UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥))

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

(8)    (>(+(i162[1], 1), 0)=TRUE>=(i165[1], 0)=TRUE>(i162[1], 0)=TRUE<(i162[1], i6[1])=TRUELOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥NonInfC∧LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])∧(UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥))

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

(9)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i165[1] + [(-1)bni_36]i162[1] + [bni_36]i6[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(10)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i165[1] + [(-1)bni_36]i162[1] + [bni_36]i6[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(11)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i165[1] + [(-1)bni_36]i162[1] + [bni_36]i6[1] ≥ 0∧[(-1)bso_37] ≥ 0)

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

(12)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_36 + (-1)Bound*bni_36] + [bni_36]i165[1] + [(-1)bni_36]i162[1] + [bni_36]i6[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(13)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] + [-2] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_36 + (-1)Bound*bni_36] + [bni_36]i165[1] + [(-1)bni_36]i162[1] + [bni_36]i6[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

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

(14)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_36] + [bni_36]i165[1] + [bni_36]i6[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

For Pair COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), +(i162, 1), +(i165, -1), i260) the following chains were created:
• We consider the chain LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]), COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2]), LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) which results in the following constraint:

(15)    (i165[1]=i165[2]i162[1]=i162[2]i6[1]=i6[2]a2251data[1]=a2251data[2]&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0))=TRUEi164[1]=i164[2]+(i165[2], -1)=i165[0]i6[2]=i6[0]a2251data[2]=a2251data[0]+(i162[2], 1)=i162[0]i260[2]=i164[0]COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2])≥NonInfC∧COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2])≥LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥))

We simplified constraint (15) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(16)    (>(+(i162[1], 1), 0)=TRUE>=(i165[1], 0)=TRUE>(i162[1], 0)=TRUE<(i162[1], i6[1])=TRUECOND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥NonInfC∧COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥LOAD1423(java.lang.Object(ARRAY(i6[1], a2251data[1])), +(i162[1], 1), +(i165[1], -1), i260[2])∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥))

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

(17)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(18)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(19)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(20)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

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

(21)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] + [-2] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

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

(22)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_38] + [bni_38]i165[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

• We consider the chain LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]), COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2]), LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) which results in the following constraint:

(23)    (i165[1]=i165[2]i162[1]=i162[2]i6[1]=i6[2]a2251data[1]=a2251data[2]&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0))=TRUEi164[1]=i164[2]i260[2]=i175[3]i6[2]=i6[3]a2251data[2]=a2251data[3]+(i165[2], -1)=i166[3]+(i162[2], 1)=i162[3]COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2])≥NonInfC∧COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2])≥LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥))

We simplified constraint (23) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(24)    (>(+(i162[1], 1), 0)=TRUE>=(i165[1], 0)=TRUE>(i162[1], 0)=TRUE<(i162[1], i6[1])=TRUECOND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥NonInfC∧COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])≥LOAD1423(java.lang.Object(ARRAY(i6[1], a2251data[1])), +(i162[1], 1), +(i165[1], -1), i260[2])∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥))

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

(25)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(26)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(27)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧[2 + (-1)bso_39] ≥ 0)

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

(28)    (i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] + [-1] ≥ 0∧i6[1] + [-1] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

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

(29)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] + [-2] + [-1]i162[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_38 + (-1)Bound*bni_38] + [bni_38]i165[1] + [(-1)bni_38]i162[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

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

(30)    ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_38] + [bni_38]i165[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

For Pair LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → COND_LOAD1423(&&(>=(i175, 0), <(i166, 0)), java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)) which results in the following constraint:

(31)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

We simplified constraint (31) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(32)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUELOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

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

(33)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i166[3] + [(-1)bni_40]i162[3] + [bni_40]i6[3] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(34)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i166[3] + [(-1)bni_40]i162[3] + [bni_40]i6[3] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(35)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i166[3] + [(-1)bni_40]i162[3] + [bni_40]i6[3] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(36)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40] = 0∧0 = 0∧[bni_40] = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

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

(37)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40] = 0∧0 = 0∧[bni_40] = 0∧[(-2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

For Pair COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, +(i175, -1)) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)), LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) which results in the following constraint:

(38)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]i166[4]=i165[0]i162[4]=i162[0]+(i175[4], -1)=i164[0]i6[4]=i6[0]a2251data[4]=a2251data[0]COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

We simplified constraint (38) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(39)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUECOND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], +(i175[3], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(40)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(41)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(42)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(43)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

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

(44)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-2)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)), LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) which results in the following constraint:

(45)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]+(i175[4], -1)=i175[3]1i162[4]=i162[3]1i6[4]=i6[3]1a2251data[4]=a2251data[3]1i166[4]=i166[3]1COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

We simplified constraint (45) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(46)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUECOND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], +(i175[3], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(47)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(48)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(49)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] + [(-1)bni_42]i162[3] + [bni_42]i6[3] ≥ 0∧[(-1)bso_43] ≥ 0)

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

(50)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

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

(51)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-2)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → LOAD1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
• ((UIncreasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

• LOAD1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → COND_LOAD1423ARR1(&&(&&(&&(>(i162, 0), <(i162, i6)), >=(i165, 0)), >(+(i162, 1), 0)), java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
• ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_36] + [bni_36]i165[1] + [bni_36]i6[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

• COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), +(i162, 1), +(i165, -1), i260)
• ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_38] + [bni_38]i165[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)
• ([1] + i162[1] ≥ 0∧i165[1] ≥ 0∧i162[1] ≥ 0∧i6[1] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_38] + [bni_38]i165[1] + [bni_38]i6[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_39] ≥ 0)

• LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → COND_LOAD1423(&&(>=(i175, 0), <(i166, 0)), java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175)
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_40] = 0∧0 = 0∧[bni_40] = 0∧[(-2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

• COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6, a2251data)), i162, i166, i175) → LOAD1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i166, +(i175, -1))
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-2)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_42] = 0∧0 = 0∧[bni_42] = 0∧[(-2)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 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(LOAD1423(x1, x2, x3, x4)) = [-1] + x3 + [-1]x2 + [-1]x1
POL(java.lang.Object(x1)) = [-1] + [-1]x1
POL(ARRAY(x1, x2)) = [-1] + x1
POL(LOAD1423ARR1(x1, x2, x3, x4)) = [-1] + x3 + [-1]x2 + [-1]x1
POL(COND_LOAD1423ARR1(x1, x2, x3, x4, x5)) = [-1] + x4 + [-1]x3 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]
POL(-1) = [-1]
POL(COND_LOAD1423(x1, x2, x3, x4, x5)) = [-1] + x4 + [-1]x3 + [-1]x2

The following pairs are in P>:

COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])

The following pairs are in Pbound:

LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
COND_LOAD1423ARR1(TRUE, java.lang.Object(ARRAY(i6[2], a2251data[2])), i162[2], i165[2], i164[2]) → LOAD1423(java.lang.Object(ARRAY(i6[2], a2251data[2])), +(i162[2], 1), +(i165[2], -1), i260[2])

The following pairs are in P:

LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(&&(&&(&&(>(i162[1], 0), <(i162[1], i6[1])), >=(i165[1], 0)), >(+(i162[1], 1), 0)), java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))

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

FALSE1&&(FALSE, TRUE)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:
(0): LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])
(1): LOAD1423ARR1(java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1]) → COND_LOAD1423ARR1(i162[1] > 0 && i162[1] < i6[1] && i165[1] >= 0 && i162[1] + 1 > 0, java.lang.Object(ARRAY(i6[1], a2251data[1])), i162[1], i165[1], i164[1])
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

(4) -> (0), if ((i166[4]* i165[0])∧(i162[4]* i162[0])∧(i175[4] + -1* i164[0])∧((i6[4]* i6[0])∧(a2251data[4]* a2251data[0])))

(0) -> (1), if ((i164[0]* i164[1])∧((i6[0]* i6[1])∧(a2251data[0]* a2251data[1]))∧(i165[0]* i165[1])∧(i162[0]* i162[1]))

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧((i6[4]* i6[3])∧(a2251data[4]* a2251data[3]))∧(i166[4]* i166[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧((i6[3]* i6[4])∧(a2251data[3]* a2251data[4]))∧(i175[3]* i175[4]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(16) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(17) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧((i6[4]* i6[3])∧(a2251data[4]* a2251data[3]))∧(i166[4]* i166[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧((i6[3]* i6[4])∧(a2251data[3]* a2251data[4]))∧(i175[3]* i175[4]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(18) IDPNonInfProof (SOUND transformation)

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

For Pair COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)), LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) which results in the following constraint:

(1)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]+(i175[4], -1)=i175[3]1i162[4]=i162[3]1i6[4]=i6[3]1a2251data[4]=a2251data[3]1i166[4]=i166[3]1COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(2)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUECOND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], +(i175[3], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(3)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[(-1)bso_23] ≥ 0)

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

(4)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[(-1)bso_23] ≥ 0)

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

(5)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[(-1)bso_23] ≥ 0)

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

(6)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

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

(7)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_22 + bni_22] + [bni_22]i175[3] + [bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

For Pair LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)) which results in the following constraint:

(8)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

We simplified constraint (8) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(9)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUELOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

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

(10)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[1 + (-1)bso_25] ≥ 0)

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

(11)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[1 + (-1)bso_25] ≥ 0)

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

(12)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[1 + (-1)bso_25] ≥ 0)

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

(13)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)

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

(14)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_22 + bni_22] + [bni_22]i175[3] + [bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

• LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_25] ≥ 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(COND_LOAD1423(x1, x2, x3, x4, x5)) = x5 + [-1]x4 + [-1]x2 + [-1]x1
POL(java.lang.Object(x1)) = [-1] + [-1]x1
POL(ARRAY(x1, x2)) = [-1]
POL(LOAD1423(x1, x2, x3, x4)) = [1] + x4 + [-1]x3 + [-1]x1
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(&&(x1, x2)) = 0
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]

The following pairs are in P>:

LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

The following pairs are in Pbound:

COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))
LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

The following pairs are in P:

COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))

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

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

(20) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(21) IDependencyGraphProof (EQUIVALENT transformation)

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

(23) 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 is empty.

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(24) IDependencyGraphProof (EQUIVALENT transformation)

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

(26) 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): LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0]) → LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)

(4) -> (0), if ((i166[4]* i165[0])∧(i162[4]* i162[0])∧(i175[4] + -1* i164[0])∧((i6[4]* i6[0])∧(a2251data[4]* a2251data[0])))

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧((i6[4]* i6[3])∧(a2251data[4]* a2251data[3]))∧(i166[4]* i166[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧((i6[3]* i6[4])∧(a2251data[3]* a2251data[4]))∧(i175[3]* i175[4]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(27) IDependencyGraphProof (EQUIVALENT transformation)

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

(28) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(4): COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4] + -1)
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

(4) -> (3), if ((i175[4] + -1* i175[3])∧(i162[4]* i162[3])∧((i6[4]* i6[3])∧(a2251data[4]* a2251data[3]))∧(i166[4]* i166[3]))

(3) -> (4), if ((i166[3]* i166[4])∧(i175[3] >= 0 && i166[3] < 0* TRUE)∧(i162[3]* i162[4])∧((i6[3]* i6[4])∧(a2251data[3]* a2251data[4]))∧(i175[3]* i175[4]))

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(29) IDPNonInfProof (SOUND transformation)

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

For Pair COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)), LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) which results in the following constraint:

(1)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]+(i175[4], -1)=i175[3]1i162[4]=i162[3]1i6[4]=i6[3]1a2251data[4]=a2251data[3]1i166[4]=i166[3]1COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4])≥LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(2)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUECOND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], +(i175[3], -1))∧(UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥))

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

(3)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

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

(4)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

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

(5)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

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

(6)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]i175[3] + [(-1)bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

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

(7)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

For Pair LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) the following chains were created:
• We consider the chain LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]), COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1)) which results in the following constraint:

(8)    (i166[3]=i166[4]&&(>=(i175[3], 0), <(i166[3], 0))=TRUEi162[3]=i162[4]i6[3]=i6[4]a2251data[3]=a2251data[4]i175[3]=i175[4]LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

We simplified constraint (8) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(9)    (>=(i175[3], 0)=TRUE<(i166[3], 0)=TRUELOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥NonInfC∧LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])≥COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])∧(UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥))

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

(10)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(11)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(12)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(13)    (i175[3] ≥ 0∧[-1] + [-1]i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i175[3] + [(-1)bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

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

(14)    (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_24] + [bni_24]i175[3] + [bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_22] + [bni_22]i175[3] + [bni_22]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_23] ≥ 0)

• LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])
• (i175[3] ≥ 0∧i166[3] ≥ 0 ⇒ (UIncreasing(COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_24] + [bni_24]i175[3] + [bni_24]i166[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 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) = [1]
POL(COND_LOAD1423(x1, x2, x3, x4, x5)) = [-1] + x5 + [-1]x4 + [-1]x2 + [-1]x1
POL(java.lang.Object(x1)) = [-1] + [-1]x1
POL(ARRAY(x1, x2)) = [-1]
POL(LOAD1423(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3 + [-1]x1
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(&&(x1, x2)) = 0
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]

The following pairs are in P>:

COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))

The following pairs are in Pbound:

COND_LOAD1423(TRUE, java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], i175[4]) → LOAD1423(java.lang.Object(ARRAY(i6[4], a2251data[4])), i162[4], i166[4], +(i175[4], -1))
LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

The following pairs are in P:

LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(&&(>=(i175[3], 0), <(i166[3], 0)), java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

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

(31) 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:
(3): LOAD1423(java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3]) → COND_LOAD1423(i175[3] >= 0 && i166[3] < 0, java.lang.Object(ARRAY(i6[3], a2251data[3])), i162[3], i166[3], i175[3])

The set Q consists of the following terms:
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(32) IDependencyGraphProof (EQUIVALENT transformation)

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

(34) 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 is empty.

The set Q consists of the following terms: