Termination proof of /tmp/tmpecoZnV/PastaC11.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇐)

↳2 FIGraph

↳3 FIGtoITRSProof (⇐)

↳4 ITRS

↳5 ITRSFilterProcessorProof (⇐)

↳6 ITRS

↳7 ITRStoIDPProof (⇔)

↳8 IDP

↳9 UsableRulesProof (⇔)

↳10 IDP

↳11 ItpfGraphProof (⇔)

↳12 IDP

↳13 IDPNonInfProof (⇐)

↳14 AND

    ↳15 IDP

        ↳16 IDependencyGraphProof (⇔)

        ↳17 IDP

        ↳18 IDPNonInfProof (⇐)

        ↳19 AND

            ↳20 IDP

                ↳21 IDependencyGraphProof (⇔)

                ↳22 TRUE

            ↳23 IDP

                ↳24 IDependencyGraphProof (⇔)

                ↳25 TRUE

    ↳26 IDP

        ↳27 IDependencyGraphProof (⇔)

        ↳28 IDP

        ↳29 IDPNonInfProof (⇐)

        ↳30 AND

            ↳31 IDP

                ↳32 IDependencyGraphProof (⇔)

                ↳33 TRUE

            ↳34 IDP

                ↳35 IDependencyGraphProof (⇔)

                ↳36 TRUE

(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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
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:

Load1423ARR1(x1, x2, x3, x4, x5) → Load1423ARR1(x1, x2, x3, x4)
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:
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Cond_Load1423(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)

(7) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(8) Obligation:

IDP problem:
The following function symbols are pre-defined:

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
Load1423(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164) → Load1423ARR1(java.lang.Object(ARRAY(i6, a2251data)), i162, i165, i164)
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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
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]))

(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]))

(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

(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]))

(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:
(1)    (i164[0]=i164[1]∧i6[0]=i6[1]∧a2251data[0]=a2251data[1]∧i165[0]=i165[1]∧i162[0]=i162[1] ⇒ LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])≥NonInfC∧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])∧(U^Increasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (LOAD1423(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])≥NonInfC∧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])∧(U^Increasing(LOAD1423ARR1(java.lang.Object(ARRAY(i6[0], a2251data[0])), i162[0], i165[0], i164[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    ((U^Increasing(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)    ((U^Increasing(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)    ((U^Increasing(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)    ((U^Increasing(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))=TRUE∧i164[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])∧(U^Increasing(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])=TRUE ⇒ 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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i164[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])∧(U^Increasing(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])=TRUE ⇒ COND_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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i164[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])∧(U^Increasing(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])=TRUE ⇒ COND_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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i162[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])∧(U^Increasing(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)=TRUE ⇒ 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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i162[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))∧(U^Increasing(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)=TRUE ⇒ COND_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))∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i162[3]=i162[4]∧i6[3]=i6[4]∧a2251data[3]=a2251data[4]∧i175[3]=i175[4]∧+(i175[4], -1)=i175[3]1∧i162[4]=i162[3]1∧i6[4]=i6[3]1∧a2251data[4]=a2251data[3]1∧i166[4]=i166[3]1 ⇒ 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))∧(U^Increasing(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)=TRUE ⇒ COND_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))∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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)
- ((U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 P_bound 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 P_bound.
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 P_bound:

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_≥:

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])
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

(14) Complex Obligation (AND)

(15) Obligation:

IDP problem:
The following function symbols are pre-defined:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 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]))

(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]))

(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))=TRUE∧i162[3]=i162[4]∧i6[3]=i6[4]∧a2251data[3]=a2251data[4]∧i175[3]=i175[4]∧+(i175[4], -1)=i175[3]1∧i162[4]=i162[3]1∧i6[4]=i6[3]1∧a2251data[4]=a2251data[3]1∧i166[4]=i166[3]1 ⇒ 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))∧(U^Increasing(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)=TRUE ⇒ COND_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))∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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))=TRUE∧i162[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])∧(U^Increasing(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)=TRUE ⇒ 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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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)

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 P_bound:

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

(19) Complex Obligation (AND)

(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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
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.

(22) TRUE

(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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
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.

(25) TRUE

(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

(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]))

(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

(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]))

(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))=TRUE∧i162[3]=i162[4]∧i6[3]=i6[4]∧a2251data[3]=a2251data[4]∧i175[3]=i175[4]∧+(i175[4], -1)=i175[3]1∧i162[4]=i162[3]1∧i6[4]=i6[3]1∧a2251data[4]=a2251data[3]1∧i166[4]=i166[3]1 ⇒ 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))∧(U^Increasing(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)=TRUE ⇒ COND_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))∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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)

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))=TRUE∧i162[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])∧(U^Increasing(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)=TRUE ⇒ 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])∧(U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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 ⇒ (U^Increasing(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)

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 P_bound:

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

(30) Complex Obligation (AND)

(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:
Load1423(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1423ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
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.

(33) TRUE

(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

(35) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) ITRSFilterProcessorProof (SOUND transformation)

(6) Obligation:

(7) ITRStoIDPProof (EQUIVALENT transformation)

(8) Obligation:

(9) UsableRulesProof (EQUIVALENT transformation)

(10) Obligation:

(11) ItpfGraphProof (EQUIVALENT transformation)

(12) Obligation:

(13) IDPNonInfProof (SOUND transformation)

(14) Complex Obligation (AND)

(15) Obligation:

(16) IDependencyGraphProof (EQUIVALENT transformation)

(17) Obligation:

(18) IDPNonInfProof (SOUND transformation)

(19) Complex Obligation (AND)

(20) Obligation:

(21) IDependencyGraphProof (EQUIVALENT transformation)

(22) TRUE

(23) Obligation:

(24) IDependencyGraphProof (EQUIVALENT transformation)

(25) TRUE

(26) Obligation:

(27) IDependencyGraphProof (EQUIVALENT transformation)

(28) Obligation:

(29) IDPNonInfProof (SOUND transformation)

(30) Complex Obligation (AND)

(31) Obligation:

(32) IDependencyGraphProof (EQUIVALENT transformation)

(33) TRUE

(34) Obligation:

(35) IDependencyGraphProof (EQUIVALENT transformation)

(36) TRUE