Termination proof of /tmp/tmpdWQh2E/PastaC9.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 TRUE

    ↳18 IDP

        ↳19 IDependencyGraphProof (⇔)

        ↳20 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC9

/**
 * 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 PastaC9 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x > 0 && y > 0) {
            if (Random.random() < 42) {
                x--;
                y = Random.random();
            } else {
                y--;
            }
        }
    } 
}


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 317 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:
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR1(i138 >= 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1, i76, i78 + -1)
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i406)), java.lang.Object(java.lang.String(i138)))
Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i406)), java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR2(i73 + 1 > 0 && i73 + 1 < i4 && i138 < 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i406)), java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i406)), java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1 + 1, i76 + -1, i406)
The set Q consists of the following terms:
Load1243(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1243ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Load1243ARR2(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)), java.lang.Object(java.lang.String(x6)))

(5) ITRSFilterProcessorProof (SOUND transformation)

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

Load1243ARR2(x1, x2, x3, x4, x5, x6) → Load1243ARR2(x1, x2, x3, x4, x6)
Cond_Load1243ARR2(x1, x2, x3, x4, x5, x6, x7) → Cond_Load1243ARR2(x1, x2, x3, x4, x5, x7)

(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:
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR1(i138 >= 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1, i76, i78 + -1)
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR2(i73 + 1 > 0 && i73 + 1 < i4 && i138 < 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1 + 1, i76 + -1, i406)
The set Q consists of the following terms:
Load1243(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1243ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Load1243ARR2(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))

(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:
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Load1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR1(i138 >= 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1, i76, i78 + -1)
Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Load1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Cond_Load1243ARR2(i73 + 1 > 0 && i73 + 1 < i4 && i138 < 42 && i73 > 0 && i73 < i4 && i78 > 0 && i76 > 0 && i73 + 1 + 1 > 0, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → Load1243(java.lang.Object(ARRAY(i4, a2089data)), i73 + 1 + 1, i76 + -1, i406)

The integer pair graph contains the following rules and edges:
(0): LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0]) → LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))
(1): LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(i138[1] >= 42 && i73[1] > 0 && i73[1] < i4[1] && i78[1] > 0 && i76[1] > 0 && i73[1] + 1 > 0, java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))
(2): COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2]))) → LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2] + 1, i76[2], i78[2] + -1)
(3): LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3]) → LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))
(4): LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(i73[4] + 1 > 0 && i73[4] + 1 < i4[4] && i138[4] < 42 && i73[4] > 0 && i73[4] < i4[4] && i78[4] > 0 && i76[4] > 0 && i73[4] + 1 + 1 > 0, java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))
(5): COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5]))) → LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5] + 1 + 1, i76[5] + -1, i406[5])

(0) -> (1), if ((i76[0] →^* i76[1])∧(java.lang.Object(ARRAY(i4[0], a2089data[0])) →^* java.lang.Object(ARRAY(i4[1], a2089data[1])))∧(i78[0] →^* i78[1])∧(java.lang.Object(java.lang.String(i138[0])) →^* java.lang.Object(java.lang.String(i138[1])))∧(i73[0] →^* i73[1]))

(1) -> (2), if ((i76[1] →^* i76[2])∧(java.lang.Object(java.lang.String(i138[1])) →^* java.lang.Object(java.lang.String(i138[2])))∧(i73[1] →^* i73[2])∧(i78[1] →^* i78[2])∧(java.lang.Object(ARRAY(i4[1], a2089data[1])) →^* java.lang.Object(ARRAY(i4[2], a2089data[2])))∧(i138[1] >= 42 && i73[1] > 0 && i73[1] < i4[1] && i78[1] > 0 && i76[1] > 0 && i73[1] + 1 > 0 →^* TRUE))

(2) -> (0), if ((java.lang.Object(ARRAY(i4[2], a2089data[2])) →^* java.lang.Object(ARRAY(i4[0], a2089data[0])))∧(i78[2] + -1 →^* i78[0])∧(i73[2] + 1 →^* i73[0])∧(i76[2] →^* i76[0]))

(2) -> (3), if ((java.lang.Object(ARRAY(i4[2], a2089data[2])) →^* java.lang.Object(ARRAY(i4[3], a2089data[3])))∧(i78[2] + -1 →^* i78[3])∧(i73[2] + 1 →^* i73[3])∧(i76[2] →^* i76[3]))

(3) -> (4), if ((java.lang.Object(ARRAY(i4[3], a2089data[3])) →^* java.lang.Object(ARRAY(i4[4], a2089data[4])))∧(i78[3] →^* i78[4])∧(java.lang.Object(java.lang.String(i138[3])) →^* java.lang.Object(java.lang.String(i138[4])))∧(i76[3] →^* i76[4])∧(i73[3] →^* i73[4]))

(4) -> (5), if ((i76[4] →^* i76[5])∧(i73[4] + 1 > 0 && i73[4] + 1 < i4[4] && i138[4] < 42 && i73[4] > 0 && i73[4] < i4[4] && i78[4] > 0 && i76[4] > 0 && i73[4] + 1 + 1 > 0 →^* TRUE)∧(i78[4] →^* i78[5])∧(i73[4] →^* i73[5])∧(java.lang.Object(java.lang.String(i138[4])) →^* java.lang.Object(java.lang.String(i138[5])))∧(java.lang.Object(ARRAY(i4[4], a2089data[4])) →^* java.lang.Object(ARRAY(i4[5], a2089data[5]))))

(5) -> (0), if ((i76[5] + -1 →^* i76[0])∧(java.lang.Object(ARRAY(i4[5], a2089data[5])) →^* java.lang.Object(ARRAY(i4[0], a2089data[0])))∧(i406[5] →^* i78[0])∧(i73[5] + 1 + 1 →^* i73[0]))

(5) -> (3), if ((i76[5] + -1 →^* i76[3])∧(i406[5] →^* i78[3])∧(java.lang.Object(ARRAY(i4[5], a2089data[5])) →^* java.lang.Object(ARRAY(i4[3], a2089data[3])))∧(i73[5] + 1 + 1 →^* i73[3]))

The set Q consists of the following terms:
Load1243(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4)
Load1243ARR1(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1243ARR1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Load1243ARR2(java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))
Cond_Load1243ARR2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3, x4, java.lang.Object(java.lang.String(x5)))

(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): LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0]) → LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))
(1): LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(i138[1] >= 42 && i73[1] > 0 && i73[1] < i4[1] && i78[1] > 0 && i76[1] > 0 && i73[1] + 1 > 0, java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))
(2): COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2]))) → LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2] + 1, i76[2], i78[2] + -1)
(3): LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3]) → LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))
(4): LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(i73[4] + 1 > 0 && i73[4] + 1 < i4[4] && i138[4] < 42 && i73[4] > 0 && i73[4] < i4[4] && i78[4] > 0 && i76[4] > 0 && i73[4] + 1 + 1 > 0, java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))
(5): COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5]))) → LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5] + 1 + 1, i76[5] + -1, i406[5])

(2) -> (0), if ((java.lang.Object(ARRAY(i4[2], a2089data[2])) →^* java.lang.Object(ARRAY(i4[0], a2089data[0])))∧(i78[2] + -1 →^* i78[0])∧(i73[2] + 1 →^* i73[0])∧(i76[2] →^* i76[0]))

(2) -> (3), if ((java.lang.Object(ARRAY(i4[2], a2089data[2])) →^* java.lang.Object(ARRAY(i4[3], a2089data[3])))∧(i78[2] + -1 →^* i78[3])∧(i73[2] + 1 →^* i73[3])∧(i76[2] →^* i76[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 ((i76[0] →^* i76[1])∧((i4[0] →^* i4[1])∧(a2089data[0] →^* a2089data[1]))∧(i78[0] →^* i78[1])∧((i138[0] →^* i138[1]))∧(i73[0] →^* i73[1]))

(1) -> (2), if ((i76[1] →^* i76[2])∧((i138[1] →^* i138[2]))∧(i73[1] →^* i73[2])∧(i78[1] →^* i78[2])∧((i4[1] →^* i4[2])∧(a2089data[1] →^* a2089data[2]))∧(i138[1] >= 42 && i73[1] > 0 && i73[1] < i4[1] && i78[1] > 0 && i76[1] > 0 && i73[1] + 1 > 0 →^* TRUE))

(2) -> (0), if (((i4[2] →^* i4[0])∧(a2089data[2] →^* a2089data[0]))∧(i78[2] + -1 →^* i78[0])∧(i73[2] + 1 →^* i73[0])∧(i76[2] →^* i76[0]))

(2) -> (3), if (((i4[2] →^* i4[3])∧(a2089data[2] →^* a2089data[3]))∧(i78[2] + -1 →^* i78[3])∧(i73[2] + 1 →^* i73[3])∧(i76[2] →^* i76[3]))

(3) -> (4), if (((i4[3] →^* i4[4])∧(a2089data[3] →^* a2089data[4]))∧(i78[3] →^* i78[4])∧((i138[3] →^* i138[4]))∧(i76[3] →^* i76[4])∧(i73[3] →^* i73[4]))

(4) -> (5), if ((i76[4] →^* i76[5])∧(i73[4] + 1 > 0 && i73[4] + 1 < i4[4] && i138[4] < 42 && i73[4] > 0 && i73[4] < i4[4] && i78[4] > 0 && i76[4] > 0 && i73[4] + 1 + 1 > 0 →^* TRUE)∧(i78[4] →^* i78[5])∧(i73[4] →^* i73[5])∧((i138[4] →^* i138[5]))∧((i4[4] →^* i4[5])∧(a2089data[4] →^* a2089data[5])))

(5) -> (0), if ((i76[5] + -1 →^* i76[0])∧((i4[5] →^* i4[0])∧(a2089data[5] →^* a2089data[0]))∧(i406[5] →^* i78[0])∧(i73[5] + 1 + 1 →^* i73[0]))

(5) -> (3), if ((i76[5] + -1 →^* i76[3])∧(i406[5] →^* i78[3])∧((i4[5] →^* i4[3])∧(a2089data[5] →^* a2089data[3]))∧(i73[5] + 1 + 1 →^* i73[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 LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → LOAD1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) the following chains were created:

We consider the chain LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0]) → LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0]))) which results in the following constraint:
(1)    (LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0])≥NonInfC∧LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0])≥LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))∧(U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥))

We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(2)    ((U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥)∧[(-1)bso_22] ≥ 0)

We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(3)    ((U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥)∧[(-1)bso_22] ≥ 0)

We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(4)    ((U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥)∧[(-1)bso_22] ≥ 0)

We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(5)    ((U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_22] ≥ 0)

For Pair LOAD1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138, 42), >(i73, 0)), <(i73, i4)), >(i78, 0)), >(i76, 0)), >(+(i73, 1), 0)), java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) the following chains were created:

We consider the chain LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))), COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2]))) → LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1)) which results in the following constraint:
(6)    (i76[1]=i76[2]∧i138[1]=i138[2]∧i73[1]=i73[2]∧i78[1]=i78[2]∧i4[1]=i4[2]∧a2089data[1]=a2089data[2]∧&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0))=TRUE ⇒ LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))≥NonInfC∧LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))≥COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))∧(U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥))

We simplified constraint (6) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(7)    (>(+(i73[1], 1), 0)=TRUE∧>(i76[1], 0)=TRUE∧>(i78[1], 0)=TRUE∧<(i73[1], i4[1])=TRUE∧>=(i138[1], 42)=TRUE∧>(i73[1], 0)=TRUE ⇒ LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))≥NonInfC∧LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))≥COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))∧(U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    (i73[1] ≥ 0∧i76[1] + [-1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-1] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧[(-2)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    (i73[1] ≥ 0∧i76[1] + [-1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-1] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧[(-2)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    (i73[1] ≥ 0∧i76[1] + [-1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-1] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧[(-2)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    (i73[1] ≥ 0∧i76[1] + [-1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-1] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] + [-1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-2)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(12)    ([1] + i73[1] ≥ 0∧i76[1] + [-1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-2] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-3)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    ([1] + i73[1] ≥ 0∧i76[1] ≥ 0∧i78[1] + [-1] ≥ 0∧i4[1] + [-2] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-3)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    ([1] + i73[1] ≥ 0∧i76[1] ≥ 0∧i78[1] ≥ 0∧i4[1] + [-2] + [-1]i73[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-3)bni_23 + (-1)Bound*bni_23] + [(-1)bni_23]i73[1] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    ([1] + i73[1] ≥ 0∧i76[1] ≥ 0∧i78[1] ≥ 0∧i4[1] ≥ 0∧i138[1] + [-42] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    ([1] + i73[1] ≥ 0∧i76[1] ≥ 0∧i78[1] ≥ 0∧i4[1] ≥ 0∧i138[1] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

For Pair COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), +(i73, 1), i76, +(i78, -1)) the following chains were created:

We consider the chain COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2]))) → LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1)) which results in the following constraint:
(17)    (COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2])))≥NonInfC∧COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2])))≥LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))∧(U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥))

We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(18)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥)∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(19)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥)∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(20)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥)∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (20) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(21)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_26] ≥ 0)

For Pair LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → LOAD1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) the following chains were created:

We consider the chain LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3]) → LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3]))) which results in the following constraint:
(22)    (LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3])≥NonInfC∧LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3])≥LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))∧(U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥))

We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(23)    ((U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥)∧[(-1)bso_28] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(24)    ((U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥)∧[(-1)bso_28] ≥ 0)

We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(25)    ((U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥)∧[(-1)bso_28] ≥ 0)

We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(26)    ((U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)

For Pair LOAD1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73, 1), 0), <(+(i73, 1), i4)), <(i138, 42)), >(i73, 0)), <(i73, i4)), >(i78, 0)), >(i76, 0)), >(+(+(i73, 1), 1), 0)), java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) the following chains were created:

We consider the chain LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))), COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5]))) → LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5]) which results in the following constraint:
(27)    (i76[4]=i76[5]∧&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0))=TRUE∧i78[4]=i78[5]∧i73[4]=i73[5]∧i138[4]=i138[5]∧i4[4]=i4[5]∧a2089data[4]=a2089data[5] ⇒ LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))≥NonInfC∧LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))≥COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))∧(U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥))

We simplified constraint (27) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(28)    (>(+(+(i73[4], 1), 1), 0)=TRUE∧>(i76[4], 0)=TRUE∧>(i78[4], 0)=TRUE∧<(i73[4], i4[4])=TRUE∧>(i73[4], 0)=TRUE∧<(i138[4], 42)=TRUE∧>(+(i73[4], 1), 0)=TRUE∧<(+(i73[4], 1), i4[4])=TRUE ⇒ LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))≥NonInfC∧LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))≥COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))∧(U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥))

We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(29)    (i73[4] + [1] ≥ 0∧i76[4] + [-1] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-1] + [-1]i73[4] ≥ 0∧i73[4] + [-1] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧i73[4] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(30)    (i73[4] + [1] ≥ 0∧i76[4] + [-1] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-1] + [-1]i73[4] ≥ 0∧i73[4] + [-1] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧i73[4] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(31)    (i73[4] + [1] ≥ 0∧i76[4] + [-1] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-1] + [-1]i73[4] ≥ 0∧i73[4] + [-1] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧i73[4] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(32)    (i73[4] + [1] ≥ 0∧i76[4] + [-1] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-1] + [-1]i73[4] ≥ 0∧i73[4] + [-1] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧i73[4] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(33)    ([2] + i73[4] ≥ 0∧i76[4] + [-1] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] + [-3] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-3)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] + [-1] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] + [-3] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-3)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧i4[4] + [-2] + [-1]i73[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] + [-3] + [-1]i73[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-3)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i73[4] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(36)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧[-1] + i4[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (36) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(37)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧[1] + i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(38)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧[1] + i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] ≥ 0∧i138[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

(39)    ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧[1] + i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] ≥ 0∧i138[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

For Pair COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), +(+(i73, 1), 1), +(i76, -1), i406) the following chains were created:

We consider the chain COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5]))) → LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5]) which results in the following constraint:
(40)    (COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5])))≥NonInfC∧COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5])))≥LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])∧(U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥))

We simplified constraint (40) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(41)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥)∧[2 + (-1)bso_32] ≥ 0)

We simplified constraint (41) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(42)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥)∧[2 + (-1)bso_32] ≥ 0)

We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(43)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥)∧[2 + (-1)bso_32] ≥ 0)

We simplified constraint (43) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(44)    ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_32] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → LOAD1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
- ((U^Increasing(LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_22] ≥ 0)
LOAD1243ARR1(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138, 42), >(i73, 0)), <(i73, i4)), >(i78, 0)), >(i76, 0)), >(+(i73, 1), 0)), java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
- ([1] + i73[1] ≥ 0∧i76[1] ≥ 0∧i78[1] ≥ 0∧i4[1] ≥ 0∧i138[1] ≥ 0∧i73[1] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))), ≥)∧0 = 0∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i4[1] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)
COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), +(i73, 1), i76, +(i78, -1))
- ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_26] ≥ 0)
LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78) → LOAD1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
- ((U^Increasing(LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)
LOAD1243ARR2(java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73, 1), 0), <(+(i73, 1), i4)), <(i138, 42)), >(i73, 0)), <(i73, i4)), >(i78, 0)), >(i76, 0)), >(+(+(i73, 1), 1), 0)), java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138)))
- ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧[1] + i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] ≥ 0∧i138[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)
- ([2] + i73[4] ≥ 0∧i76[4] ≥ 0∧i78[4] ≥ 0∧[1] + i4[4] ≥ 0∧i73[4] ≥ 0∧[41] + [-1]i138[4] ≥ 0∧[1] + i73[4] ≥ 0∧i4[4] ≥ 0∧i138[4] ≥ 0 ⇒ (U^Increasing(COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]i4[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)
COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4, a2089data)), i73, i76, i78, java.lang.Object(java.lang.String(i138))) → LOAD1243(java.lang.Object(ARRAY(i4, a2089data)), +(+(i73, 1), 1), +(i76, -1), i406)
- ((U^Increasing(LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_32] ≥ 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(LOAD1243(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [1] + [-1]x₁
POL(LOAD1243ARR1(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.String(x₁)) = x₁
POL(COND_LOAD1243ARR1(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [-1]x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(42) = [42]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(-1) = [-1]
POL(LOAD1243ARR2(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_LOAD1243ARR2(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [-1]x₃ + [-1]x₂

The following pairs are in P_>:

COND_LOAD1243ARR1(TRUE, java.lang.Object(ARRAY(i4[2], a2089data[2])), i73[2], i76[2], i78[2], java.lang.Object(java.lang.String(i138[2]))) → LOAD1243(java.lang.Object(ARRAY(i4[2], a2089data[2])), +(i73[2], 1), i76[2], +(i78[2], -1))
COND_LOAD1243ARR2(TRUE, java.lang.Object(ARRAY(i4[5], a2089data[5])), i73[5], i76[5], i78[5], java.lang.Object(java.lang.String(i138[5]))) → LOAD1243(java.lang.Object(ARRAY(i4[5], a2089data[5])), +(+(i73[5], 1), 1), +(i76[5], -1), i406[5])

The following pairs are in P_bound:

LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))
LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))

The following pairs are in P_≥:

LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0]) → LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))
LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(&&(&&(&&(&&(&&(>=(i138[1], 42), >(i73[1], 0)), <(i73[1], i4[1])), >(i78[1], 0)), >(i76[1], 0)), >(+(i73[1], 1), 0)), java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))
LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3]) → LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))
LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(&&(&&(&&(&&(&&(&&(&&(>(+(i73[4], 1), 0), <(+(i73[4], 1), i4[4])), <(i138[4], 42)), >(i73[4], 0)), <(i73[4], i4[4])), >(i78[4], 0)), >(i76[4], 0)), >(+(+(i73[4], 1), 1), 0)), java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))

There are no usable rules.

(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): LOAD1243(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0]) → LOAD1243ARR1(java.lang.Object(ARRAY(i4[0], a2089data[0])), i73[0], i76[0], i78[0], java.lang.Object(java.lang.String(i138[0])))
(1): LOAD1243ARR1(java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1]))) → COND_LOAD1243ARR1(i138[1] >= 42 && i73[1] > 0 && i73[1] < i4[1] && i78[1] > 0 && i76[1] > 0 && i73[1] + 1 > 0, java.lang.Object(ARRAY(i4[1], a2089data[1])), i73[1], i76[1], i78[1], java.lang.Object(java.lang.String(i138[1])))
(3): LOAD1243(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3]) → LOAD1243ARR2(java.lang.Object(ARRAY(i4[3], a2089data[3])), i73[3], i76[3], i78[3], java.lang.Object(java.lang.String(i138[3])))
(4): LOAD1243ARR2(java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4]))) → COND_LOAD1243ARR2(i73[4] + 1 > 0 && i73[4] + 1 < i4[4] && i138[4] < 42 && i73[4] > 0 && i73[4] < i4[4] && i78[4] > 0 && i76[4] > 0 && i73[4] + 1 + 1 > 0, java.lang.Object(ARRAY(i4[4], a2089data[4])), i73[4], i76[4], i78[4], java.lang.Object(java.lang.String(i138[4])))

(0) -> (1), if ((i76[0] →^* i76[1])∧((i4[0] →^* i4[1])∧(a2089data[0] →^* a2089data[1]))∧(i78[0] →^* i78[1])∧((i138[0] →^* i138[1]))∧(i73[0] →^* i73[1]))

(3) -> (4), if (((i4[3] →^* i4[4])∧(a2089data[3] →^* a2089data[4]))∧(i78[3] →^* i78[4])∧((i138[3] →^* i138[4]))∧(i76[3] →^* i76[4])∧(i73[3] →^* i73[4]))

(16) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(17) TRUE

(18) Obligation:

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

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

The following domains are used:

Integer

(2) -> (0), if (((i4[2] →^* i4[0])∧(a2089data[2] →^* a2089data[0]))∧(i78[2] + -1 →^* i78[0])∧(i73[2] + 1 →^* i73[0])∧(i76[2] →^* i76[0]))

(5) -> (0), if ((i76[5] + -1 →^* i76[0])∧((i4[5] →^* i4[0])∧(a2089data[5] →^* a2089data[0]))∧(i406[5] →^* i78[0])∧(i73[5] + 1 + 1 →^* i73[0]))

(2) -> (3), if (((i4[2] →^* i4[3])∧(a2089data[2] →^* a2089data[3]))∧(i78[2] + -1 →^* i78[3])∧(i73[2] + 1 →^* i73[3])∧(i76[2] →^* i76[3]))

(5) -> (3), if ((i76[5] + -1 →^* i76[3])∧(i406[5] →^* i78[3])∧((i4[5] →^* i4[3])∧(a2089data[5] →^* a2089data[3]))∧(i73[5] + 1 + 1 →^* i73[3]))

(19) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(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) TRUE

(18) Obligation:

(19) IDependencyGraphProof (EQUIVALENT transformation)

(20) TRUE