Termination proof of /tmp/tmp3lgpvE/BubbleSortR.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 AND

    ↳5 IDP

        ↳6 IDPNonInfProof (⇒)

        ↳7 AND

            ↳8 IDP

                ↳9 IDependencyGraphProof (⇔)

                ↳10 TRUE

            ↳11 IDP

                ↳12 IDependencyGraphProof (⇔)

                ↳13 TRUE

    ↳14 IDP

        ↳15 IDPNonInfProof (⇒)

        ↳16 AND

            ↳17 IDP

                ↳18 IDependencyGraphProof (⇔)

                ↳19 TRUE

            ↳20 IDP

                ↳21 IDependencyGraphProof (⇔)

                ↳22 TRUE

    ↳23 IDP

        ↳24 IDPNonInfProof (⇒)

        ↳25 AND

            ↳26 IDP

                ↳27 IDependencyGraphProof (⇔)

                ↳28 TRUE

            ↳29 IDP

                ↳30 IDependencyGraphProof (⇔)

                ↳31 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: BubbleSortR

class BubbleSortR {
    public static void main(String[] args) {
	Random.args = args;
	int dim = Random.random()*Random.random();
	int[] t = new int[dim] ;
	for(int i = 0; i < t.length; i++)
	    t[i] = Random.random();
	sort(t);
    }

    public static void sort(int[] x) {
	int n = x.length;
	for (int pass=1; pass < n; pass++)  // count how many times
	    // This next loop becomes shorter and shorter
	    aux(0,n-pass,x);
	//for (int i = 0; i < x.length; i++)
	//    System.out.print(x[i]+ " ");
		}

    private static void aux(int min, int max, int[] x) {
	if (min >= max) return;
	int i = min;
	if (x[i] > x[i+1]) {
	    // exchange elements
	    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
	}
	aux(min+1,max,x);
    }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
      if (index >= args.length)
	  return 0;

      String string = args[index];
      index++;
      return string.length();
  }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
BubbleSortR.main([Ljava/lang/String;)V: Graph of 414 nodes with 2 SCCs.

BubbleSortR.aux(II[I)V: Graph of 217 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 51 rules for P and 165 rules for R.

Combined rules. Obtained 4 rules for P and 9 rules for R.

Filtered ground terms:

4199_0_aux_Load(x1, x2, x3, x4, x5) → 4199_0_aux_Load(x2, x3, x4, x5)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4854_0_aux_LE(x1, x3, x4, x5, x6, x7, x8)
4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → 4854_0_aux_LE(x2, x3, x4, x5, x6, x7)
Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4853_0_aux_LE(x1, x3, x4, x5, x6, x7, x8)
4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → 4853_0_aux_LE(x2, x3, x4, x5, x6, x7)
Cond_4199_0_aux_Load1(x1, x2, x3, x4, x5, x6) → Cond_4199_0_aux_Load1(x1, x3, x4, x5, x6)
Cond_4199_0_aux_Load(x1, x2, x3, x4, x5, x6) → Cond_4199_0_aux_Load(x1, x3, x4, x5, x6)
5778_0_aux_InvokeMethod(x1, x2, x3, x4) → 5778_0_aux_InvokeMethod(x2, x3, x4)
6211_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 6211_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
6115_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9) → 6115_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8, x9)
6068_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) → 6068_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8, x9, x10)
5775_0_aux_Return(x1) → 5775_0_aux_Return
5579_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5579_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
5338_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8) → 5338_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8)
5100_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5100_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
4295_0_aux_Return(x1, x2, x3, x4) → 4295_0_aux_Return(x2, x3, x4)

Filtered duplicate args:

4199_0_aux_Load(x1, x2, x3, x4) → 4199_0_aux_Load(x2, x3, x4)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_4854_0_aux_LE(x1, x3, x4, x5, x6, x7)
4854_0_aux_LE(x1, x2, x3, x4, x5, x6) → 4854_0_aux_LE(x2, x3, x4, x5, x6)
Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_4853_0_aux_LE(x1, x3, x4, x5, x6, x7)
4853_0_aux_LE(x1, x2, x3, x4, x5, x6) → 4853_0_aux_LE(x2, x3, x4, x5, x6)
Cond_4199_0_aux_Load1(x1, x2, x3, x4, x5) → Cond_4199_0_aux_Load1(x1, x3, x4, x5)
Cond_4199_0_aux_Load(x1, x2, x3, x4, x5) → Cond_4199_0_aux_Load(x1, x3, x4, x5)
6211_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 6211_0_aux_ArrayAccess(x1, x2, x4, x5, x6)
6115_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8) → 6115_0_aux_ArrayAccess(x2, x5, x6, x7, x8)
6068_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9) → 6068_0_aux_ArrayAccess(x2, x5, x7, x8, x9)
5579_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 5579_0_aux_ArrayAccess(x2, x5, x6)
5338_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5338_0_aux_ArrayAccess(x2, x4, x5, x6, x7)
5100_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 5100_0_aux_ArrayAccess(x2, x5, x6)

Filtered unneeded arguments:

Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6) → Cond_4853_0_aux_LE(x1, x2, x3, x4)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6) → Cond_4854_0_aux_LE(x1, x2, x3, x4)

Combined rules. Obtained 4 rules for P and 9 rules for R.

Finished conversion. Obtained 4 rules for P and 9 rules for R. System has predefined symbols.

Log for SCC 1:

Generated 18 rules for P and 242 rules for R.

Combined rules. Obtained 2 rules for P and 28 rules for R.

Filtered ground terms:

6187_0_aux_Load(x1, x2, x3, x4) → 6187_0_aux_Load(x3, x4)
6187_1_sort_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → 6187_1_sort_InvokeMethod(x1, x2, x3, x4, x6, x7)
5775_0_aux_Return(x1) → 5775_0_aux_Return
4295_0_aux_Return(x1, x2, x3, x4) → 4295_0_aux_Return(x2, x3, x4)
5778_0_aux_InvokeMethod(x1, x2, x3, x4) → 5778_0_aux_InvokeMethod(x2, x3, x4)
6211_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 6211_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
6115_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9) → 6115_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8, x9)
6068_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) → 6068_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8, x9, x10)
5579_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5579_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
5338_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8) → 5338_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7, x8)
5100_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5100_0_aux_ArrayAccess(x2, x3, x4, x5, x6, x7)
4204_0_aux_LT(x1, x2, x3, x4, x5, x6) → 4204_0_aux_LT(x2, x3, x4, x5, x6)
Cond_4854_0_aux_LE2(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4854_0_aux_LE2(x1, x3, x4, x5, x6, x7, x8)
4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → 4854_0_aux_LE(x2, x3, x4, x5, x6, x7)
Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4853_0_aux_LE(x1, x3, x4, x5, x6, x7, x8)
4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → 4853_0_aux_LE(x2, x3, x4, x5, x6, x7)
Cond_4854_0_aux_LE1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4854_0_aux_LE1(x1, x3, x4, x5, x6, x7, x8)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_4854_0_aux_LE(x1, x3, x4, x5, x6, x7, x8)
Cond_4204_0_aux_LT4(x1, x2, x3, x4, x5, x6, x7) → Cond_4204_0_aux_LT4(x1, x3, x4, x5, x6, x7)
Cond_4204_0_aux_LT3(x1, x2, x3, x4, x5, x6, x7) → Cond_4204_0_aux_LT3(x1, x3, x4, x5, x6, x7)
Cond_4204_0_aux_LT2(x1, x2, x3, x4, x5, x6, x7) → Cond_4204_0_aux_LT2(x1, x3, x4, x5, x6, x7)
Cond_4204_0_aux_LT1(x1, x2, x3, x4, x5, x6, x7) → Cond_4204_0_aux_LT1(x1, x3, x4, x5, x6, x7)
Cond_4204_0_aux_LT(x1, x2, x3, x4, x5, x6, x7) → Cond_4204_0_aux_LT(x1, x3, x4, x5, x6, x7)
6255_0_main_InvokeMethod(x1, x2) → 6255_0_main_InvokeMethod(x2)

Filtered duplicate args:

6187_1_sort_InvokeMethod(x1, x2, x3, x4, x5, x6) → 6187_1_sort_InvokeMethod(x1, x3, x4, x5, x6)
6211_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 6211_0_aux_ArrayAccess(x1, x2, x4, x5, x6)
6115_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8) → 6115_0_aux_ArrayAccess(x2, x5, x6, x7, x8)
6068_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7, x8, x9) → 6068_0_aux_ArrayAccess(x2, x5, x7, x8, x9)
5579_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 5579_0_aux_ArrayAccess(x2, x5, x6)
5338_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6, x7) → 5338_0_aux_ArrayAccess(x2, x4, x5, x6, x7)
5100_0_aux_ArrayAccess(x1, x2, x3, x4, x5, x6) → 5100_0_aux_ArrayAccess(x2, x5, x6)
4204_0_aux_LT(x1, x2, x3, x4, x5) → 4204_0_aux_LT(x3, x4, x5)
Cond_4854_0_aux_LE2(x1, x2, x3, x4, x5, x6, x7) → Cond_4854_0_aux_LE2(x1, x3, x4, x5, x6, x7)
4854_0_aux_LE(x1, x2, x3, x4, x5, x6) → 4854_0_aux_LE(x2, x3, x4, x5, x6)
Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_4853_0_aux_LE(x1, x3, x4, x5, x6, x7)
4853_0_aux_LE(x1, x2, x3, x4, x5, x6) → 4853_0_aux_LE(x2, x3, x4, x5, x6)
Cond_4854_0_aux_LE1(x1, x2, x3, x4, x5, x6, x7) → Cond_4854_0_aux_LE1(x1, x3, x4, x5, x6, x7)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_4854_0_aux_LE(x1, x3, x4, x5, x6, x7)
Cond_4204_0_aux_LT4(x1, x2, x3, x4, x5, x6) → Cond_4204_0_aux_LT4(x1, x4, x5, x6)
Cond_4204_0_aux_LT3(x1, x2, x3, x4, x5, x6) → Cond_4204_0_aux_LT3(x1, x4, x5, x6)
Cond_4204_0_aux_LT2(x1, x2, x3, x4, x5, x6) → Cond_4204_0_aux_LT2(x1, x4, x5, x6)
Cond_4204_0_aux_LT1(x1, x2, x3, x4, x5, x6) → Cond_4204_0_aux_LT1(x1, x4, x5, x6)
Cond_4204_0_aux_LT(x1, x2, x3, x4, x5, x6) → Cond_4204_0_aux_LT(x1, x4, x5, x6)

Filtered unneeded arguments:

Cond_4204_0_aux_LT(x1, x2, x3, x4) → Cond_4204_0_aux_LT(x1, x2, x4)
Cond_4204_0_aux_LT1(x1, x2, x3, x4) → Cond_4204_0_aux_LT1(x1, x2)
Cond_4204_0_aux_LT4(x1, x2, x3, x4) → Cond_4204_0_aux_LT4(x1, x2)
Cond_4854_0_aux_LE(x1, x2, x3, x4, x5, x6) → Cond_4854_0_aux_LE(x1, x3)
Cond_4854_0_aux_LE1(x1, x2, x3, x4, x5, x6) → Cond_4854_0_aux_LE1(x1, x3)
Cond_4853_0_aux_LE(x1, x2, x3, x4, x5, x6) → Cond_4853_0_aux_LE(x1, x2, x3, x4)
Cond_4854_0_aux_LE2(x1, x2, x3, x4, x5, x6) → Cond_4854_0_aux_LE2(x1, x2, x3, x4)

Combined rules. Obtained 2 rules for P and 26 rules for R.

Finished conversion. Obtained 2 rules for P and 26 rules for R. System has predefined symbols.

Log for SCC 2:

Generated 45 rules for P and 438 rules for R.

Combined rules. Obtained 6 rules for P and 0 rules for R.

Filtered ground terms:

2614_0_main_Load(x1, x2, x3, x4) → 2614_0_main_Load(x2, x3, x4)
2680_0_random_LT(x1, x2, x3) → 2680_0_random_LT(x2, x3)
2777_0_random_IntArithmetic(x1, x2, x3, x4) → 2777_0_random_IntArithmetic(x2, x3)
2720_0_random_ArrayAccess(x1, x2, x3) → 2720_0_random_ArrayAccess(x2, x3)
2678_0_random_LT(x1, x2, x3) → 2678_0_random_LT(x2, x3)
Cond_2614_0_main_Load1(x1, x2, x3, x4, x5) → Cond_2614_0_main_Load1(x1, x3, x4, x5)
Cond_2614_0_main_Load(x1, x2, x3, x4, x5) → Cond_2614_0_main_Load(x1, x3, x4, x5)

Filtered duplicate args:

2614_0_main_Load(x1, x2, x3) → 2614_0_main_Load(x1, x3)
Cond_2680_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_2680_1_main_InvokeMethod(x1, x2, x5, x6)
2680_1_main_InvokeMethod(x1, x2, x3, x4, x5) → 2680_1_main_InvokeMethod(x1, x4, x5)
Cond_2777_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_2777_1_main_InvokeMethod(x1, x2, x5, x6)
2777_1_main_InvokeMethod(x1, x2, x3, x4, x5) → 2777_1_main_InvokeMethod(x1, x4, x5)
Cond_2720_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_2720_1_main_InvokeMethod(x1, x2, x5, x6)
2720_1_main_InvokeMethod(x1, x2, x3, x4, x5) → 2720_1_main_InvokeMethod(x1, x4, x5)
Cond_2678_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_2678_1_main_InvokeMethod(x1, x2, x5, x6)
2678_1_main_InvokeMethod(x1, x2, x3, x4, x5) → 2678_1_main_InvokeMethod(x1, x4, x5)
Cond_2614_0_main_Load1(x1, x2, x3, x4) → Cond_2614_0_main_Load1(x1, x2, x4)
Cond_2614_0_main_Load(x1, x2, x3, x4) → Cond_2614_0_main_Load(x1, x2, x4)

Filtered all free variables:

2678_1_main_InvokeMethod(x1, x2, x3) → 2678_1_main_InvokeMethod(x2, x3)
2680_1_main_InvokeMethod(x1, x2, x3) → 2680_1_main_InvokeMethod(x2, x3)
Cond_2678_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_2678_1_main_InvokeMethod(x1, x3, x4)
2720_1_main_InvokeMethod(x1, x2, x3) → 2720_1_main_InvokeMethod(x2, x3)
Cond_2720_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_2720_1_main_InvokeMethod(x1, x3, x4)
2777_1_main_InvokeMethod(x1, x2, x3) → 2777_1_main_InvokeMethod(x2, x3)
Cond_2777_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_2777_1_main_InvokeMethod(x1, x3, x4)
Cond_2680_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_2680_1_main_InvokeMethod(x1, x3, x4)

Combined rules. Obtained 1 rules for P and 0 rules for R.

Finished conversion. Obtained 1 rules for P and 0 rules for R. System has predefined symbols.

(4) Complex Obligation (AND)

(5) 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:
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(0): 4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]) → COND_4199_0_AUX_LOAD(x2[0] > x0[0] && x2[0] > x0[0] + 1 && x1[0] > x0[0] && x0[0] >= 0 && 1 <= x0[0] + 1, x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])
(1): COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])
(2): 4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]) → COND_4199_0_AUX_LOAD1(x2[2] > x0[2] && x2[2] > x0[2] + 1 && x1[2] > x0[2] && x0[2] >= 0 && 1 <= x0[2] + 1, x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])
(3): COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])
(4): 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]) → COND_4853_0_AUX_LE(x5[4] >= x4[4] && x0[4] >= 0, x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])
(5): COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5] + 1)
(6): 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]) → COND_4853_0_AUX_LE(x5[6] < x4[6] && x2[6] > x0[6] && x2[6] > x0[6] + 1 && x0[6] >= 0 && 1 <= x0[6] + 1, x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])

(0) -> (1), if ((x2[0] > x0[0] && x2[0] > x0[0] + 1 && x1[0] > x0[0] && x0[0] >= 0 && 1 <= x0[0] + 1 →^* TRUE)∧(x1[0] →^* x1[1])∧(java.lang.Object(ARRAY(x2[0], x3[0])) →^* java.lang.Object(ARRAY(x2[1], x3[1])))∧(x0[0] →^* x0[1]))

(1) -> (4), if ((x1[1] →^* x1[4])∧(java.lang.Object(ARRAY(x2[1], x3[1])) →^* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x0[1] →^* x0[4])∧(x4[1] →^* x4[4])∧(x5[1] →^* x5[4]))

(2) -> (3), if ((x2[2] > x0[2] && x2[2] > x0[2] + 1 && x1[2] > x0[2] && x0[2] >= 0 && 1 <= x0[2] + 1 →^* TRUE)∧(x1[2] →^* x1[3])∧(java.lang.Object(ARRAY(x2[2], x3[2])) →^* java.lang.Object(ARRAY(x2[3], x3[3])))∧(x0[2] →^* x0[3]))

(3) -> (6), if ((x1[3] →^* x1[6])∧(java.lang.Object(ARRAY(x2[3], x3[3])) →^* java.lang.Object(ARRAY(x2[6], x3[6])))∧(x0[3] →^* x0[6])∧(x4[3] →^* x4[6])∧(x5[3] →^* x5[6]))

(4) -> (5), if ((x5[4] >= x4[4] && x0[4] >= 0 →^* TRUE)∧(x1[4] →^* x1[5])∧(java.lang.Object(ARRAY(x2[4], x3[4])) →^* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x0[4] →^* x0[5])∧(x4[4] →^* x4[5])∧(x5[4] →^* x5[5]))

(5) -> (0), if ((x1[5] →^* x1[0])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →^* java.lang.Object(ARRAY(x2[0], x3[0])))∧(x0[5] + 1 →^* x0[0]))

(5) -> (2), if ((x1[5] →^* x1[2])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →^* java.lang.Object(ARRAY(x2[2], x3[2])))∧(x0[5] + 1 →^* x0[2]))

(6) -> (5), if ((x5[6] < x4[6] && x2[6] > x0[6] && x2[6] > x0[6] + 1 && x0[6] >= 0 && 1 <= x0[6] + 1 →^* TRUE)∧(x1[6] →^* x1[5])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →^* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x0[6] →^* x0[5])∧(x4[6] →^* x4[5])∧(x5[6] →^* x5[5]))

The set Q consists of the following terms:
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x1, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x2, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x4, x0, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7)))

(6) 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 4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), x0) → COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2, x0), >(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0) the following chains were created:

We consider the chain 4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]) → COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]), COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1]) which results in the following constraint:
(1)    (&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1)))=TRUE∧x1[0]=x1[1]∧java.lang.Object(ARRAY(x2[0], x3[0]))=java.lang.Object(ARRAY(x2[1], x3[1]))∧x0[0]=x0[1] ⇒ 4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])≥NonInfC∧4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])≥COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])∧(U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (<=(1, +(x0[0], 1))=TRUE∧>=(x0[0], 0)=TRUE∧>(x1[0], x0[0])=TRUE∧>(x2[0], x0[0])=TRUE∧>(x2[0], +(x0[0], 1))=TRUE ⇒ 4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])≥NonInfC∧4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])≥COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])∧(U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-2] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧[(-1)Bound*bni_32] + [(-1)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-2] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧[(-1)Bound*bni_32] + [(-1)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-2] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧[(-1)Bound*bni_32] + [(-1)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-2] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_32] + [(-1)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] + [-2] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + (2)bni_32] + [bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(8)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0∧x2[0] ≥ 0∧[-1] + x2[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + (3)bni_32] + [(2)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(9)    (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + (4)bni_32] + [(2)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

For Pair COND_4199_0_AUX_LOAD(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0) → 4853_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) the following chains were created:

We consider the chain COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1]) which results in the following constraint:
(10)    (COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1])≥NonInfC∧COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1])≥4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])∧(U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    ((U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥)∧[(-1)bso_35] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    ((U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥)∧[(-1)bso_35] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    ((U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥)∧[(-1)bso_35] ≥ 0)

We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(14)    ((U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)

For Pair 4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), x0) → COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2, x0), >(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0) the following chains were created:

We consider the chain 4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]) → COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]), COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3]) which results in the following constraint:
(15)    (&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1)))=TRUE∧x1[2]=x1[3]∧java.lang.Object(ARRAY(x2[2], x3[2]))=java.lang.Object(ARRAY(x2[3], x3[3]))∧x0[2]=x0[3] ⇒ 4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])≥NonInfC∧4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])≥COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])∧(U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥))

We simplified constraint (15) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(16)    (<=(1, +(x0[2], 1))=TRUE∧>=(x0[2], 0)=TRUE∧>(x1[2], x0[2])=TRUE∧>(x2[2], x0[2])=TRUE∧>(x2[2], +(x0[2], 1))=TRUE ⇒ 4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])≥NonInfC∧4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])≥COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])∧(U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧[(-1)Bound*bni_36] + [(-1)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧[(-1)Bound*bni_36] + [(-1)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧[(-1)Bound*bni_36] + [(-1)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(20)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧0 = 0∧[(-1)Bound*bni_36] + [(-1)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧0 = 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x2[2] + [-2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧0 = 0∧[(-1)Bound*bni_36 + (2)bni_36] + [bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧0 = 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(22)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] ≥ 0∧[-1] + x2[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧0 = 0∧[(-1)Bound*bni_36 + (3)bni_36] + [(2)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧0 = 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(23)    (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] + x2[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧0 = 0∧[(-1)Bound*bni_36 + (4)bni_36] + [(2)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧0 = 0∧[(-1)bso_37] ≥ 0)

For Pair COND_4199_0_AUX_LOAD1(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0) → 4854_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) the following chains were created:

We consider the chain COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3]) which results in the following constraint:
(24)    (COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3])≥NonInfC∧COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3])≥4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])∧(U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥)∧[(-1)bso_39] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)

For Pair 4853_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → COND_4853_0_AUX_LE(&&(>=(x5, x4), >=(x0, 0)), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) the following chains were created:

We consider the chain 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]) → COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]), COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1)) which results in the following constraint:
(29)    (&&(>=(x5[4], x4[4]), >=(x0[4], 0))=TRUE∧x1[4]=x1[5]∧java.lang.Object(ARRAY(x2[4], x3[4]))=java.lang.Object(ARRAY(x2[5], x3[5]))∧x0[4]=x0[5]∧x4[4]=x4[5]∧x5[4]=x5[5] ⇒ 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])≥NonInfC∧4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])≥COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])∧(U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥))

We simplified constraint (29) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>=(x5[4], x4[4])=TRUE∧>=(x0[4], 0)=TRUE ⇒ 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])≥NonInfC∧4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])≥COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])∧(U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x5[4] + [-1]x4[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] + [bni_40]x2[4] + [(2)bni_40]x1[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x5[4] + [-1]x4[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] + [bni_40]x2[4] + [(2)bni_40]x1[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x5[4] + [-1]x4[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] + [bni_40]x2[4] + [(2)bni_40]x1[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (33) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(34)    (x5[4] + [-1]x4[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x5[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(36)    (x5[4] ≥ 0∧x0[4] ≥ 0∧x4[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

(37)    (x5[4] ≥ 0∧x0[4] ≥ 0∧x4[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

For Pair COND_4853_0_AUX_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), +(x0, 1)) the following chains were created:

We consider the chain COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1)) which results in the following constraint:
(38)    (COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5])≥NonInfC∧COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5])≥4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))∧(U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    ((U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥)∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    ((U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥)∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    ((U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥)∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(42)    ((U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)

For Pair 4854_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5, x4), >(x2, x0)), >(x2, +(x0, 1))), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) the following chains were created:

We consider the chain 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]) → COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]), COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1)) which results in the following constraint:
(43)    (&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1)))=TRUE∧x1[6]=x1[5]∧java.lang.Object(ARRAY(x2[6], x3[6]))=java.lang.Object(ARRAY(x2[5], x3[5]))∧x0[6]=x0[5]∧x4[6]=x4[5]∧x5[6]=x5[5] ⇒ 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])≥NonInfC∧4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])≥COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])∧(U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥))

We simplified constraint (43) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(44)    (<=(1, +(x0[6], 1))=TRUE∧>=(x0[6], 0)=TRUE∧>(x2[6], +(x0[6], 1))=TRUE∧<(x5[6], x4[6])=TRUE∧>(x2[6], x0[6])=TRUE ⇒ 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])≥NonInfC∧4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])≥COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])∧(U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] + [-2] + [-1]x0[6] ≥ 0∧x4[6] + [-1] + [-1]x5[6] ≥ 0∧x2[6] + [-1] + [-1]x0[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]x0[6] + [bni_44]x2[6] + [(2)bni_44]x1[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] + [-2] + [-1]x0[6] ≥ 0∧x4[6] + [-1] + [-1]x5[6] ≥ 0∧x2[6] + [-1] + [-1]x0[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]x0[6] + [bni_44]x2[6] + [(2)bni_44]x1[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] + [-2] + [-1]x0[6] ≥ 0∧x4[6] + [-1] + [-1]x5[6] ≥ 0∧x2[6] + [-1] + [-1]x0[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]x0[6] + [bni_44]x2[6] + [(2)bni_44]x1[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] + [-2] + [-1]x0[6] ≥ 0∧x4[6] + [-1] + [-1]x5[6] ≥ 0∧x2[6] + [-1] + [-1]x0[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44] + [(-1)bni_44]x0[6] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] + [-1] + [-1]x5[6] ≥ 0∧[1] + x2[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (49) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(50)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] ≥ 0∧[1] + x2[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (50) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(51)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] ≥ 0∧[1] + x2[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

(52)    (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] ≥ 0∧[1] + x2[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

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

4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), x0) → COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2, x0), >(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0)
- (x0[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + (4)bni_32] + [(2)bni_32]x0[0] + [bni_32]x2[0] + [(2)bni_32]x1[0] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)
COND_4199_0_AUX_LOAD(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0) → 4853_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
- ((U^Increasing(4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_35] ≥ 0)
4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), x0) → COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2, x0), >(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0)
- (x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] + x2[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])), ≥)∧0 = 0∧[(-1)Bound*bni_36 + (4)bni_36] + [(2)bni_36]x0[2] + [bni_36]x2[2] + [(2)bni_36]x1[2] ≥ 0∧0 = 0∧[(-1)bso_37] ≥ 0)
COND_4199_0_AUX_LOAD1(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0) → 4854_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
- ((U^Increasing(4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)
4853_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → COND_4853_0_AUX_LE(&&(>=(x5, x4), >=(x0, 0)), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
- (x5[4] ≥ 0∧x0[4] ≥ 0∧x4[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
- (x5[4] ≥ 0∧x0[4] ≥ 0∧x4[4] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])), ≥)∧0 = 0∧[bni_40] = 0∧[(2)bni_40] = 0∧[(-1)Bound*bni_40] + [(-1)bni_40]x0[4] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
COND_4853_0_AUX_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 4199_0_AUX_LOAD(x1, java.lang.Object(ARRAY(x2, x3)), +(x0, 1))
- ((U^Increasing(4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)
4854_0_AUX_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5, x4), >(x2, x0)), >(x2, +(x0, 1))), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
- (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] ≥ 0∧[1] + x2[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)
- (x0[6] ≥ 0∧x0[6] ≥ 0∧x2[6] ≥ 0∧x4[6] ≥ 0∧[1] + x2[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])), ≥)∧0 = 0∧[(2)bni_44] = 0∧[(-1)Bound*bni_44 + (2)bni_44] + [bni_44]x2[6] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 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(5704_1_aux_InvokeMethod(x₁, x₂, x₃, x₄)) = [-1]
POL(4295_0_aux_Return(x₁, x₂, x₃)) = [-1]
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₁
POL(5775_0_aux_Return) = [-1]
POL(5100_0_aux_ArrayAccess(x₁, x₂, x₃)) = [-1]
POL(5778_0_aux_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(5338_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(5579_0_aux_ArrayAccess(x₁, x₂, x₃)) = [-1]
POL(6068_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(6115_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(6211_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(4199_0_AUX_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [2]x₁
POL(COND_4199_0_AUX_LOAD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [2]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<=(x₁, x₂)) = [-1]
POL(4853_0_AUX_LE(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₃ + [-1]x₂ + [2]x₁
POL(COND_4199_0_AUX_LOAD1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [2]x₂
POL(4854_0_AUX_LE(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₃ + [-1]x₂ + [2]x₁
POL(COND_4853_0_AUX_LE(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [-1]x₄ + [-1]x₃ + [2]x₂
POL(<(x₁, x₂)) = [-1]

The following pairs are in P_>:

COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), +(x0[5], 1))

The following pairs are in P_bound:

4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]) → COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])
4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]) → COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])

The following pairs are in P_≥:

4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]) → COND_4199_0_AUX_LOAD(&&(&&(&&(&&(>(x2[0], x0[0]), >(x2[0], +(x0[0], 1))), >(x1[0], x0[0])), >=(x0[0], 0)), <=(1, +(x0[0], 1))), x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])
COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])
4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]) → COND_4199_0_AUX_LOAD1(&&(&&(&&(&&(>(x2[2], x0[2]), >(x2[2], +(x0[2], 1))), >(x1[2], x0[2])), >=(x0[2], 0)), <=(1, +(x0[2], 1))), x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])
COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])
4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]) → COND_4853_0_AUX_LE(&&(>=(x5[4], x4[4]), >=(x0[4], 0)), x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])
4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]) → COND_4853_0_AUX_LE(&&(&&(&&(&&(<(x5[6], x4[6]), >(x2[6], x0[6])), >(x2[6], +(x0[6], 1))), >=(x0[6], 0)), <=(1, +(x0[6], 1))), x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])

There are no usable rules.

(7) Complex Obligation (AND)

(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:
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(0): 4199_0_AUX_LOAD(x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0]) → COND_4199_0_AUX_LOAD(x2[0] > x0[0] && x2[0] > x0[0] + 1 && x1[0] > x0[0] && x0[0] >= 0 && 1 <= x0[0] + 1, x1[0], java.lang.Object(ARRAY(x2[0], x3[0])), x0[0])
(1): COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])
(2): 4199_0_AUX_LOAD(x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2]) → COND_4199_0_AUX_LOAD1(x2[2] > x0[2] && x2[2] > x0[2] + 1 && x1[2] > x0[2] && x0[2] >= 0 && 1 <= x0[2] + 1, x1[2], java.lang.Object(ARRAY(x2[2], x3[2])), x0[2])
(3): COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])
(4): 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]) → COND_4853_0_AUX_LE(x5[4] >= x4[4] && x0[4] >= 0, x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])
(6): 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]) → COND_4853_0_AUX_LE(x5[6] < x4[6] && x2[6] > x0[6] && x2[6] > x0[6] + 1 && x0[6] >= 0 && 1 <= x0[6] + 1, x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])

(1) -> (4), if ((x1[1] →^* x1[4])∧(java.lang.Object(ARRAY(x2[1], x3[1])) →^* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x0[1] →^* x0[4])∧(x4[1] →^* x4[4])∧(x5[1] →^* x5[4]))

(3) -> (6), if ((x1[3] →^* x1[6])∧(java.lang.Object(ARRAY(x2[3], x3[3])) →^* java.lang.Object(ARRAY(x2[6], x3[6])))∧(x0[3] →^* x0[6])∧(x4[3] →^* x4[6])∧(x5[3] →^* x5[6]))

(9) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes.

(10) TRUE

(11) 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:
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(1): COND_4199_0_AUX_LOAD(TRUE, x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1]) → 4853_0_AUX_LE(x1[1], java.lang.Object(ARRAY(x2[1], x3[1])), x0[1], x4[1], x5[1])
(3): COND_4199_0_AUX_LOAD1(TRUE, x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3]) → 4854_0_AUX_LE(x1[3], java.lang.Object(ARRAY(x2[3], x3[3])), x0[3], x4[3], x5[3])
(4): 4853_0_AUX_LE(x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4]) → COND_4853_0_AUX_LE(x5[4] >= x4[4] && x0[4] >= 0, x1[4], java.lang.Object(ARRAY(x2[4], x3[4])), x0[4], x4[4], x5[4])
(5): COND_4853_0_AUX_LE(TRUE, x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5], x4[5], x5[5]) → 4199_0_AUX_LOAD(x1[5], java.lang.Object(ARRAY(x2[5], x3[5])), x0[5] + 1)
(6): 4854_0_AUX_LE(x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6]) → COND_4853_0_AUX_LE(x5[6] < x4[6] && x2[6] > x0[6] && x2[6] > x0[6] + 1 && x0[6] >= 0 && 1 <= x0[6] + 1, x1[6], java.lang.Object(ARRAY(x2[6], x3[6])), x0[6], x4[6], x5[6])

(1) -> (4), if ((x1[1] →^* x1[4])∧(java.lang.Object(ARRAY(x2[1], x3[1])) →^* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x0[1] →^* x0[4])∧(x4[1] →^* x4[4])∧(x5[1] →^* x5[4]))

(3) -> (6), if ((x1[3] →^* x1[6])∧(java.lang.Object(ARRAY(x2[3], x3[3])) →^* java.lang.Object(ARRAY(x2[6], x3[6])))∧(x0[3] →^* x0[6])∧(x4[3] →^* x4[6])∧(x5[3] →^* x5[6]))

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 5 less nodes.

(13) TRUE

(14) 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

The ITRS R consists of the following rules:
6187_0_aux_Load(x1, java.lang.Object(ARRAY(x2, x3))) → 4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), 0, x1)
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x1, 0, x5, java.lang.Object(ARRAY(x2, x3)), x6), x7, x8, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x6, x7, x1, java.lang.Object(ARRAY(x4, x5))), java.lang.Object(ARRAY(x4, x5))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x1, x5, 0, java.lang.Object(ARRAY(x2, x3)), x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x1, x5, java.lang.Object(ARRAY(x2, x3)), 0, x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x8, x9, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT(x1 <= x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT1(x2 <= x0 && x1 > x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT2(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT3(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT4(x2 > x0 && x2 <= x0 + 1 && x1 > x0 && x0 >= 0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE(x5 < x4 && x2 <= x0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE1(x5 < x4 && x2 > x0 && x2 <= x0 + 1 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 6068_0_aux_ArrayAccess(x1, x6, x0, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 >= x4 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4853_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5704_1_aux_InvokeMethod(4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0 + 1, x1), x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)))
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 < x4 && x2 > x0 && x2 > x0 + 1 && x0 >= 0 && 1 <= x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(0): 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))) → COND_6187_2_MAIN_INVOKEMETHOD(x4[0] > x5[0] + 1, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))
(1): COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1] + 1, x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))
(2): 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))) → COND_6187_2_MAIN_INVOKEMETHOD1(x2[2] > x3[2] + 1, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))
(3): COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], x3[3] + 1, x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))

(0) -> (1), if ((x4[0] > x5[0] + 1 →^* TRUE)∧(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))) →^* 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))))∧(java.lang.Object(ARRAY(x2[0], x3[0])) →^* java.lang.Object(ARRAY(x2[1], x3[1]))))

(1) -> (0), if ((6187_1_sort_InvokeMethod(6187_0_aux_Load(x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1] + 1, x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))) →^* 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))))∧(java.lang.Object(ARRAY(x2[1], x3[1])) →^* java.lang.Object(ARRAY(x2[0], x3[0]))))

(1) -> (2), if ((6187_1_sort_InvokeMethod(6187_0_aux_Load(x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1] + 1, x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))) →^* 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))))∧(java.lang.Object(ARRAY(x2[1], x3[1])) →^* java.lang.Object(ARRAY(x0[2], x1[2]))))

(2) -> (3), if ((x2[2] > x3[2] + 1 →^* TRUE)∧(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))) →^* 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))))∧(java.lang.Object(ARRAY(x0[2], x1[2])) →^* java.lang.Object(ARRAY(x0[3], x1[3]))))

(3) -> (0), if ((6187_1_sort_InvokeMethod(6187_0_aux_Load(x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], x3[3] + 1, x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))) →^* 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))))∧(java.lang.Object(ARRAY(x6[3], x7[3])) →^* java.lang.Object(ARRAY(x2[0], x3[0]))))

(3) -> (2), if ((6187_1_sort_InvokeMethod(6187_0_aux_Load(x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], x3[3] + 1, x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))) →^* 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))))∧(java.lang.Object(ARRAY(x6[3], x7[3])) →^* java.lang.Object(ARRAY(x0[2], x1[2]))))

The set Q consists of the following terms:
6187_0_aux_Load(x0, java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x0, 0, x1, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, 0, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), 0, x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4), x5, x6, x0, java.lang.Object(ARRAY(x7, x8))), java.lang.Object(ARRAY(x7, x8)))
4204_0_aux_LT(java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
4854_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
4853_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4853_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x1, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x2, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x4, x0, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7)))

(15) 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 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → COND_6187_2_MAIN_INVOKEMETHOD(>(x4, +(x5, 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) the following chains were created:

We consider the chain 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))) → COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))), COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) which results in the following constraint:
(1)    (>(x4[0], +(x5[0], 1))=TRUE∧6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0])))=6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1])))∧java.lang.Object(ARRAY(x2[0], x3[0]))=java.lang.Object(ARRAY(x2[1], x3[1])) ⇒ 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))≥NonInfC∧6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))≥COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))∧(U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(2)    (>(x4[0], +(x5[0], 1))=TRUE ⇒ 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))≥NonInfC∧6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))≥COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))∧(U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x4[0] + [-2] + [-1]x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]x5[0] + [bni_70]x4[0] ≥ 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x4[0] + [-2] + [-1]x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]x5[0] + [bni_70]x4[0] ≥ 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x4[0] + [-2] + [-1]x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]x5[0] + [bni_70]x4[0] ≥ 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x4[0] + [-2] + [-1]x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]x5[0] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x4[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_70 + (-1)Bound*bni_70] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(8)    (x4[0] ≥ 0∧x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_70 + (-1)Bound*bni_70] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

(9)    (x4[0] ≥ 0∧x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_70 + (-1)Bound*bni_70] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)

For Pair COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4, +(x5, 1)), java.lang.Object(ARRAY(x2, x3))), x4, +(x5, 1), -(x4, +(x5, 1)), java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) the following chains were created:

We consider the chain COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) which results in the following constraint:
(10)    (COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))≥NonInfC∧COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))≥6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))∧(U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥)∧[1 + (-1)bso_73] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥)∧[1 + (-1)bso_73] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥)∧[1 + (-1)bso_73] ≥ 0)

We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(14)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_73] ≥ 0)

For Pair 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1))) → COND_6187_2_MAIN_INVOKEMETHOD1(>(x2, +(x3, 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1))) the following chains were created:

We consider the chain 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))) → COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))), COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3]))) which results in the following constraint:
(15)    (>(x2[2], +(x3[2], 1))=TRUE∧6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2])))=6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3])))∧java.lang.Object(ARRAY(x0[2], x1[2]))=java.lang.Object(ARRAY(x0[3], x1[3])) ⇒ 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))≥NonInfC∧6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))≥COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))∧(U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥))

We simplified constraint (15) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(16)    (>(x2[2], +(x3[2], 1))=TRUE ⇒ 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))≥NonInfC∧6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))≥COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))∧(U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x2[2] + [-2] + [-1]x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]x3[2] + [bni_74]x2[2] ≥ 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x2[2] + [-2] + [-1]x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]x3[2] + [bni_74]x2[2] ≥ 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x2[2] + [-2] + [-1]x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]x3[2] + [bni_74]x2[2] ≥ 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(20)    (x2[2] + [-2] + [-1]x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]x3[2] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x2[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_74 + (-1)Bound*bni_74] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(22)    (x2[2] ≥ 0∧x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_74 + (-1)Bound*bni_74] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

(23)    (x2[2] ≥ 0∧x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_74 + (-1)Bound*bni_74] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)

For Pair COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2, +(x3, 1)), java.lang.Object(ARRAY(x6, x7))), x2, +(x3, 1), -(x2, +(x3, 1)), java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7))) the following chains were created:

We consider the chain COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3]))) which results in the following constraint:
(24)    (COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3])))≥NonInfC∧COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3])))≥6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))∧(U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥)∧[1 + (-1)bso_77] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥)∧[1 + (-1)bso_77] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥)∧[1 + (-1)bso_77] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_77] ≥ 0)

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

6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → COND_6187_2_MAIN_INVOKEMETHOD(>(x4, +(x5, 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
- (x4[0] ≥ 0∧x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_70 + (-1)Bound*bni_70] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)
- (x4[0] ≥ 0∧x5[0] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_70 + (-1)Bound*bni_70] + [bni_70]x4[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_71] ≥ 0)
COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4, +(x5, 1)), java.lang.Object(ARRAY(x2, x3))), x4, +(x5, 1), -(x4, +(x5, 1)), java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
- ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_73] ≥ 0)
6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1))) → COND_6187_2_MAIN_INVOKEMETHOD1(>(x2, +(x3, 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1)))
- (x2[2] ≥ 0∧x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_74 + (-1)Bound*bni_74] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)
- (x2[2] ≥ 0∧x3[2] ≥ 0 ⇒ (U^Increasing(COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_74 + (-1)Bound*bni_74] + [bni_74]x2[2] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_75] ≥ 0)
COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2, x3, x5, java.lang.Object(ARRAY(x0, x1))), java.lang.Object(ARRAY(x0, x1))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2, +(x3, 1)), java.lang.Object(ARRAY(x6, x7))), x2, +(x3, 1), -(x2, +(x3, 1)), java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7)))
- ((U^Increasing(6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_77] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(6187_0_aux_Load(x₁, x₂)) = [-1] + [-1]x₂
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₂
POL(4204_0_aux_LT(x₁, x₂, x₃)) = x₂ + [-1]x₁
POL(0) = 0
POL(6187_2_main_InvokeMethod(x₁, x₂)) = [-1]
POL(6187_1_sort_InvokeMethod(x₁, x₂, x₃, x₄, x₅)) = [-1]x₅ + x₃ + [-1]x₂
POL(5100_0_aux_ArrayAccess(x₁, x₂, x₃)) = [-1] + [-1]x₁ + x₃ + [-1]x₂
POL(6255_0_main_InvokeMethod(x₁)) = [-1]
POL(5338_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1] + [2]x₅ + x₁ + x₂ + [-1]x₄
POL(5579_0_aux_ArrayAccess(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂
POL(5778_0_aux_InvokeMethod(x₁, x₂, x₃)) = [-1]x₃ + x₁
POL(6068_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₅ + [-1]x₂ + x₃ + [-1]x₄
POL(6115_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₅ + [-1]x₄ + [-1]x₃ + x₂ + [-1]x₁
POL(6211_0_aux_ArrayAccess(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₅ + x₄ + [-1]x₃ + x₂ + [2]x₁
POL(Cond_4204_0_aux_LT(x₁, x₂, x₃, x₄)) = [1] + x₃ + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(4295_0_aux_Return(x₁, x₂, x₃)) = x₁ + [-1]x₃
POL(Cond_4204_0_aux_LT1(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(Cond_4204_0_aux_LT2(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(>=(x₁, x₂)) = [-1]
POL(4853_0_aux_LE(x₁, x₂, x₃, x₄, x₅)) = [2] + [2]x₁ + x₃ + [-1]x₂ + [2]x₅ + [2]x₄
POL(Cond_4204_0_aux_LT3(x₁, x₂, x₃, x₄)) = [1] + x₃ + [-1]x₂
POL(4854_0_aux_LE(x₁, x₂, x₃, x₄, x₅)) = [-1] + [2]x₅ + [2]x₄ + x₃ + [-1]x₂
POL(Cond_4204_0_aux_LT4(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₂
POL(Cond_4854_0_aux_LE(x₁, x₂, x₃, x₄, x₅, x₆)) = [-1] + [2]x₆ + [2]x₅ + x₄ + [-1]x₃
POL(<(x₁, x₂)) = [-1]
POL(Cond_4854_0_aux_LE1(x₁, x₂, x₃, x₄, x₅, x₆)) = [2] + [2]x₆ + [2]x₅ + x₄ + [-1]x₃
POL(Cond_4853_0_aux_LE(x₁, x₂, x₃, x₄, x₅, x₆)) = [1] + x₄ + [-1]x₃ + [2]x₆ + [2]x₅
POL(5704_1_aux_InvokeMethod(x₁, x₂, x₃, x₄)) = x₂ + [-1]x₁ + [-1]x₄
POL(5775_0_aux_Return) = 0
POL(6187_2_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_6187_2_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_6187_2_MAIN_INVOKEMETHOD1(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂

The following pairs are in P_>:

COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], +(x5[1], 1), -(x4[1], +(x5[1], 1)), java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))
COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(-(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], +(x3[3], 1), -(x2[3], +(x3[3], 1)), java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))

The following pairs are in P_bound:

6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))) → COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))
6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))) → COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))

The following pairs are in P_≥:

6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))) → COND_6187_2_MAIN_INVOKEMETHOD(>(x4[0], +(x5[0], 1)), 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))
6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))) → COND_6187_2_MAIN_INVOKEMETHOD1(>(x2[2], +(x3[2], 1)), 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))

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

Cond_4204_0_aux_LT(<=(x1, x0), java.lang.Object(ARRAY(x2, x3)), x0, x1)¹ → 4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1)¹
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1)¹ → Cond_4204_0_aux_LT2(&&(&&(&&(&&(>(x2, x0), >(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), <=(1, +(x0, 1))), java.lang.Object(ARRAY(x2, x3)), x0, x1)¹
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1)¹ → Cond_4204_0_aux_LT4(&&(&&(&&(>(x2, x0), <=(x2, +(x0, 1))), >(x1, x0)), >=(x0, 0)), java.lang.Object(ARRAY(x2, x3)), x0, x1)¹
Cond_4853_0_aux_LE(&&(&&(&&(&&(<(x5, x4), >(x2, x0)), >(x2, +(x0, 1))), >=(x0, 0)), <=(1, +(x0, 1))), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹ → 4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3)))¹ → 5775_0_aux_Return¹
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹ → Cond_4854_0_aux_LE(&&(<(x5, x4), <=(x2, x0)), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹
Cond_4854_0_aux_LE1(&&(&&(&&(<(x5, x4), >(x2, x0)), <=(x2, +(x0, 1))), >=(x0, 0)), x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹ → 4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)¹

(16) Complex Obligation (AND)

(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

The ITRS R consists of the following rules:
6187_0_aux_Load(x1, java.lang.Object(ARRAY(x2, x3))) → 4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), 0, x1)
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x1, 0, x5, java.lang.Object(ARRAY(x2, x3)), x6), x7, x8, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x6, x7, x1, java.lang.Object(ARRAY(x4, x5))), java.lang.Object(ARRAY(x4, x5))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x1, x5, 0, java.lang.Object(ARRAY(x2, x3)), x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x1, x5, java.lang.Object(ARRAY(x2, x3)), 0, x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x8, x9, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT(x1 <= x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT1(x2 <= x0 && x1 > x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT2(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT3(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT4(x2 > x0 && x2 <= x0 + 1 && x1 > x0 && x0 >= 0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE(x5 < x4 && x2 <= x0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE1(x5 < x4 && x2 > x0 && x2 <= x0 + 1 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 6068_0_aux_ArrayAccess(x1, x6, x0, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 >= x4 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4853_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5704_1_aux_InvokeMethod(4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0 + 1, x1), x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)))
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 < x4 && x2 > x0 && x2 > x0 + 1 && x0 >= 0 && 1 <= x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(0): 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0]))) → COND_6187_2_MAIN_INVOKEMETHOD(x4[0] > x5[0] + 1, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), x4[0], x5[0], x1[0], java.lang.Object(ARRAY(x2[0], x3[0]))), java.lang.Object(ARRAY(x2[0], x3[0])))
(2): 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2]))) → COND_6187_2_MAIN_INVOKEMETHOD1(x2[2] > x3[2] + 1, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[2], x3[2], x5[2], java.lang.Object(ARRAY(x0[2], x1[2]))), java.lang.Object(ARRAY(x0[2], x1[2])))

The set Q consists of the following terms:
6187_0_aux_Load(x0, java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x0, 0, x1, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, 0, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), 0, x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4), x5, x6, x0, java.lang.Object(ARRAY(x7, x8))), java.lang.Object(ARRAY(x7, x8)))
4204_0_aux_LT(java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
4854_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
4853_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4853_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x1, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x2, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x4, x0, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7)))

(18) IDependencyGraphProof (EQUIVALENT transformation)

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

(19) TRUE

(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, Boolean

The ITRS R consists of the following rules:
6187_0_aux_Load(x1, java.lang.Object(ARRAY(x2, x3))) → 4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), 0, x1)
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x1, 0, x5, java.lang.Object(ARRAY(x2, x3)), x6), x7, x8, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), 0), x6, x7, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x6, x7, x1, java.lang.Object(ARRAY(x4, x5))), java.lang.Object(ARRAY(x4, x5))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x1, x5, 0, java.lang.Object(ARRAY(x2, x3)), x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x1, x5, java.lang.Object(ARRAY(x2, x3)), 0, x7), x8, x9, x1, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x8, x9, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7))) → 6255_0_main_InvokeMethod(java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT(x1 <= x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3)))
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT1(x2 <= x0 && x1 > x0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT2(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT3(x2 > x0 && x2 > x0 + 1 && x1 > x0 && x0 >= 0 && 1 <= x0 + 1, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0, x1) → Cond_4204_0_aux_LT4(x2 > x0 && x2 <= x0 + 1 && x1 > x0 && x0 >= 0, java.lang.Object(ARRAY(x2, x3)), x0, x1)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x2, x3)), x0, x1) → 5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE(x5 < x4 && x2 <= x0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0)
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4854_0_aux_LE1(x5 < x4 && x2 > x0 && x2 <= x0 + 1 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 6068_0_aux_ArrayAccess(x1, x6, x0, java.lang.Object(ARRAY(x2, x3)), x0 + 1)
4853_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 >= x4 && x0 >= 0, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
Cond_4853_0_aux_LE(TRUE, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → 5704_1_aux_InvokeMethod(4204_0_aux_LT(java.lang.Object(ARRAY(x2, x3)), x0 + 1, x1), x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)))
4854_0_aux_LE(x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5) → Cond_4853_0_aux_LE(x5 < x4 && x2 > x0 && x2 > x0 + 1 && x0 >= 0 && 1 <= x0 + 1, x1, java.lang.Object(ARRAY(x2, x3)), x0, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x1, x0, x4, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x1, java.lang.Object(ARRAY(x2, x3)), x0), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5775_0_aux_Return
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6))) → 5778_0_aux_InvokeMethod(x4, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x1, x4, x0, java.lang.Object(ARRAY(x2, x3)), x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x1, x4, java.lang.Object(ARRAY(x2, x3)), x0, x5), x0, x1, java.lang.Object(ARRAY(x2, x3))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7))) → 5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3)))

The integer pair graph contains the following rules and edges:
(1): COND_6187_2_MAIN_INVOKEMETHOD(TRUE, 6187_1_sort_InvokeMethod(4295_0_aux_Return(0, x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1], x1[1], java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), x4[1], x5[1] + 1, x4[1] - x5[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1]))), java.lang.Object(ARRAY(x2[1], x3[1])))
(3): COND_6187_2_MAIN_INVOKEMETHOD1(TRUE, 6187_1_sort_InvokeMethod(5775_0_aux_Return, x2[3], x3[3], x5[3], java.lang.Object(ARRAY(x0[3], x1[3]))), java.lang.Object(ARRAY(x0[3], x1[3]))) → 6187_2_MAIN_INVOKEMETHOD(6187_1_sort_InvokeMethod(6187_0_aux_Load(x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), x2[3], x3[3] + 1, x2[3] - x3[3] + 1, java.lang.Object(ARRAY(x6[3], x7[3]))), java.lang.Object(ARRAY(x6[3], x7[3])))

The set Q consists of the following terms:
6187_0_aux_Load(x0, java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5338_0_aux_ArrayAccess(x0, 0, x1, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), 0), x3, x4, x0, java.lang.Object(ARRAY(x1, x2))), java.lang.Object(ARRAY(x1, x2)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x5, x1, java.lang.Object(ARRAY(x6, x7))), java.lang.Object(ARRAY(x6, x7)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, 0, java.lang.Object(ARRAY(x2, x3)), x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), 0, x4), x5, x6, x0, java.lang.Object(ARRAY(x2, x3))), java.lang.Object(ARRAY(x2, x3)))
6187_2_main_InvokeMethod(6187_1_sort_InvokeMethod(6211_0_aux_ArrayAccess(0, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4), x5, x6, x0, java.lang.Object(ARRAY(x7, x8))), java.lang.Object(ARRAY(x7, x8)))
4204_0_aux_LT(java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT1(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT2(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT3(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
Cond_4204_0_aux_LT4(TRUE, java.lang.Object(ARRAY(x0, x1)), x2, x3)
4854_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4854_0_aux_LE1(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
4853_0_aux_LE(x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
Cond_4853_0_aux_LE(TRUE, x0, java.lang.Object(ARRAY(x1, x2)), x3, x4, x5)
5704_1_aux_InvokeMethod(4295_0_aux_Return(x0, x1, java.lang.Object(ARRAY(x2, x3))), x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5100_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5338_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x1, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(5579_0_aux_ArrayAccess(x0, java.lang.Object(ARRAY(x1, x2)), x3), x3, x0, java.lang.Object(ARRAY(x1, x2)))
5704_1_aux_InvokeMethod(5775_0_aux_Return, x0, x1, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(5778_0_aux_InvokeMethod(x0, x1, java.lang.Object(ARRAY(x2, x3))), x4, x1, java.lang.Object(ARRAY(x5, x6)))
5704_1_aux_InvokeMethod(6068_0_aux_ArrayAccess(x0, x1, x2, java.lang.Object(ARRAY(x3, x4)), x5), x2, x0, java.lang.Object(ARRAY(x3, x4)))
5704_1_aux_InvokeMethod(6115_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x4, x0, java.lang.Object(ARRAY(x2, x3)))
5704_1_aux_InvokeMethod(6211_0_aux_ArrayAccess(x0, x1, java.lang.Object(ARRAY(x2, x3)), x4, x5), x0, x1, java.lang.Object(ARRAY(x6, x7)))

(21) IDependencyGraphProof (EQUIVALENT transformation)

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

(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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) → COND_2614_0_MAIN_LOAD(x2[0] >= 0 && x2[0] < x0[0], java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])
(1): COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1] + 1)

(0) -> (1), if ((x2[0] >= 0 && x2[0] < x0[0] →^* TRUE)∧(java.lang.Object(ARRAY(x0[0], x1[0])) →^* java.lang.Object(ARRAY(x0[1], x1[1])))∧(x2[0] →^* x2[1]))

(1) -> (0), if ((java.lang.Object(ARRAY(x0[1], x1[1])) →^* java.lang.Object(ARRAY(x0[0], x1[0])))∧(x2[1] + 1 →^* x2[0]))

The set Q is empty.

(24) 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 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x2) → COND_2614_0_MAIN_LOAD(&&(>=(x2, 0), <(x2, x0)), java.lang.Object(ARRAY(x0, x1)), x2) the following chains were created:

We consider the chain 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) → COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1)) which results in the following constraint:
(1)    (&&(>=(x2[0], 0), <(x2[0], x0[0]))=TRUE∧java.lang.Object(ARRAY(x0[0], x1[0]))=java.lang.Object(ARRAY(x0[1], x1[1]))∧x2[0]=x2[1] ⇒ 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])≥NonInfC∧2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])≥COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧(U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x2[0], 0)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])≥NonInfC∧2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])≥COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧(U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]x2[0] + [bni_11]x0[0] ≥ 0∧[(-1)bso_12] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]x2[0] + [bni_11]x0[0] ≥ 0∧[(-1)bso_12] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]x2[0] + [bni_11]x0[0] ≥ 0∧[(-1)bso_12] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧0 = 0∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]x2[0] + [bni_11]x0[0] ≥ 0∧0 = 0∧[(-1)bso_12] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧0 = 0∧[(-1)Bound*bni_11] + [bni_11]x0[0] ≥ 0∧0 = 0∧[(-1)bso_12] ≥ 0)

For Pair COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0, x1)), x2) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), +(x2, 1)) the following chains were created:

We consider the chain COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1)) which results in the following constraint:
(8)    (COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])≥NonInfC∧COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])≥2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))∧(U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    ((U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥)∧[1 + (-1)bso_14] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    ((U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥)∧[1 + (-1)bso_14] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    ((U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥)∧[1 + (-1)bso_14] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    ((U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

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

2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x2) → COND_2614_0_MAIN_LOAD(&&(>=(x2, 0), <(x2, x0)), java.lang.Object(ARRAY(x0, x1)), x2)
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])), ≥)∧0 = 0∧[(-1)Bound*bni_11] + [bni_11]x0[0] ≥ 0∧0 = 0∧[(-1)bso_12] ≥ 0)
COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0, x1)), x2) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), +(x2, 1))
- ((U^Increasing(2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(2614_0_MAIN_LOAD(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1]x₁
POL(COND_2614_0_MAIN_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]

The following pairs are in P_>:

COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), +(x2[1], 1))

The following pairs are in P_bound:

2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) → COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])

The following pairs are in P_≥:

2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) → COND_2614_0_MAIN_LOAD(&&(>=(x2[0], 0), <(x2[0], x0[0])), java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])

There are no usable rules.

(25) Complex Obligation (AND)

(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

(27) IDependencyGraphProof (EQUIVALENT transformation)

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

(28) TRUE

(29) 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:
(1): COND_2614_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]) → 2614_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1] + 1)

The set Q is empty.

(30) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) IDPNonInfProof (SOUND transformation)

(7) Complex Obligation (AND)

(8) Obligation:

(9) IDependencyGraphProof (EQUIVALENT transformation)

(10) TRUE

(11) Obligation:

(12) IDependencyGraphProof (EQUIVALENT transformation)

(13) TRUE

(14) Obligation:

(15) IDPNonInfProof (SOUND transformation)

(16) Complex Obligation (AND)

(17) Obligation:

(18) IDependencyGraphProof (EQUIVALENT transformation)

(19) TRUE

(20) Obligation:

(21) IDependencyGraphProof (EQUIVALENT transformation)

(22) TRUE

(23) Obligation:

(24) IDPNonInfProof (SOUND transformation)

(25) Complex Obligation (AND)

(26) Obligation:

(27) IDependencyGraphProof (EQUIVALENT transformation)

(28) TRUE

(29) Obligation:

(30) IDependencyGraphProof (EQUIVALENT transformation)

(31) TRUE