Termination proof of /tmp/tmpmJeiTH/PastaC10.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 IDP

↳5 IDPNonInfProof (⇒)

↳6 AND

    ↳7 IDP

        ↳8 IDependencyGraphProof (⇔)

        ↳9 TRUE

    ↳10 IDP

        ↳11 IDependencyGraphProof (⇔)

        ↳12 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC10

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaC10 {
    public static void main(String[] args) {
        Random.args = args;
        int i = Random.random();
        int j = Random.random();

        while (i - j >= 1) {
			i = i - Random.random();
			int r = Random.random() + 1;
			j = j + r;
        }
    } 
}


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

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
PastaC10.main([Ljava/lang/String;)V: Graph of 299 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 54 rules for P and 94 rules for R.

Combined rules. Obtained 4 rules for P and 0 rules for R.

Filtered ground terms:

3316_0_random_ArrayAccess(x1, x2, x3) → 3316_0_random_ArrayAccess(x2, x3)
3687_0_random_IntArithmetic(x1, x2, x3, x4) → 3687_0_random_IntArithmetic(x2, x3)
3586_0_random_ArrayAccess(x1, x2, x3) → 3586_0_random_ArrayAccess(x2, x3)
3347_0_random_IntArithmetic(x1, x2, x3, x4) → 3347_0_random_IntArithmetic(x2, x3)

Combined rules. Obtained 4 rules for P and 0 rules for R.

Finished conversion. Obtained 4 rules for P and 0 rules for R. System has predefined symbols.

(4) 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): 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])
(1): COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(2): 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(x2[2] > 0 && x1[2] >= 0, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
(3): COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), x5[3] - x1[3], x4[3])
(4): 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(x2[4] >= 3 && x2[4] < x0[4], 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])
(5): COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])
(6): 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(x2[6] > 0 && x1[6] >= 0 && 1 <= x4[6] - x5[6] + x1[6] + 1 && 0 < x1[6] + 1, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])
(7): COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), x5[7] + x1[7] + 1, x4[7])

(0) -> (1), if ((x2[0] >= 2 && x2[0] < x0[0] →^* TRUE)∧(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) →^* 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]))∧(x3[0] →^* x3[1])∧(x4[0] →^* x4[1]))

(1) -> (2), if ((3347_0_random_IntArithmetic(x5[1], x6[1]) →^* 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]))∧(x3[1] →^* x4[2])∧(x4[1] →^* x5[2]))

(2) -> (3), if ((x2[2] > 0 && x1[2] >= 0 →^* TRUE)∧(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]) →^* 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]))∧(x4[2] →^* x4[3])∧(x5[2] →^* x5[3]))

(3) -> (4), if ((3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]) →^* 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]))∧(x5[3] - x1[3] →^* x3[4])∧(x4[3] →^* x4[4]))

(4) -> (5), if ((x2[4] >= 3 && x2[4] < x0[4] →^* TRUE)∧(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]) →^* 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]))∧(x3[4] →^* x3[5])∧(x4[4] →^* x4[5]))

(5) -> (6), if ((3687_0_random_IntArithmetic(x5[5], x6[5]) →^* 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]))∧(x3[5] →^* x4[6])∧(x4[5] →^* x5[6]))

(6) -> (7), if ((x2[6] > 0 && x1[6] >= 0 && 1 <= x4[6] - x5[6] + x1[6] + 1 && 0 < x1[6] + 1 →^* TRUE)∧(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]) →^* 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]))∧(x4[6] →^* x4[7])∧(x5[6] →^* x5[7]))

(7) -> (0), if ((3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]) →^* 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x5[7] + x1[7] + 1 →^* x3[0])∧(x4[7] →^* x4[0]))

The set Q is empty.

(5) 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 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) the following chains were created:

We consider the chain 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) which results in the following constraint:
(1)    (&&(>=(x2[0], 2), <(x2[0], x0[0]))=TRUE∧3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]∧x4[0]=x4[1] ⇒ 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x2[0], 2)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x2[0] ≥ 0∧x0[0] + [-3] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(8)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

For Pair COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5, x6), x3, x4) the following chains were created:

We consider the chain COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]), 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]), 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) which results in the following constraint:
(9)    (3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧+(x5[7], +(x1[7], 1))=x3[0]∧x4[7]=x4[0]∧&&(>=(x2[0], 2), <(x2[0], x0[0]))=TRUE∧3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]∧x4[0]=x4[1]∧3347_0_random_IntArithmetic(x5[1], x6[1])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])∧x3[1]=x4[2]∧x4[1]=x5[2] ⇒ COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥NonInfC∧COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])∧(U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (9) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(10)    (>=(x2[0], 2)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x7[7])), x2[0]), +(x5[7], +(x1[7], 1)), x4[7])≥NonInfC∧COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x7[7])), x2[0]), +(x5[7], +(x1[7], 1)), x4[7])≥3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x6[1]), +(x5[7], +(x1[7], 1)), x4[7])∧(U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(14)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (x2[0] ≥ 0∧x0[0] + [-3] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

For Pair 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), >=(x1, 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:

We consider the chain 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]), COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]) which results in the following constraint:
(17)    (&&(>(x2[2], 0), >=(x1[2], 0))=TRUE∧3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3])∧x4[2]=x4[3]∧x5[2]=x5[3] ⇒ 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (17) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(18)    (>(x2[2], 0)=TRUE∧>=(x1[2], 0)=TRUE ⇒ 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(21)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (21) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(22)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(23)    (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)

For Pair COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(x5, x1), x4) the following chains were created:

We consider the chain COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]), 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]), COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]), 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) which results in the following constraint:
(24)    (3347_0_random_IntArithmetic(x5[1], x6[1])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])∧x3[1]=x4[2]∧x4[1]=x5[2]∧&&(>(x2[2], 0), >=(x1[2], 0))=TRUE∧3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3])∧x4[2]=x4[3]∧x5[2]=x5[3]∧3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])∧-(x5[3], x1[3])=x3[4]∧x4[3]=x4[4] ⇒ COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥NonInfC∧COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])∧(U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥))

We simplified constraint (24) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(25)    (>(x2[2], 0)=TRUE∧>=(x1[2], 0)=TRUE ⇒ COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x3[1], x4[1])≥NonInfC∧COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x3[1], x4[1])≥3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x4[1], x1[2]), x3[1])∧(U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥))

We simplified constraint (25) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(26)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (26) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(27)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (27) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(28)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (28) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(29)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (29) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(30)    (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)

For Pair 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) the following chains were created:

We consider the chain 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]), COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]) which results in the following constraint:
(31)    (&&(>=(x2[4], 3), <(x2[4], x0[4]))=TRUE∧3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5])∧x3[4]=x3[5]∧x4[4]=x4[5] ⇒ 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥NonInfC∧3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])∧(U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥))

We simplified constraint (31) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(32)    (>=(x2[4], 3)=TRUE∧<(x2[4], x0[4])=TRUE ⇒ 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥NonInfC∧3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])∧(U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥))

We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(33)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(34)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (34) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(35)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (35) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(36)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (36) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(37)    (x2[4] ≥ 0∧x0[4] + [-4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(38)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

For Pair COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5, x6), x3, x4) the following chains were created:

We consider the chain COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]), 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]), COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]), 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) which results in the following constraint:
(39)    (3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])∧-(x5[3], x1[3])=x3[4]∧x4[3]=x4[4]∧&&(>=(x2[4], 3), <(x2[4], x0[4]))=TRUE∧3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5])∧x3[4]=x3[5]∧x4[4]=x4[5]∧3687_0_random_IntArithmetic(x5[5], x6[5])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])∧x3[5]=x4[6]∧x4[5]=x5[6] ⇒ COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5])≥NonInfC∧COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5])≥3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])∧(U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥))

We simplified constraint (39) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(40)    (>=(x2[4], 3)=TRUE∧<(x2[4], x0[4])=TRUE ⇒ COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x7[3])), x2[4]), -(x5[3], x1[3]), x4[3])≥NonInfC∧COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x7[3])), x2[4]), -(x5[3], x1[3]), x4[3])≥3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x6[5]), -(x5[3], x1[3]), x4[3])∧(U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥))

We simplified constraint (40) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(41)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (41) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(42)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(43)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (43) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(44)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(45)    (x2[4] ≥ 0∧x0[4] + [-4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(46)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

For Pair 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2, 0), >=(x1, 0)), <=(1, -(x4, +(x5, +(x1, 1))))), <(0, +(x1, 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:

We consider the chain 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]), COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]) which results in the following constraint:
(47)    (&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1)))=TRUE∧3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7])∧x4[6]=x4[7]∧x5[6]=x5[7] ⇒ 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])∧(U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥))

We simplified constraint (47) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(48)    (<(0, +(x1[6], 1))=TRUE∧<=(1, -(x4[6], +(x5[6], +(x1[6], 1))))=TRUE∧>(x2[6], 0)=TRUE∧>=(x1[6], 0)=TRUE ⇒ 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])∧(U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥))

We simplified constraint (48) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(49)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (49) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(50)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (50) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(51)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (51) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(52)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(53)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(54)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(55)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

(56)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

For Pair COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x5, +(x1, 1)), x4) the following chains were created:

We consider the chain COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]), 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]), COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]), 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) which results in the following constraint:
(57)    (3687_0_random_IntArithmetic(x5[5], x6[5])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])∧x3[5]=x4[6]∧x4[5]=x5[6]∧&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1)))=TRUE∧3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7])∧x4[6]=x4[7]∧x5[6]=x5[7]∧3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧+(x5[7], +(x1[7], 1))=x3[0]∧x4[7]=x4[0] ⇒ COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7])≥NonInfC∧COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7])≥3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])∧(U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥))

We simplified constraint (57) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(58)    (<(0, +(x1[6], 1))=TRUE∧<=(1, -(x4[6], +(x5[6], +(x1[6], 1))))=TRUE∧>(x2[6], 0)=TRUE∧>=(x1[6], 0)=TRUE ⇒ COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[6], +(x1[6], 1)), x4[6])∧(U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥))

We simplified constraint (58) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(59)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(60)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(61)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (61) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(62)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(63)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(64)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(65)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

(66)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

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

3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4)
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)
COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5, x6), x3, x4)
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)
3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), >=(x1, 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
- (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)
COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(x5, x1), x4)
- (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)
3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4)
- (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)
COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5, x6), x3, x4)
- (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)
3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2, 0), >=(x1, 0)), <=(1, -(x4, +(x5, +(x1, 1))))), <(0, +(x1, 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
- (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)
- (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)
COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x5, +(x1, 1)), x4)
- (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)
- (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (U^Increasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 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(3316_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [1] + [-1]x₁ + [-1]x₂ + x₃
POL(3316_0_random_ArrayAccess(x₁, x₂)) = [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1]
POL(COND_3316_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1]x₂ + [-1]x₃ + x₄
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(2) = [2]
POL(<(x₁, x₂)) = [-1]
POL(3347_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂
POL(3347_0_random_IntArithmetic(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.String(x₁, x₂)) = [-1] + x₂
POL(COND_3347_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₄ + [-1]x₃
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(3586_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃
POL(3586_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_3586_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₄
POL(3) = [3]
POL(3687_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₃
POL(3687_0_random_IntArithmetic(x₁, x₂)) = [-1] + [-1]x₁
POL(COND_3687_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₂ + x₃
POL(<=(x₁, x₂)) = [-1]
POL(1) = [1]
POL(+(x₁, x₂)) = x₁ + x₂

The following pairs are in P_>:

3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])

The following pairs are in P_bound:

3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])
COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])

The following pairs are in P_≥:

COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])
3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])
COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])
3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])
COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])

There are no usable rules.

(6) Complex Obligation (AND)

(7) Obligation:

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

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(2): 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(x2[2] > 0 && x1[2] >= 0, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
(3): COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), x5[3] - x1[3], x4[3])
(4): 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(x2[4] >= 3 && x2[4] < x0[4], 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])
(5): COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])
(6): 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(x2[6] > 0 && x1[6] >= 0 && 1 <= x4[6] - x5[6] + x1[6] + 1 && 0 < x1[6] + 1, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])
(7): COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), x5[7] + x1[7] + 1, x4[7])

(1) -> (2), if ((3347_0_random_IntArithmetic(x5[1], x6[1]) →^* 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]))∧(x3[1] →^* x4[2])∧(x4[1] →^* x5[2]))

(5) -> (6), if ((3687_0_random_IntArithmetic(x5[5], x6[5]) →^* 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]))∧(x3[5] →^* x4[6])∧(x4[5] →^* x5[6]))

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 7 less nodes.

(9) TRUE

(10) Obligation:

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

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

The following domains are used:

Boolean, Integer

(1) -> (2), if ((3347_0_random_IntArithmetic(x5[1], x6[1]) →^* 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]))∧(x3[1] →^* x4[2])∧(x4[1] →^* x5[2]))

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) IDPNonInfProof (SOUND transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) IDependencyGraphProof (EQUIVALENT transformation)

(9) TRUE

(10) Obligation:

(11) IDependencyGraphProof (EQUIVALENT transformation)

(12) TRUE