Termination proof of /tmp/tmpov7tZW/PastaC9.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 IDP

        ↳10 IDPNonInfProof (⇒)

        ↳11 AND

            ↳12 IDP

                ↳13 IDependencyGraphProof (⇔)

                ↳14 TRUE

            ↳15 IDP

                ↳16 IDependencyGraphProof (⇔)

                ↳17 TRUE

    ↳18 IDP

        ↳19 IDependencyGraphProof (⇔)

        ↳20 TRUE

(0) Obligation:

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

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

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

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


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

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
PastaC9.main([Ljava/lang/String;)V: Graph of 300 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 54 rules for P and 97 rules for R.

Combined rules. Obtained 5 rules for P and 0 rules for R.

Filtered ground terms:

1987_0_random_ArrayAccess(x1, x2, x3) → 1987_0_random_ArrayAccess(x2, x3)
2025_0_random_IntArithmetic(x1, x2, x3, x4) → 2025_0_random_IntArithmetic(x2, x3)
2515_0_random_IntArithmetic(x1, x2, x3, x4) → 2515_0_random_IntArithmetic(x2, x3)
2401_0_random_ArrayAccess(x1, x2, x3) → 2401_0_random_ArrayAccess(x2, x3)

Filtered unneeded arguments:

Cond_2025_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_2025_1_main_InvokeMethod(x1, x2, x3)

Combined rules. Obtained 5 rules for P and 0 rules for R.

Finished conversion. Obtained 5 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): 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])
(1): COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(2): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_2025_1_MAIN_INVOKEMETHOD(x4[2] > 0 && x2[2] > 0 && x1[2] < 42, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
(3): COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), x4[3] + -1)
(4): 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4]) → COND_2401_1_MAIN_INVOKEMETHOD(x2[4] >= 3 && x2[4] < x0[4], 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])
(5): COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5]) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])
(6): 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]) → COND_2515_1_MAIN_INVOKEMETHOD(x4[6] > 0 && x2[6] > 0 && x1[6] > 0, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])
(7): COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])
(8): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(x5[8] > 0 && x4[8] > 0 && x2[8] > 0 && x1[8] >= 42 && 0 < x5[8] + -1, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
(9): COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], x5[9] + -1)

(0) -> (1), if ((x2[0] >= 2 && x2[0] < x0[0] →^* TRUE)∧(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]) →^* 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]))∧(x3[0] →^* x3[1])∧(x4[0] →^* x4[1]))

(1) -> (2), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]))∧(x3[1] →^* x4[2])∧(x4[1] →^* x5[2]))

(1) -> (8), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]))∧(x3[1] →^* x4[8])∧(x4[1] →^* x5[8]))

(2) -> (3), if ((x4[2] > 0 && x2[2] > 0 && x1[2] < 42 →^* TRUE)∧(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]) →^* 2025_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 ((2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]) →^* 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]))∧(x4[3] + -1 →^* x3[4]))

(4) -> (5), if ((x2[4] >= 3 && x2[4] < x0[4] →^* TRUE)∧(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]) →^* 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]))∧(x3[4] →^* x3[5]))

(5) -> (6), if ((2515_0_random_IntArithmetic(x4[5], x5[5]) →^* 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]))∧(x3[5] →^* x4[6]))

(6) -> (7), if ((x4[6] > 0 && x2[6] > 0 && x1[6] > 0 →^* TRUE)∧(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]) →^* 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]))∧(x4[6] →^* x4[7]))

(7) -> (0), if ((1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]) →^* 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x4[7] →^* x3[0])∧(x1[7] →^* x4[0]))

(8) -> (9), if ((x5[8] > 0 && x4[8] > 0 && x2[8] > 0 && x1[8] >= 42 && 0 < x5[8] + -1 →^* TRUE)∧(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]))∧(x4[8] →^* x4[9])∧(x5[8] →^* x5[9]))

(9) -> (0), if ((1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]) →^* 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]))∧(x4[9] →^* x3[0])∧(x5[9] + -1 →^* 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 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) the following chains were created:

We consider the chain 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_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∧1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]∧x4[0]=x4[1] ⇒ 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_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 ⇒ 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x3[0] ≥ 0∧[(-1)bso_41] ≥ 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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x3[0] ≥ 0∧[(-1)bso_41] ≥ 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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x3[0] ≥ 0∧[(-1)bso_41] ≥ 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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧0 = 0∧[bni_40] = 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧0 = 0∧[bni_40] = 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 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_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧0 = 0∧[bni_40] = 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

For Pair COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5, x6), x3, x4) the following chains were created:

We consider the chain COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) which results in the following constraint:
(9)    (COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥NonInfC∧COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])∧(U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_43] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_43] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_43] ≥ 0)

We simplified constraint (12) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(13)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

For Pair 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4, 0), >(x2, 0)), <(x1, 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:

We consider the chain 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]), COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1)) which results in the following constraint:
(14)    (&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42))=TRUE∧2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])=2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3])∧x4[2]=x4[3]∧x5[2]=x5[3] ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (14) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(15)    (<(x1[2], 42)=TRUE∧>(x4[2], 0)=TRUE∧>(x2[2], 0)=TRUE ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(16)    ([41] + [-1]x1[2] ≥ 0∧x4[2] + [-1] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(17)    ([41] + [-1]x1[2] ≥ 0∧x4[2] + [-1] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (17) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(18)    ([41] + [-1]x1[2] ≥ 0∧x4[2] + [-1] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (18) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(19)    ([41] + [-1]x1[2] ≥ 0∧x4[2] + [-1] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_44 + (-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(20)    ([41] + [-1]x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    ([41] + [-1]x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(22)    ([41] + [-1]x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

(23)    ([41] + x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

For Pair COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x4, -1)) the following chains were created:

We consider the chain COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1)) which results in the following constraint:
(24)    (COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥NonInfC∧COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))∧(U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥)∧[(-1)bso_47] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥)∧[(-1)bso_47] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥)∧[(-1)bso_47] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

For Pair 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) the following chains were created:

We consider the chain 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4]) → COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4]), COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5]) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5]) which results in the following constraint:
(29)    (&&(>=(x2[4], 3), <(x2[4], x0[4]))=TRUE∧2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])=2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5])∧x3[4]=x3[5] ⇒ 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])≥NonInfC∧2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])≥COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])∧(U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥))

We simplified constraint (29) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>=(x2[4], 3)=TRUE∧<(x2[4], x0[4])=TRUE ⇒ 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])≥NonInfC∧2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])≥COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])∧(U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]x3[4] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]x3[4] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[(-1)Bound*bni_48] + [bni_48]x3[4] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (33) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(34)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[bni_48] = 0∧0 = 0∧[(-1)Bound*bni_48] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x2[4] ≥ 0∧x0[4] + [-4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[bni_48] = 0∧0 = 0∧[(-1)Bound*bni_48] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(36)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[bni_48] = 0∧0 = 0∧[(-1)Bound*bni_48] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

For Pair COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4, x5), x3) the following chains were created:

We consider the chain COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5]) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5]) which results in the following constraint:
(37)    (COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5])≥NonInfC∧COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5])≥2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])∧(U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    ((U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    ((U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    ((U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥)∧[(-1)bso_51] ≥ 0)

We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(41)    ((U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)

For Pair 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4) → COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4, 0), >(x2, 0)), >(x1, 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4) the following chains were created:

We consider the chain 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]) → COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]), COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7]) which results in the following constraint:
(42)    (&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0))=TRUE∧2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])=2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7])∧x4[6]=x4[7] ⇒ 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])≥NonInfC∧2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])≥COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])∧(U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥))

We simplified constraint (42) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(43)    (>(x1[6], 0)=TRUE∧>(x4[6], 0)=TRUE∧>(x2[6], 0)=TRUE ⇒ 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])≥NonInfC∧2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])≥COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])∧(U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥))

We simplified constraint (43) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(44)    (x1[6] + [-1] ≥ 0∧x4[6] + [-1] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧[(-1)Bound*bni_52] + [bni_52]x4[6] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (44) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(45)    (x1[6] + [-1] ≥ 0∧x4[6] + [-1] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧[(-1)Bound*bni_52] + [bni_52]x4[6] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (45) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(46)    (x1[6] + [-1] ≥ 0∧x4[6] + [-1] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧[(-1)Bound*bni_52] + [bni_52]x4[6] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (46) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(47)    (x1[6] + [-1] ≥ 0∧x4[6] + [-1] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧0 = 0∧[(-1)Bound*bni_52] + [bni_52]x4[6] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(48)    (x1[6] ≥ 0∧x4[6] + [-1] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧0 = 0∧[(-1)Bound*bni_52] + [bni_52]x4[6] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧0 = 0∧[(-1)Bound*bni_52 + bni_52] + [bni_52]x4[6] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (49) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(50)    (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧0 = 0∧[(-1)Bound*bni_52 + bni_52] + [bni_52]x4[6] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

For Pair COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), x4, x1) the following chains were created:

We consider the chain COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7]) which results in the following constraint:
(51)    (COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7])≥NonInfC∧COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7])≥1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])∧(U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥)∧[1 + (-1)bso_55] ≥ 0)

We simplified constraint (52) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(53)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥)∧[1 + (-1)bso_55] ≥ 0)

We simplified constraint (53) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(54)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥)∧[1 + (-1)bso_55] ≥ 0)

We simplified constraint (54) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(55)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)

For Pair 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5, 0), >(x4, 0)), >(x2, 0)), >=(x1, 42)), <(0, +(x5, -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:

We consider the chain 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]), COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1)) which results in the following constraint:
(56)    (&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1)))=TRUE∧2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8])=2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9])∧x4[8]=x4[9]∧x5[8]=x5[9] ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥))

We simplified constraint (56) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(57)    (<(0, +(x5[8], -1))=TRUE∧>=(x1[8], 42)=TRUE∧>(x2[8], 0)=TRUE∧>(x5[8], 0)=TRUE∧>(x4[8], 0)=TRUE ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥))

We simplified constraint (57) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(58)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(59)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (59) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(60)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (60) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(61)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (61) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(62)    (x5[8] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(63)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] + [-1] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(64)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(65)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), x4, +(x5, -1)) the following chains were created:

We consider the chain COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1)) which results in the following constraint:
(66)    (COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9])≥NonInfC∧COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9])≥1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))∧(U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥))

We simplified constraint (66) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(67)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[(-1)bso_59] ≥ 0)

We simplified constraint (67) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(68)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[(-1)bso_59] ≥ 0)

We simplified constraint (68) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(69)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[(-1)bso_59] ≥ 0)

We simplified constraint (69) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(70)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

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

1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4)
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧0 = 0∧[bni_40] = 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5, x6), x3, x4)
- ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4, 0), >(x2, 0)), <(x1, 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
- ([41] + [-1]x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)
- ([41] + x1[2] ≥ 0∧x4[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_44] + [bni_44]x4[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)
COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x4, -1))
- ((U^Increasing(2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3)
- (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])), ≥)∧[bni_48] = 0∧0 = 0∧[(-1)Bound*bni_48] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)
COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4, x5), x3)
- ((U^Increasing(2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_51] ≥ 0)
2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4) → COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4, 0), >(x2, 0)), >(x1, 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4)
- (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])), ≥)∧0 = 0∧[(-1)Bound*bni_52 + bni_52] + [bni_52]x4[6] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)
COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5, x6)), x7), x4, x1)
- ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_55] ≥ 0)
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5, 0), >(x4, 0)), >(x2, 0)), >=(x1, 42)), <(0, +(x5, -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
- (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_56] + [bni_56]x4[8] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)
COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), x4, +(x5, -1))
- ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 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(1987_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + x₂
POL(1987_0_random_ArrayAccess(x₁, x₂)) = [-1] + [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1]
POL(COND_1987_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + x₃
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(2) = [2]
POL(<(x₁, x₂)) = [-1]
POL(2025_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + x₂
POL(2025_0_random_IntArithmetic(x₁, x₂)) = 0
POL(java.lang.String(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_2025_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + x₃
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(42) = [42]
POL(2401_1_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1] + x₂ + x₁
POL(2401_0_random_ArrayAccess(x₁, x₂)) = [2] + x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(COND_2401_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃ + x₂
POL(3) = [3]
POL(2515_1_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1] + [-1]x₁ + x₂
POL(2515_0_random_IntArithmetic(x₁, x₂)) = [-1]
POL(COND_2515_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂
POL(COND_2025_1_MAIN_INVOKEMETHOD1(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₂

The following pairs are in P_>:

COND_2515_1_MAIN_INVOKEMETHOD(TRUE, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x5[7], x6[7])), x7[7]), x4[7], x1[7])

The following pairs are in P_bound:

2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]) → COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])

The following pairs are in P_≥:

1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])
COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_2025_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[2], 0), >(x2[2], 0)), <(x1[2], 42)), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), +(x4[3], -1))
2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4]) → COND_2401_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])
COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5]) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])
2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]) → COND_2515_1_MAIN_INVOKEMETHOD(&&(&&(>(x4[6], 0), >(x2[6], 0)), >(x1[6], 0)), 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))

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:
(0): 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])
(1): COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(2): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_2025_1_MAIN_INVOKEMETHOD(x4[2] > 0 && x2[2] > 0 && x1[2] < 42, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])
(3): COND_2025_1_MAIN_INVOKEMETHOD(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), x4[3] + -1)
(4): 2401_1_MAIN_INVOKEMETHOD(2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4]) → COND_2401_1_MAIN_INVOKEMETHOD(x2[4] >= 3 && x2[4] < x0[4], 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4])
(5): COND_2401_1_MAIN_INVOKEMETHOD(TRUE, 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5]) → 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(x4[5], x5[5]), x3[5])
(6): 2515_1_MAIN_INVOKEMETHOD(2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6]) → COND_2515_1_MAIN_INVOKEMETHOD(x4[6] > 0 && x2[6] > 0 && x1[6] > 0, 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6])
(8): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(x5[8] > 0 && x4[8] > 0 && x2[8] > 0 && x1[8] >= 42 && 0 < x5[8] + -1, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
(9): COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], x5[9] + -1)

(1) -> (2), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]))∧(x3[1] →^* x4[2])∧(x4[1] →^* x5[2]))

(3) -> (4), if ((2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]) →^* 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]))∧(x4[3] + -1 →^* x3[4]))

(5) -> (6), if ((2515_0_random_IntArithmetic(x4[5], x5[5]) →^* 2515_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]))∧(x3[5] →^* x4[6]))

(1) -> (8), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]))∧(x3[1] →^* x4[8])∧(x4[1] →^* x5[8]))

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.

(9) Obligation:

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

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(9): COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], x5[9] + -1)
(8): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(x5[8] > 0 && x4[8] > 0 && x2[8] > 0 && x1[8] >= 42 && 0 < x5[8] + -1, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
(1): COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(0): 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])

(1) -> (8), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]))∧(x3[1] →^* x4[8])∧(x4[1] →^* x5[8]))

The set Q is empty.

(10) IDPNonInfProof (SOUND transformation)

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

For Pair COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1)) the following chains were created:

We consider the chain COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1)) which results in the following constraint:
(1)    (COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9])≥NonInfC∧COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9])≥1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))∧(U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥))

We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(2)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[1 + (-1)bso_17] ≥ 0)

We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(3)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[1 + (-1)bso_17] ≥ 0)

We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(4)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧[1 + (-1)bso_17] ≥ 0)

We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(5)    ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_17] ≥ 0)

For Pair 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) the following chains were created:

We consider the chain 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]), COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1)) which results in the following constraint:
(6)    (&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1)))=TRUE∧2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8])=2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9])∧x4[8]=x4[9]∧x5[8]=x5[9] ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥))

We simplified constraint (6) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(7)    (<(0, +(x5[8], -1))=TRUE∧>=(x1[8], 42)=TRUE∧>(x2[8], 0)=TRUE∧>(x5[8], 0)=TRUE∧>(x4[8], 0)=TRUE ⇒ 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥NonInfC∧2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])≥COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])∧(U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    (x5[8] + [-2] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧x5[8] + [-1] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(12)    (x5[8] ≥ 0∧x1[8] + [-42] ≥ 0∧x2[8] + [-1] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] + [-1] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_18 + (2)bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)

For Pair COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) the following chains were created:

We consider the chain COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) which results in the following constraint:
(16)    (COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥NonInfC∧COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])∧(U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-1)bso_21] ≥ 0)

We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(20)    ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

For Pair 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) the following chains were created:

We consider the chain 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) which results in the following constraint:
(21)    (&&(>=(x2[0], 2), <(x2[0], x0[0]))=TRUE∧1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]∧x4[0]=x4[1] ⇒ 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (21) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(22)    (>=(x2[0], 2)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (22) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(23)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x4[0] + [bni_22]x3[0] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(24)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x4[0] + [bni_22]x3[0] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(25)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x4[0] + [bni_22]x3[0] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(26)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[bni_22] = 0∧0 = 0∧[bni_22] = 0∧[(-1)bni_22 + (-1)Bound*bni_22] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (x2[0] ≥ 0∧x0[0] + [-3] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[bni_22] = 0∧0 = 0∧[bni_22] = 0∧[(-1)bni_22 + (-1)Bound*bni_22] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[bni_22] = 0∧0 = 0∧[bni_22] = 0∧[(-1)bni_22 + (-1)Bound*bni_22] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

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

COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))
- ((U^Increasing(1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_17] ≥ 0)
2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
- (x5[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧[1] + x5[8] ≥ 0∧x4[8] ≥ 0 ⇒ (U^Increasing(COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_18 + (2)bni_18] + [bni_18]x4[8] + [bni_18]x5[8] ≥ 0∧0 = 0∧[(-1)bso_19] ≥ 0)
COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
- ((U^Increasing(2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)
1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])
- (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[bni_22] = 0∧0 = 0∧[bni_22] = 0∧[(-1)bni_22 + (-1)Bound*bni_22] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(COND_2025_1_MAIN_INVOKEMETHOD1(x₁, x₂, x₃, x₄)) = [-1] + x₃ + x₄
POL(2025_0_random_IntArithmetic(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(java.lang.Object(x₁)) = x₁
POL(java.lang.String(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(1987_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₁ + x₂
POL(1987_0_random_ArrayAccess(x₁, x₂)) = 0
POL(ARRAY(x₁, x₂)) = [-1]x₂ + [-1]x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(2025_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₂ + x₃
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(>=(x₁, x₂)) = [-1]
POL(42) = [42]
POL(<(x₁, x₂)) = [-1]
POL(COND_1987_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₃ + x₄ + [-1]x₂
POL(2) = [2]

The following pairs are in P_>:

COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], +(x5[9], -1))

The following pairs are in P_bound:

2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])

The following pairs are in P_≥:

2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x5[8], 0), >(x4[8], 0)), >(x2[8], 0)), >=(x1[8], 42)), <(0, +(x5[8], -1))), 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])

There are no usable rules.

(11) Complex Obligation (AND)

(12) Obligation:

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

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(8): 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8]) → COND_2025_1_MAIN_INVOKEMETHOD1(x5[8] > 0 && x4[8] > 0 && x2[8] > 0 && x1[8] >= 42 && 0 < x5[8] + -1, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]), x4[8], x5[8])
(1): COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(0): 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])

(1) -> (8), if ((2025_0_random_IntArithmetic(x5[1], x6[1]) →^* 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[8], x1[8])), x2[8]))∧(x3[1] →^* x4[8])∧(x4[1] →^* x5[8]))

The set Q is empty.

(13) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(14) TRUE

(15) Obligation:

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

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(9): COND_2025_1_MAIN_INVOKEMETHOD1(TRUE, 2025_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[9], x1[9])), x2[9]), x4[9], x5[9]) → 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[9], x7[9])), x8[9]), x4[9], x5[9] + -1)
(1): COND_1987_1_MAIN_INVOKEMETHOD(TRUE, 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 2025_1_MAIN_INVOKEMETHOD(2025_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])
(0): 1987_1_MAIN_INVOKEMETHOD(1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_1987_1_MAIN_INVOKEMETHOD(x2[0] >= 2 && x2[0] < x0[0], 1987_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])

The set Q is empty.

(16) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(17) TRUE

(18) Obligation:

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

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

The following domains are used:

Boolean, Integer

(3) -> (4), if ((2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]) →^* 2401_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]))∧(x4[3] + -1 →^* x3[4]))

The set Q is empty.

(19) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 7 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) Obligation:

(10) IDPNonInfProof (SOUND transformation)

(11) Complex Obligation (AND)

(12) Obligation:

(13) IDependencyGraphProof (EQUIVALENT transformation)

(14) TRUE

(15) Obligation:

(16) IDependencyGraphProof (EQUIVALENT transformation)

(17) TRUE

(18) Obligation:

(19) IDependencyGraphProof (EQUIVALENT transformation)

(20) TRUE