### (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]))=TRUE1987_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])∧(UIncreasing(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])=TRUE1987_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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))=TRUE2025_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])∧(UIncreasing(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)=TRUE2025_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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]))=TRUE2401_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])∧(UIncreasing(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])=TRUE2401_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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))=TRUE2515_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])∧(UIncreasing(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)=TRUE2515_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)))=TRUE2025_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])∧(UIncreasing(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)=TRUE2025_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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 ⇒ (UIncreasing(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)
• ((UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))
• ((UIncreasing(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 ⇒ (UIncreasing(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)
• ((UIncreasing(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 ⇒ (UIncreasing(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)
• ((UIncreasing(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 ⇒ (UIncreasing(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))
• ((UIncreasing(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 Pbound 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 Pbound.
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 Pbound:

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.

### (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)

(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]))

(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]))

(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]))

(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]))

(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]))

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])

(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]))

(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) -> (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]))

(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]))

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))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)))=TRUE2025_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])∧(UIncreasing(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)=TRUE2025_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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]))=TRUE1987_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])∧(UIncreasing(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])=TRUE1987_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))
• ((UIncreasing(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 ⇒ (UIncreasing(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])
• ((UIncreasing(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 ⇒ (UIncreasing(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)

The constraints for P> respective Pbound 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 Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

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 Pbound:

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.

### (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])

(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) -> (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.

### (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])

(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]))

(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]))

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.

### (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

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])
(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])
(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])
(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)

(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]))

(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]))

(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]))

(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]))

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.