(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC10
`/** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */public class PastaC10 {    public static void main(String[] args) {        Random.args = args;        int i = Random.random();        int j = Random.random();        while (i - j >= 1) {			i = i - Random.random();			int r = Random.random() + 1;			j = j + r;        }    } }public class Random {  static String[] args;  static int index = 0;  public static int random() {    String string = args[index];    index++;    return string.length();  }}`

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

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

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 54 rules for P and 94 rules for R.

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

Filtered ground terms:

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

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

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

(4) Obligation:

IDP problem:
The following function symbols are pre-defined:
 != ~ Neq: (Integer, Integer) -> Boolean * ~ Mul: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean -1 ~ UnaryMinus: (Integer) -> Integer | ~ Bwor: (Integer, Integer) -> Integer / ~ Div: (Integer, Integer) -> Integer = ~ Eq: (Integer, Integer) -> Boolean ~ Bwxor: (Integer, Integer) -> Integer || ~ Lor: (Boolean, Boolean) -> Boolean ! ~ Lnot: (Boolean) -> Boolean < ~ Lt: (Integer, Integer) -> Boolean - ~ Sub: (Integer, Integer) -> Integer <= ~ Le: (Integer, Integer) -> Boolean > ~ Gt: (Integer, Integer) -> Boolean ~ ~ Bwnot: (Integer) -> Integer % ~ Mod: (Integer, Integer) -> Integer & ~ Bwand: (Integer, Integer) -> Integer + ~ Add: (Integer, Integer) -> Integer && ~ Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

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

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

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

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

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

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

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

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

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

The set Q is empty.

(5) IDPNonInfProof (SOUND transformation)

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

For Pair 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) the following chains were created:
• We consider the chain 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]) which results in the following constraint:

(1)    (&&(>=(x2[0], 2), <(x2[0], x0[0]))=TRUE3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]x4[0]=x4[1]3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(2)    (>=(x2[0], 2)=TRUE<(x2[0], x0[0])=TRUE3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥NonInfC∧3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])≥COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])∧(UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(3)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(4)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(5)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧[(-1)Bound*bni_55] + [(-1)bni_55]x3[0] + [bni_55]x4[0] ≥ 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(6)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(7)    (x2[0] ≥ 0∧x0[0] + [-3] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(8)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

For Pair COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5, x6), x3, x4) the following chains were created:
• We consider the chain COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]), 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]), COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]), 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) which results in the following constraint:

(9)    (3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧+(x5[7], +(x1[7], 1))=x3[0]x4[7]=x4[0]&&(>=(x2[0], 2), <(x2[0], x0[0]))=TRUE3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1])∧x3[0]=x3[1]x4[0]=x4[1]3347_0_random_IntArithmetic(x5[1], x6[1])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])∧x3[1]=x4[2]x4[1]=x5[2]COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥NonInfC∧COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1])≥3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])∧(UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (9) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(10)    (>=(x2[0], 2)=TRUE<(x2[0], x0[0])=TRUECOND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x7[7])), x2[0]), +(x5[7], +(x1[7], 1)), x4[7])≥NonInfC∧COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x7[7])), x2[0]), +(x5[7], +(x1[7], 1)), x4[7])≥3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x6[1]), +(x5[7], +(x1[7], 1)), x4[7])∧(UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(11)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(12)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(13)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧[(-2)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x5[7] + [(-1)bni_57]x1[7] + [bni_57]x4[7] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(14)    (x2[0] + [-2] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(15)    (x2[0] ≥ 0∧x0[0] + [-3] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(16)    (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

For Pair 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), >=(x1, 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:
• We consider the chain 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]), COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]) which results in the following constraint:

(17)    (&&(>(x2[2], 0), >=(x1[2], 0))=TRUE3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3])∧x4[2]=x4[3]x5[2]=x5[3]3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (17) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(18)    (>(x2[2], 0)=TRUE>=(x1[2], 0)=TRUE3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥NonInfC∧3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])≥COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])∧(UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(19)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(20)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(21)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x5[2] + [(-1)bni_59]x4[2] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (21) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(22)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(23)    (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)

For Pair COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(x5, x1), x4) the following chains were created:
• We consider the chain COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[1], x1[1])), x2[1]), x3[1], x4[1]) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1]), 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2]), COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]), 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) which results in the following constraint:

(24)    (3347_0_random_IntArithmetic(x5[1], x6[1])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])∧x3[1]=x4[2]x4[1]=x5[2]&&(>(x2[2], 0), >=(x1[2], 0))=TRUE3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2])=3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3])∧x4[2]=x4[3]x5[2]=x5[3]3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])∧-(x5[3], x1[3])=x3[4]x4[3]=x4[4]COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥NonInfC∧COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3])≥3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])∧(UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥))

We simplified constraint (24) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(25)    (>(x2[2], 0)=TRUE>=(x1[2], 0)=TRUECOND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x3[1], x4[1])≥NonInfC∧COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x3[1], x4[1])≥3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x4[1], x1[2]), x3[1])∧(UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥))

We simplified constraint (25) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(26)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (26) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(27)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (27) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(28)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [bni_61]x4[1] + [(-1)bni_61]x3[1] ≥ 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (28) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(29)    (x2[2] + [-1] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)

We simplified constraint (29) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(30)    (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)

For Pair 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) the following chains were created:
• We consider the chain 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]), COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]) which results in the following constraint:

(31)    (&&(>=(x2[4], 3), <(x2[4], x0[4]))=TRUE3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5])∧x3[4]=x3[5]x4[4]=x4[5]3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥NonInfC∧3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])∧(UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥))

We simplified constraint (31) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(32)    (>=(x2[4], 3)=TRUE<(x2[4], x0[4])=TRUE3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥NonInfC∧3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])≥COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])∧(UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥))

We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(33)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(34)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (34) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(35)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x3[4] + [(-1)bni_63]x4[4] ≥ 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (35) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(36)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (36) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(37)    (x2[4] ≥ 0∧x0[4] + [-4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(38)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

For Pair COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5, x6), x3, x4) the following chains were created:
• We consider the chain COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[3], x1[3])), x2[3]), x4[3], x5[3]) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3]), 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4]), COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]), 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) which results in the following constraint:

(39)    (3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])∧-(x5[3], x1[3])=x3[4]x4[3]=x4[4]&&(>=(x2[4], 3), <(x2[4], x0[4]))=TRUE3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4])=3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5])∧x3[4]=x3[5]x4[4]=x4[5]3687_0_random_IntArithmetic(x5[5], x6[5])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])∧x3[5]=x4[6]x4[5]=x5[6]COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5])≥NonInfC∧COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5])≥3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])∧(UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥))

We simplified constraint (39) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(40)    (>=(x2[4], 3)=TRUE<(x2[4], x0[4])=TRUECOND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x7[3])), x2[4]), -(x5[3], x1[3]), x4[3])≥NonInfC∧COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x7[3])), x2[4]), -(x5[3], x1[3]), x4[3])≥3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x6[5]), -(x5[3], x1[3]), x4[3])∧(UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥))

We simplified constraint (40) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(41)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (41) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(42)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(43)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x5[3] + [(-1)bni_65]x1[3] + [(-1)bni_65]x4[3] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (43) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(44)    (x2[4] + [-3] ≥ 0∧x0[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(45)    (x2[4] ≥ 0∧x0[4] + [-4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(46)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

For Pair 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2, 0), >=(x1, 0)), <=(1, -(x4, +(x5, +(x1, 1))))), <(0, +(x1, 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) the following chains were created:
• We consider the chain 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]), COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]) which results in the following constraint:

(47)    (&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1)))=TRUE3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7])∧x4[6]=x4[7]x5[6]=x5[7]3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])∧(UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥))

We simplified constraint (47) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(48)    (<(0, +(x1[6], 1))=TRUE<=(1, -(x4[6], +(x5[6], +(x1[6], 1))))=TRUE>(x2[6], 0)=TRUE>=(x1[6], 0)=TRUE3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])∧(UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥))

We simplified constraint (48) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(49)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (49) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(50)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (50) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(51)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (51) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(52)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x4[6] + [(-1)bni_67]x5[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

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

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

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

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

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

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

For Pair COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x5, +(x1, 1)), x4) the following chains were created:
• We consider the chain COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[5], x1[5])), x2[5]), x3[5], x4[5]) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5]), 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6]), COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7]) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7]), 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0]) which results in the following constraint:

(57)    (3687_0_random_IntArithmetic(x5[5], x6[5])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])∧x3[5]=x4[6]x4[5]=x5[6]&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1)))=TRUE3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6])=3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7])∧x4[6]=x4[7]x5[6]=x5[7]3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7])=3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0])∧+(x5[7], +(x1[7], 1))=x3[0]x4[7]=x4[0]COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7])≥NonInfC∧COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[7], x1[7])), x2[7]), x4[7], x5[7])≥3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])∧(UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥))

We simplified constraint (57) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(58)    (<(0, +(x1[6], 1))=TRUE<=(1, -(x4[6], +(x5[6], +(x1[6], 1))))=TRUE>(x2[6], 0)=TRUE>=(x1[6], 0)=TRUECOND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥NonInfC∧COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])≥3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[6], +(x1[6], 1)), x4[6])∧(UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥))

We simplified constraint (58) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(59)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(60)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(61)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (61) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(62)    (x1[6] ≥ 0∧x4[6] + [-2] + [-1]x5[6] + [-1]x1[6] ≥ 0∧x2[6] + [-1] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]x5[6] + [(-1)bni_69]x1[6] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

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

We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

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

We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

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

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

To summarize, we get the following constraints P for the following pairs.
• 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2, 2), <(x2, x0)), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4)
• (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_3316_1_MAIN_INVOKEMETHOD(&&(>=(x2[0], 2), <(x2[0], x0[0])), 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[0], x1[0])), x2[0]), x3[0], x4[0])), ≥)∧0 = 0∧[(-1)bni_55] = 0∧[bni_55] = 0∧[(-1)Bound*bni_55] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

• COND_3316_1_MAIN_INVOKEMETHOD(TRUE, 3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5, x6), x3, x4)
• (x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(x5[1], x6[1]), x3[1], x4[1])), ≥)∧0 = 0∧[(-1)bni_57] = 0∧[(-1)bni_57] = 0∧[bni_57] = 0∧[(-2)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)

• 3347_1_MAIN_INVOKEMETHOD(3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2, 0), >=(x1, 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
• (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3347_1_MAIN_INVOKEMETHOD(&&(>(x2[2], 0), >=(x1[2], 0)), 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[2], x1[2])), x2[2]), x4[2], x5[2])), ≥)∧0 = 0∧[bni_59] = 0∧[(-1)bni_59] = 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_60] ≥ 0)

• COND_3347_1_MAIN_INVOKEMETHOD(TRUE, 3347_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), -(x5, x1), x4)
• (x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[3], x7[3])), x8[3]), -(x5[3], x1[3]), x4[3])), ≥)∧[bni_61] = 0∧0 = 0∧[(-1)bni_61] = 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_62] + x1[2] ≥ 0)

• 3586_1_MAIN_INVOKEMETHOD(3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2, 3), <(x2, x0)), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4)
• (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_3586_1_MAIN_INVOKEMETHOD(&&(>=(x2[4], 3), <(x2[4], x0[4])), 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0[4], x1[4])), x2[4]), x3[4], x4[4])), ≥)∧0 = 0∧[bni_63] = 0∧[(-1)bni_63] = 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_64] ≥ 0)

• COND_3586_1_MAIN_INVOKEMETHOD(TRUE, 3586_0_random_ArrayAccess(java.lang.Object(ARRAY(x0, x1)), x2), x3, x4) → 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5, x6), x3, x4)
• (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(x5[5], x6[5]), x3[5], x4[5])), ≥)∧0 = 0∧[bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65] = 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_66] ≥ 0)

• 3687_1_MAIN_INVOKEMETHOD(3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2, 0), >=(x1, 0)), <=(1, -(x4, +(x5, +(x1, 1))))), <(0, +(x1, 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5)
• (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)
• (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_3687_1_MAIN_INVOKEMETHOD(&&(&&(&&(>(x2[6], 0), >=(x1[6], 0)), <=(1, -(x4[6], +(x5[6], +(x1[6], 1))))), <(0, +(x1[6], 1))), 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0[6], x1[6])), x2[6]), x4[6], x5[6])), ≥)∧0 = 0∧[bni_67 + (-1)Bound*bni_67] + [bni_67]x1[6] + [bni_67]x4[6] ≥ 0∧0 = 0∧[(-1)bso_68] + x1[6] ≥ 0)

• COND_3687_1_MAIN_INVOKEMETHOD(TRUE, 3687_0_random_IntArithmetic(java.lang.Object(java.lang.String(x0, x1)), x2), x4, x5) → 3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6, x7)), x8), +(x5, +(x1, 1)), x4)
• (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)
• (x1[6] ≥ 0∧x4[6] ≥ 0∧x2[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(3316_1_MAIN_INVOKEMETHOD(3316_0_random_ArrayAccess(java.lang.Object(ARRAY(x6[7], x7[7])), x8[7]), +(x5[7], +(x1[7], 1)), x4[7])), ≥)∧0 = 0∧[bni_69 + (-1)Bound*bni_69] + [bni_69]x4[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_70] ≥ 0)

The constraints for P> respective 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(3316_1_MAIN_INVOKEMETHOD(x1, x2, x3)) = [1] + [-1]x1 + [-1]x2 + x3
POL(3316_0_random_ArrayAccess(x1, x2)) = [-1]x1
POL(java.lang.Object(x1)) = x1
POL(ARRAY(x1, x2)) = [-1]
POL(COND_3316_1_MAIN_INVOKEMETHOD(x1, x2, x3, x4)) = [-1]x2 + [-1]x3 + x4
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(2) = [2]
POL(<(x1, x2)) = [-1]
POL(3347_1_MAIN_INVOKEMETHOD(x1, x2, x3)) = [-1] + x3 + [-1]x2
POL(3347_0_random_IntArithmetic(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(java.lang.String(x1, x2)) = [-1] + x2
POL(COND_3347_1_MAIN_INVOKEMETHOD(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3
POL(>(x1, x2)) = [-1]
POL(0) = 0
POL(3586_1_MAIN_INVOKEMETHOD(x1, x2, x3)) = [-1] + x2 + [-1]x3
POL(3586_0_random_ArrayAccess(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(-(x1, x2)) = x1 + [-1]x2
POL(COND_3586_1_MAIN_INVOKEMETHOD(x1, x2, x3, x4)) = [-1] + x3 + [-1]x4
POL(3) = [3]
POL(3687_1_MAIN_INVOKEMETHOD(x1, x2, x3)) = [-1] + x2 + [-1]x3
POL(3687_0_random_IntArithmetic(x1, x2)) = [-1] + [-1]x1
POL(COND_3687_1_MAIN_INVOKEMETHOD(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2 + x3
POL(<=(x1, x2)) = [-1]
POL(1) = [1]
POL(+(x1, x2)) = x1 + x2

The following pairs are in P>:

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

The following pairs are in Pbound:

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

The following pairs are in P:

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

There are no usable rules.

(7) Obligation:

IDP problem:
The following function symbols are pre-defined:
 != ~ Neq: (Integer, Integer) -> Boolean * ~ Mul: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean -1 ~ UnaryMinus: (Integer) -> Integer | ~ Bwor: (Integer, Integer) -> Integer / ~ Div: (Integer, Integer) -> Integer = ~ Eq: (Integer, Integer) -> Boolean ~ Bwxor: (Integer, Integer) -> Integer || ~ Lor: (Boolean, Boolean) -> Boolean ! ~ Lnot: (Boolean) -> Boolean < ~ Lt: (Integer, Integer) -> Boolean - ~ Sub: (Integer, Integer) -> Integer <= ~ Le: (Integer, Integer) -> Boolean > ~ Gt: (Integer, Integer) -> Boolean ~ ~ Bwnot: (Integer) -> Integer % ~ Mod: (Integer, Integer) -> Integer & ~ Bwand: (Integer, Integer) -> Integer + ~ Add: (Integer, Integer) -> Integer && ~ Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

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

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

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

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

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

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

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

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

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

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:
 != ~ Neq: (Integer, Integer) -> Boolean * ~ Mul: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean -1 ~ UnaryMinus: (Integer) -> Integer | ~ Bwor: (Integer, Integer) -> Integer / ~ Div: (Integer, Integer) -> Integer = ~ Eq: (Integer, Integer) -> Boolean ~ Bwxor: (Integer, Integer) -> Integer || ~ Lor: (Boolean, Boolean) -> Boolean ! ~ Lnot: (Boolean) -> Boolean < ~ Lt: (Integer, Integer) -> Boolean - ~ Sub: (Integer, Integer) -> Integer <= ~ Le: (Integer, Integer) -> Boolean > ~ Gt: (Integer, Integer) -> Boolean ~ ~ Bwnot: (Integer) -> Integer % ~ Mod: (Integer, Integer) -> Integer & ~ Bwand: (Integer, Integer) -> Integer + ~ Add: (Integer, Integer) -> Integer && ~ Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

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

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

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

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

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

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

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

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