### (0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Sun Microsystems Inc.) Main-Class: NestedLoop
`public class NestedLoop {	public static void main(String[] args) {		int i, j, z, n;		n = args.length;		int[] a = new int[n];		for(i = 0;i< n-1;i++){			a[i] = args[i].length();		}		for (i = 0; i < n - 1; i++) {			for (j = i + 1; j < n; j++) {				if(a[i]< a[j]){					z = a[i]; a[i] = a[j]; a[j] = z;				}			}		}		for(i = 0;i< n -1;i++){		}	}}`

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
NestedLoop.main([Ljava/lang/String;)V: Graph of 325 nodes with 3 SCCs.

### (3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 9 rules for P and 2 rules for R.

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

Filtered ground terms:

Filtered duplicate args:

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

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

Log for SCC 1:

Generated 53 rules for P and 156 rules for R.

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

Filtered ground terms:

1441_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → 1441_0_main_GE(x2, x3, x4, x5, x6, x7)
Cond_1534_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_1534_0_main_GE(x1, x3, x4, x5, x6, x7, x8)
1534_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → 1534_0_main_GE(x2, x3, x4, x5, x6, x7)
Cond_1533_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_1533_0_main_GE(x1, x3, x4, x5, x6, x7, x8)
1533_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → 1533_0_main_GE(x2, x3, x4, x5, x6, x7)
Cond_1441_0_main_GE2(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_1441_0_main_GE2(x1, x3, x4, x5, x6, x7, x8)
Cond_1441_0_main_GE1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_1441_0_main_GE1(x1, x3, x4, x5, x6, x7, x8)
Cond_1441_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_1441_0_main_GE(x1, x3, x4, x5, x6, x7, x8)

Filtered duplicate args:

1441_0_main_GE(x1, x2, x3, x4, x5, x6) → 1441_0_main_GE(x1, x4, x5, x6)
Cond_1441_0_main_GE2(x1, x2, x3, x4, x5, x6, x7) → Cond_1441_0_main_GE2(x1, x2, x5, x6, x7)
Cond_1441_0_main_GE1(x1, x2, x3, x4, x5, x6, x7) → Cond_1441_0_main_GE1(x1, x2, x5, x6, x7)
Cond_1441_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → Cond_1441_0_main_GE(x1, x2, x5, x6, x7)

Filtered unneeded arguments:

Cond_1441_0_main_GE(x1, x2, x3, x4, x5) → Cond_1441_0_main_GE(x1, x2, x3, x5)
Cond_1533_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → Cond_1533_0_main_GE(x1, x2, x3, x4, x5)
Cond_1534_0_main_GE(x1, x2, x3, x4, x5, x6, x7) → Cond_1534_0_main_GE(x1, x2, x3, x4, x5)

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.

Log for SCC 2:

Generated 23 rules for P and 283 rules for R.

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

Filtered ground terms:

555_0_main_Load(x1, x2, x3, x4, x5, x6) → 555_0_main_Load(x2, x3, x4, x5, x6)
Cond_555_0_main_Load(x1, x2, x3, x4, x5, x6, x7) → Cond_555_0_main_Load(x1, x3, x4, x5, x6, x7)

Filtered duplicate args:

Cond_555_0_main_Load(x1, x2, x3, x4, x5, x6) → Cond_555_0_main_Load(x1, x2, x4, x5, x6)

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

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

### (5) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1959_0_MAIN_LOAD(x1[0], x0[0]) → COND_1959_0_MAIN_LOAD(x1[0] >= 0 && x0[0] >= 0 && x0[0] < x1[0] - 1, x1[0], x0[0])

(0) -> (1), if ((x1[0] >= 0 && x0[0] >= 0 && x0[0] < x1[0] - 1* TRUE)∧(x1[0]* x1[1])∧(x0[0]* x0[1]))

(1) -> (0), if ((x1[1]* x1[0])∧(x0[1] + 1* x0[0]))

The set Q is empty.

### (6) IDPNonInfProof (SOUND transformation)

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

For Pair 1959_0_MAIN_LOAD(x1, x0) → COND_1959_0_MAIN_LOAD(&&(&&(>=(x1, 0), >=(x0, 0)), <(x0, -(x1, 1))), x1, x0) the following chains were created:
• We consider the chain 1959_0_MAIN_LOAD(x1[0], x0[0]) → COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0]), COND_1959_0_MAIN_LOAD(TRUE, x1[1], x0[1]) → 1959_0_MAIN_LOAD(x1[1], +(x0[1], 1)) which results in the following constraint:

(1)    (&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1)))=TRUEx1[0]=x1[1]x0[0]=x0[1]1959_0_MAIN_LOAD(x1[0], x0[0])≥NonInfC∧1959_0_MAIN_LOAD(x1[0], x0[0])≥COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])∧(UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥))

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

(2)    (<(x0[0], -(x1[0], 1))=TRUE>=(x1[0], 0)=TRUE>=(x0[0], 0)=TRUE1959_0_MAIN_LOAD(x1[0], x0[0])≥NonInfC∧1959_0_MAIN_LOAD(x1[0], x0[0])≥COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])∧(UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥))

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

(3)    (x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥)∧[(-1)bni_10 + (-1)Bound*bni_10] + [(-1)bni_10]x0[0] + [bni_10]x1[0] ≥ 0∧[(-1)bso_11] ≥ 0)

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

(4)    (x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥)∧[(-1)bni_10 + (-1)Bound*bni_10] + [(-1)bni_10]x0[0] + [bni_10]x1[0] ≥ 0∧[(-1)bso_11] ≥ 0)

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

(5)    (x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥)∧[(-1)bni_10 + (-1)Bound*bni_10] + [(-1)bni_10]x0[0] + [bni_10]x1[0] ≥ 0∧[(-1)bso_11] ≥ 0)

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

(6)    (x1[0] ≥ 0∧[2] + x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥)∧[bni_10 + (-1)Bound*bni_10] + [bni_10]x1[0] ≥ 0∧[(-1)bso_11] ≥ 0)

For Pair COND_1959_0_MAIN_LOAD(TRUE, x1, x0) → 1959_0_MAIN_LOAD(x1, +(x0, 1)) the following chains were created:
• We consider the chain COND_1959_0_MAIN_LOAD(TRUE, x1[1], x0[1]) → 1959_0_MAIN_LOAD(x1[1], +(x0[1], 1)) which results in the following constraint:

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

(8)    ((UIncreasing(1959_0_MAIN_LOAD(x1[1], +(x0[1], 1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(9)    ((UIncreasing(1959_0_MAIN_LOAD(x1[1], +(x0[1], 1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(10)    ((UIncreasing(1959_0_MAIN_LOAD(x1[1], +(x0[1], 1))), ≥)∧[1 + (-1)bso_13] ≥ 0)

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

(11)    ((UIncreasing(1959_0_MAIN_LOAD(x1[1], +(x0[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_13] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 1959_0_MAIN_LOAD(x1, x0) → COND_1959_0_MAIN_LOAD(&&(&&(>=(x1, 0), >=(x0, 0)), <(x0, -(x1, 1))), x1, x0)
• (x1[0] ≥ 0∧[2] + x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])), ≥)∧[bni_10 + (-1)Bound*bni_10] + [bni_10]x1[0] ≥ 0∧[(-1)bso_11] ≥ 0)

• ((UIncreasing(1959_0_MAIN_LOAD(x1[1], +(x0[1], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_13] ≥ 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(1959_0_MAIN_LOAD(x1, x2)) = [-1] + [-1]x2 + x1
POL(COND_1959_0_MAIN_LOAD(x1, x2, x3)) = [-1] + [-1]x3 + x2
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(+(x1, x2)) = x1 + x2

The following pairs are in P>:

The following pairs are in Pbound:

1959_0_MAIN_LOAD(x1[0], x0[0]) → COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])

The following pairs are in P:

1959_0_MAIN_LOAD(x1[0], x0[0]) → COND_1959_0_MAIN_LOAD(&&(&&(>=(x1[0], 0), >=(x0[0], 0)), <(x0[0], -(x1[0], 1))), x1[0], x0[0])

There are no usable rules.

### (8) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1959_0_MAIN_LOAD(x1[0], x0[0]) → COND_1959_0_MAIN_LOAD(x1[0] >= 0 && x0[0] >= 0 && x0[0] < x1[0] - 1, x1[0], x0[0])

The set Q is empty.

### (9) IDependencyGraphProof (EQUIVALENT transformation)

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

### (11) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:

The set Q is empty.

### (12) IDependencyGraphProof (EQUIVALENT transformation)

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

### (14) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]) → COND_1441_0_MAIN_GE(x2[0] >= 0 && x2[0] <= x1[0] && x0[0] >= 0 && 0 <= x0[0] + 1 && x2[0] - 1 > x0[0] + 1, x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])
(1): COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1]) → 1441_0_MAIN_GE(x0[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1])), x0[1] + 1 + 1, x2[1])
(2): 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(x2[2] > x1[2] && x2[2] > x0[2] && x1[2] >= 1 && x0[2] >= 0, x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
(4): 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0, x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(7): COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), x1[7] + 1, x2[7])
(8): 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0, x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])

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

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

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

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

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

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

(4) -> (5), if ((x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0* TRUE)∧(x0[4]* x0[5])∧(java.lang.Object(ARRAY(x2[4], x3[4])) →* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x1[4]* x1[5])∧(x2[4]* x2[5]))

(5) -> (8), if ((x0[5]* x0[8])∧(x1[5]* x1[8])∧(x2[5]* x2[8])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →* java.lang.Object(ARRAY(x2[8], x3[8])))∧(x4[5]* x4[8])∧(x5[5]* x5[8]))

(6) -> (7), if ((x5[6] <= x4[6] && x1[6] > 0* TRUE)∧(x0[6]* x0[7])∧(x1[6]* x1[7])∧(x2[6]* x2[7])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[6]* x4[7])∧(x5[6]* x5[7]))

(7) -> (0), if ((x0[7]* x0[0])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[0], x3[0])))∧(x1[7] + 1* x1[0])∧(x2[7]* x2[0]))

(7) -> (2), if ((x0[7]* x0[2])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[2], x3[2])))∧(x1[7] + 1* x1[2])∧(x2[7]* x2[2]))

(7) -> (4), if ((x0[7]* x0[4])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x1[7] + 1* x1[4])∧(x2[7]* x2[4]))

(8) -> (7), if ((x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0* TRUE)∧(x0[8]* x0[7])∧(x1[8]* x1[7])∧(x2[8]* x2[7])∧(java.lang.Object(ARRAY(x2[8], x3[8])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[8]* x4[7])∧(x5[8]* x5[7]))

The set Q is empty.

### (15) IDPNonInfProof (SOUND transformation)

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

For Pair 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2, 0), <=(x2, x1)), >=(x0, 0)), <=(0, +(x0, 1))), >(-(x2, 1), +(x0, 1))), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) the following chains were created:
• We consider the chain 1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]) → COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]), COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1]) → 1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1]) which results in the following constraint:

(1)    (&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1)))=TRUEx0[0]=x0[1]java.lang.Object(ARRAY(x2[0], x3[0]))=java.lang.Object(ARRAY(x2[1], x3[1]))∧x1[0]=x1[1]x2[0]=x2[1]1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])≥NonInfC∧1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])≥COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])∧(UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥))

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

(2)    (>(-(x2[0], 1), +(x0[0], 1))=TRUE<=(0, +(x0[0], 1))=TRUE>=(x0[0], 0)=TRUE>=(x2[0], 0)=TRUE<=(x2[0], x1[0])=TRUE1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])≥NonInfC∧1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])≥COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])∧(UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥))

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

(3)    (x2[0] + [-3] + [-1]x0[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] + [(-1)bni_21]x0[0] ≥ 0∧[(-1)bso_22] ≥ 0)

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

(4)    (x2[0] + [-3] + [-1]x0[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] + [(-1)bni_21]x0[0] ≥ 0∧[(-1)bso_22] ≥ 0)

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

(5)    (x2[0] + [-3] + [-1]x0[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] + [(-1)bni_21]x0[0] ≥ 0∧[(-1)bso_22] ≥ 0)

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

(6)    (x2[0] + [-3] + [-1]x0[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧0 = 0∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] + [(-1)bni_21]x0[0] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)

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

(7)    (x2[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧[3] + x0[0] + x2[0] ≥ 0∧x1[0] + [-3] + [-1]x0[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧0 = 0∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)

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

(8)    (x2[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧[3] + x0[0] + x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧0 = 0∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)

For Pair COND_1441_0_MAIN_GE(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1441_0_MAIN_GE(+(x0, 1), java.lang.Object(ARRAY(x2, x3)), +(+(x0, 1), 1), x2) the following chains were created:
• We consider the chain COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1]) → 1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1]) which results in the following constraint:

(9)    (COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1])≥NonInfC∧COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1])≥1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])∧(UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(10)    ((UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥)∧[1 + (-1)bso_24] ≥ 0)

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

(11)    ((UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥)∧[1 + (-1)bso_24] ≥ 0)

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

(12)    ((UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥)∧[1 + (-1)bso_24] ≥ 0)

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

(13)    ((UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)

For Pair 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2, x1), >(x2, x0)), >=(x1, 1)), >=(x0, 0)), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) the following chains were created:
• We consider the chain 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]), COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3]) which results in the following constraint:

(14)    (&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0))=TRUEx0[2]=x0[3]java.lang.Object(ARRAY(x2[2], x3[2]))=java.lang.Object(ARRAY(x2[3], x3[3]))∧x1[2]=x1[3]x2[2]=x2[3]1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥NonInfC∧1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])∧(UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥))

We simplified constraint (14) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(15)    (>=(x0[2], 0)=TRUE>=(x1[2], 1)=TRUE>(x2[2], x1[2])=TRUE>(x2[2], x0[2])=TRUE1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥NonInfC∧1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])∧(UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥))

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

(16)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧[(-1)bso_26] ≥ 0)

We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(17)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧[(-1)bso_26] ≥ 0)

We simplified constraint (17) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(18)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(19)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

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

(20)    (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] + [-2] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

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

(21)    (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] ≥ 0∧[1] + x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[bni_25 + (-1)Bound*bni_25] + [bni_25]x1[2] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

For Pair COND_1441_0_MAIN_GE1(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1533_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) the following chains were created:
• We consider the chain COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3]) which results in the following constraint:

(22)    (COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3])≥NonInfC∧COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3])≥1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])∧(UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥))

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

(23)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_28] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(24)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_28] ≥ 0)

We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(25)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_28] ≥ 0)

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

(26)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)

For Pair 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2, x1), >(x2, x0)), >=(x1, 1)), >=(x0, 0)), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) the following chains were created:
• We consider the chain 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]), COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5]) which results in the following constraint:

(27)    (&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0))=TRUEx0[4]=x0[5]java.lang.Object(ARRAY(x2[4], x3[4]))=java.lang.Object(ARRAY(x2[5], x3[5]))∧x1[4]=x1[5]x2[4]=x2[5]1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥NonInfC∧1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])∧(UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥))

We simplified constraint (27) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(28)    (>=(x0[4], 0)=TRUE>=(x1[4], 1)=TRUE>(x2[4], x1[4])=TRUE>(x2[4], x0[4])=TRUE1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥NonInfC∧1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])∧(UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥))

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

(29)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(30)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(31)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(32)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

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

(33)    (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] + [-2] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

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

(34)    (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] ≥ 0∧[1] + x1[4] + x2[4] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[4] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

For Pair COND_1441_0_MAIN_GE2(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1534_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) the following chains were created:
• We consider the chain COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5]) which results in the following constraint:

(35)    (COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5])≥NonInfC∧COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5])≥1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])∧(UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥))

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

(36)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_32] ≥ 0)

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

(37)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_32] ≥ 0)

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

(38)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_32] ≥ 0)

We simplified constraint (38) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(39)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_32] ≥ 0)

For Pair 1533_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → COND_1533_0_MAIN_GE(&&(<=(x5, x4), >(x1, 0)), x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) the following chains were created:
• We consider the chain 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]), COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(40)    (&&(<=(x5[6], x4[6]), >(x1[6], 0))=TRUEx0[6]=x0[7]x1[6]=x1[7]x2[6]=x2[7]java.lang.Object(ARRAY(x2[6], x3[6]))=java.lang.Object(ARRAY(x2[7], x3[7]))∧x4[6]=x4[7]x5[6]=x5[7]1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥NonInfC∧1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥))

We simplified constraint (40) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(41)    (<=(x5[6], x4[6])=TRUE>(x1[6], 0)=TRUE1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥NonInfC∧1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥))

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

(42)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x2[6] + [(-1)bni_33]x0[6] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(43)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x2[6] + [(-1)bni_33]x0[6] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(44)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x2[6] + [(-1)bni_33]x0[6] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(45)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

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

(46)    (x4[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(47)    (x4[6] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(48)    (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

(49)    (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

For Pair COND_1533_0_MAIN_GE(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), +(x1, 1), x2) the following chains were created:
• We consider the chain COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(50)    (COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7])≥NonInfC∧COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7])≥1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])∧(UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥))

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

(51)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[(-1)bso_36] ≥ 0)

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

(52)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[(-1)bso_36] ≥ 0)

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

(53)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[(-1)bso_36] ≥ 0)

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

(54)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

For Pair 1534_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5, x4), >(x2, x1)), >(x2, x0)), >(x1, 1)), >=(x0, 0)), x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) the following chains were created:
• We consider the chain 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]), COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(55)    (&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0))=TRUEx0[8]=x0[7]x1[8]=x1[7]x2[8]=x2[7]java.lang.Object(ARRAY(x2[8], x3[8]))=java.lang.Object(ARRAY(x2[7], x3[7]))∧x4[8]=x4[7]x5[8]=x5[7]1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥NonInfC∧1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥))

We simplified constraint (55) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(56)    (>=(x0[8], 0)=TRUE>(x1[8], 1)=TRUE>(x2[8], x0[8])=TRUE>(x5[8], x4[8])=TRUE>(x2[8], x1[8])=TRUE1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥NonInfC∧1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(57)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x2[8] + [(-1)bni_37]x0[8] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(58)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x2[8] + [(-1)bni_37]x0[8] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(59)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x2[8] + [(-1)bni_37]x0[8] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(60)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x2[8] + [(-1)bni_37]x0[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

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

(61)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-3] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x2[8] + [(-1)bni_37]x0[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

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

(62)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

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

(63)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

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

(64)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

(65)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2, 0), <=(x2, x1)), >=(x0, 0)), <=(0, +(x0, 1))), >(-(x2, 1), +(x0, 1))), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2)
• (x2[0] ≥ 0∧x0[0] + [1] ≥ 0∧x0[0] ≥ 0∧[3] + x0[0] + x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])), ≥)∧0 = 0∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x2[0] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)

• COND_1441_0_MAIN_GE(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1441_0_MAIN_GE(+(x0, 1), java.lang.Object(ARRAY(x2, x3)), +(+(x0, 1), 1), x2)
• ((UIncreasing(1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)

• 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2, x1), >(x2, x0)), >=(x1, 1)), >=(x0, 0)), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2)
• (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] ≥ 0∧[1] + x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[bni_25 + (-1)Bound*bni_25] + [bni_25]x1[2] + [bni_25]x2[2] + [(-1)bni_25]x0[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

• COND_1441_0_MAIN_GE1(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1533_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
• ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_28] ≥ 0)

• 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2, x1), >(x2, x0)), >=(x1, 1)), >=(x0, 0)), x0, java.lang.Object(ARRAY(x2, x3)), x1, x2)
• (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] ≥ 0∧[1] + x1[4] + x2[4] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[4] + [bni_29]x2[4] + [(-1)bni_29]x0[4] ≥ 0∧0 = 0∧[(-1)bso_30] ≥ 0)

• COND_1441_0_MAIN_GE2(TRUE, x0, java.lang.Object(ARRAY(x2, x3)), x1, x2) → 1534_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
• ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_32] ≥ 0)

• 1533_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → COND_1533_0_MAIN_GE(&&(<=(x5, x4), >(x1, 0)), x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
• (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)
• (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_33] = 0∧0 = 0∧[(-1)bni_33] = 0∧[(-1)bni_33 + (-1)Bound*bni_33] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

• COND_1533_0_MAIN_GE(TRUE, x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → 1441_0_MAIN_GE(x0, java.lang.Object(ARRAY(x2, x3)), +(x1, 1), x2)
• ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

• 1534_0_MAIN_GE(x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5, x4), >(x2, x1)), >(x2, x0)), >(x1, 1)), >=(x0, 0)), x0, x1, x2, java.lang.Object(ARRAY(x2, x3)), x4, x5)
• (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)
• (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]x2[8] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 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(1441_0_MAIN_GE(x1, x2, x3, x4)) = [-1] + x4 + [-1]x1
POL(java.lang.Object(x1)) = x1
POL(ARRAY(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(COND_1441_0_MAIN_GE(x1, x2, x3, x4, x5)) = [-1] + x5 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<=(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]
POL(>(x1, x2)) = [-1]
POL(-(x1, x2)) = x1 + [-1]x2
POL(COND_1441_0_MAIN_GE1(x1, x2, x3, x4, x5)) = [-1] + x5 + [-1]x2
POL(1533_0_MAIN_GE(x1, x2, x3, x4, x5, x6)) = [-1] + x3 + [-1]x1
POL(COND_1441_0_MAIN_GE2(x1, x2, x3, x4, x5)) = [-1] + x5 + [-1]x2
POL(1534_0_MAIN_GE(x1, x2, x3, x4, x5, x6)) = [-1] + x3 + [-1]x1
POL(COND_1533_0_MAIN_GE(x1, x2, x3, x4, x5, x6, x7)) = [-1] + x4 + [-1]x2

The following pairs are in P>:

COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1]) → 1441_0_MAIN_GE(+(x0[1], 1), java.lang.Object(ARRAY(x2[1], x3[1])), +(+(x0[1], 1), 1), x2[1])

The following pairs are in Pbound:

1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]) → COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])
1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])
1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])

The following pairs are in P:

1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]) → COND_1441_0_MAIN_GE(&&(&&(&&(&&(>=(x2[0], 0), <=(x2[0], x1[0])), >=(x0[0], 0)), <=(0, +(x0[0], 1))), >(-(x2[0], 1), +(x0[0], 1))), x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])
1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])
COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])
1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])

There are no usable rules.

### (17) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1441_0_MAIN_GE(x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0]) → COND_1441_0_MAIN_GE(x2[0] >= 0 && x2[0] <= x1[0] && x0[0] >= 0 && 0 <= x0[0] + 1 && x2[0] - 1 > x0[0] + 1, x0[0], java.lang.Object(ARRAY(x2[0], x3[0])), x1[0], x2[0])
(2): 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(x2[2] > x1[2] && x2[2] > x0[2] && x1[2] >= 1 && x0[2] >= 0, x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
(4): 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0, x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(7): COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), x1[7] + 1, x2[7])
(8): 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0, x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])

(7) -> (0), if ((x0[7]* x0[0])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[0], x3[0])))∧(x1[7] + 1* x1[0])∧(x2[7]* x2[0]))

(7) -> (2), if ((x0[7]* x0[2])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[2], x3[2])))∧(x1[7] + 1* x1[2])∧(x2[7]* x2[2]))

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

(7) -> (4), if ((x0[7]* x0[4])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x1[7] + 1* x1[4])∧(x2[7]* x2[4]))

(4) -> (5), if ((x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0* TRUE)∧(x0[4]* x0[5])∧(java.lang.Object(ARRAY(x2[4], x3[4])) →* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x1[4]* x1[5])∧(x2[4]* x2[5]))

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

(6) -> (7), if ((x5[6] <= x4[6] && x1[6] > 0* TRUE)∧(x0[6]* x0[7])∧(x1[6]* x1[7])∧(x2[6]* x2[7])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[6]* x4[7])∧(x5[6]* x5[7]))

(8) -> (7), if ((x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0* TRUE)∧(x0[8]* x0[7])∧(x1[8]* x1[7])∧(x2[8]* x2[7])∧(java.lang.Object(ARRAY(x2[8], x3[8])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[8]* x4[7])∧(x5[8]* x5[7]))

(5) -> (8), if ((x0[5]* x0[8])∧(x1[5]* x1[8])∧(x2[5]* x2[8])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →* java.lang.Object(ARRAY(x2[8], x3[8])))∧(x4[5]* x4[8])∧(x5[5]* x5[8]))

The set Q is empty.

### (18) IDependencyGraphProof (EQUIVALENT transformation)

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

### (19) 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): 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0, x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(4): 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0, x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
(7): COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), x1[7] + 1, x2[7])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
(2): 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(x2[2] > x1[2] && x2[2] > x0[2] && x1[2] >= 1 && x0[2] >= 0, x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])

(7) -> (2), if ((x0[7]* x0[2])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[2], x3[2])))∧(x1[7] + 1* x1[2])∧(x2[7]* x2[2]))

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

(7) -> (4), if ((x0[7]* x0[4])∧(java.lang.Object(ARRAY(x2[7], x3[7])) →* java.lang.Object(ARRAY(x2[4], x3[4])))∧(x1[7] + 1* x1[4])∧(x2[7]* x2[4]))

(4) -> (5), if ((x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0* TRUE)∧(x0[4]* x0[5])∧(java.lang.Object(ARRAY(x2[4], x3[4])) →* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x1[4]* x1[5])∧(x2[4]* x2[5]))

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

(6) -> (7), if ((x5[6] <= x4[6] && x1[6] > 0* TRUE)∧(x0[6]* x0[7])∧(x1[6]* x1[7])∧(x2[6]* x2[7])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[6]* x4[7])∧(x5[6]* x5[7]))

(8) -> (7), if ((x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0* TRUE)∧(x0[8]* x0[7])∧(x1[8]* x1[7])∧(x2[8]* x2[7])∧(java.lang.Object(ARRAY(x2[8], x3[8])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[8]* x4[7])∧(x5[8]* x5[7]))

(5) -> (8), if ((x0[5]* x0[8])∧(x1[5]* x1[8])∧(x2[5]* x2[8])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →* java.lang.Object(ARRAY(x2[8], x3[8])))∧(x4[5]* x4[8])∧(x5[5]* x5[8]))

The set Q is empty.

### (20) 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 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) the following chains were created:
• We consider the chain 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]), COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(1)    (&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0))=TRUEx0[8]=x0[7]x1[8]=x1[7]x2[8]=x2[7]java.lang.Object(ARRAY(x2[8], x3[8]))=java.lang.Object(ARRAY(x2[7], x3[7]))∧x4[8]=x4[7]x5[8]=x5[7]1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥NonInfC∧1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥))

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

(2)    (>=(x0[8], 0)=TRUE>(x1[8], 1)=TRUE>(x2[8], x0[8])=TRUE>(x5[8], x4[8])=TRUE>(x2[8], x1[8])=TRUE1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥NonInfC∧1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])≥COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥))

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

(3)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧[(-1)bso_21] ≥ 0)

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

(4)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧[(-1)bso_21] ≥ 0)

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

(5)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧[(-1)bso_21] ≥ 0)

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

(6)    (x0[8] ≥ 0∧x1[8] + [-2] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-1] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

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

(7)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] + [-1] + [-1]x0[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧x2[8] + [-3] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-2)bni_20] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

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

(8)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] + [-1] + [-1]x4[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(9)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (9) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(10)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

(11)    (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

For Pair COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5]) the following chains were created:
• We consider the chain COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5]) which results in the following constraint:

(12)    (COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5])≥NonInfC∧COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5])≥1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])∧(UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥))

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

(13)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_23] ≥ 0)

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

(14)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_23] ≥ 0)

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

(15)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧[(-1)bso_23] ≥ 0)

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

(16)    ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

For Pair 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) the following chains were created:
• We consider the chain 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]), COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5]) which results in the following constraint:

(17)    (&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0))=TRUEx0[4]=x0[5]java.lang.Object(ARRAY(x2[4], x3[4]))=java.lang.Object(ARRAY(x2[5], x3[5]))∧x1[4]=x1[5]x2[4]=x2[5]1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥NonInfC∧1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])∧(UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥))

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

(18)    (>=(x0[4], 0)=TRUE>=(x1[4], 1)=TRUE>(x2[4], x1[4])=TRUE>(x2[4], x0[4])=TRUE1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥NonInfC∧1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])≥COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])∧(UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥))

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

(19)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]x2[4] + [(-1)bni_24]x1[4] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(20)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]x2[4] + [(-1)bni_24]x1[4] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(21)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧[(-1)Bound*bni_24] + [bni_24]x2[4] + [(-1)bni_24]x1[4] ≥ 0∧[(-1)bso_25] ≥ 0)

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

(22)    (x0[4] ≥ 0∧x1[4] + [-1] ≥ 0∧x2[4] + [-1] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)Bound*bni_24] + [bni_24]x2[4] + [(-1)bni_24]x1[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)

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

(23)    (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] + [-2] + [-1]x1[4] ≥ 0∧x2[4] + [-1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)Bound*bni_24 + (-1)bni_24] + [bni_24]x2[4] + [(-1)bni_24]x1[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(24)    (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] ≥ 0∧[1] + x1[4] + x2[4] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)Bound*bni_24 + bni_24] + [bni_24]x2[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)

For Pair COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) the following chains were created:
• We consider the chain COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(25)    (COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7])≥NonInfC∧COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7])≥1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])∧(UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥))

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

(26)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[1 + (-1)bso_27] ≥ 0)

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

(27)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[1 + (-1)bso_27] ≥ 0)

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

(28)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧[1 + (-1)bso_27] ≥ 0)

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

(29)    ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

For Pair 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) the following chains were created:
• We consider the chain 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]), COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7]) which results in the following constraint:

(30)    (&&(<=(x5[6], x4[6]), >(x1[6], 0))=TRUEx0[6]=x0[7]x1[6]=x1[7]x2[6]=x2[7]java.lang.Object(ARRAY(x2[6], x3[6]))=java.lang.Object(ARRAY(x2[7], x3[7]))∧x4[6]=x4[7]x5[6]=x5[7]1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥NonInfC∧1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥))

We simplified constraint (30) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(31)    (<=(x5[6], x4[6])=TRUE>(x1[6], 0)=TRUE1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥NonInfC∧1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])≥COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])∧(UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥))

We simplified constraint (31) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(32)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)Bound*bni_28] + [bni_28]x2[6] + [(-1)bni_28]x1[6] ≥ 0∧[(-1)bso_29] ≥ 0)

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

(33)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)Bound*bni_28] + [bni_28]x2[6] + [(-1)bni_28]x1[6] ≥ 0∧[(-1)bso_29] ≥ 0)

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

(34)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[(-1)Bound*bni_28] + [bni_28]x2[6] + [(-1)bni_28]x1[6] ≥ 0∧[(-1)bso_29] ≥ 0)

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

(35)    (x4[6] + [-1]x5[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

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

(36)    (x4[6] ≥ 0∧x1[6] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

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

(37)    (x4[6] ≥ 0∧x1[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28 + (-1)bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

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

(38)    (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28 + (-1)bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

(39)    (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28 + (-1)bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

For Pair COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3]) the following chains were created:
• We consider the chain COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3]) which results in the following constraint:

(40)    (COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3])≥NonInfC∧COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3])≥1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])∧(UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥))

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

(41)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_31] ≥ 0)

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

(42)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_31] ≥ 0)

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

(43)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧[(-1)bso_31] ≥ 0)

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

(44)    ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)

For Pair 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) the following chains were created:
• We consider the chain 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]), COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3]) which results in the following constraint:

(45)    (&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0))=TRUEx0[2]=x0[3]java.lang.Object(ARRAY(x2[2], x3[2]))=java.lang.Object(ARRAY(x2[3], x3[3]))∧x1[2]=x1[3]x2[2]=x2[3]1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥NonInfC∧1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])∧(UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥))

We simplified constraint (45) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(46)    (>=(x0[2], 0)=TRUE>=(x1[2], 1)=TRUE>(x2[2], x1[2])=TRUE>(x2[2], x0[2])=TRUE1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥NonInfC∧1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])≥COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])∧(UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥))

We simplified constraint (46) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(47)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x2[2] + [(-1)bni_32]x1[2] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (47) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(48)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x2[2] + [(-1)bni_32]x1[2] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(49)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x2[2] + [(-1)bni_32]x1[2] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(50)    (x0[2] ≥ 0∧x1[2] + [-1] ≥ 0∧x2[2] + [-1] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)Bound*bni_32] + [bni_32]x2[2] + [(-1)bni_32]x1[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

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

(51)    (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] + [-2] + [-1]x1[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + (-1)bni_32] + [bni_32]x2[2] + [(-1)bni_32]x1[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

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

(52)    (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] ≥ 0∧[1] + x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + bni_32] + [bni_32]x2[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])
• (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)
• (x0[8] ≥ 0∧x1[8] ≥ 0∧x2[8] ≥ 0∧x5[8] ≥ 0∧[-2] + x0[8] + x2[8] + [-1]x1[8] ≥ 0∧x4[8] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])), ≥)∧0 = 0∧[(-1)Bound*bni_20 + (-1)bni_20] + [bni_20]x0[8] + [bni_20]x2[8] + [(-1)bni_20]x1[8] ≥ 0∧0 = 0∧[(-1)bso_21] ≥ 0)

• COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
• ((UIncreasing(1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

• 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
• (x0[4] ≥ 0∧x1[4] ≥ 0∧x2[4] ≥ 0∧[1] + x1[4] + x2[4] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])), ≥)∧0 = 0∧[(-1)Bound*bni_24 + bni_24] + [bni_24]x2[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)

• COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])
• ((UIncreasing(1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

• 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
• (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28 + (-1)bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)
• (x4[6] ≥ 0∧x1[6] ≥ 0∧x5[6] ≥ 0 ⇒ (UIncreasing(COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])), ≥)∧[bni_28] = 0∧0 = 0∧0 = 0∧[(-1)Bound*bni_28 + (-1)bni_28] + [(-1)bni_28]x1[6] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

• COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
• ((UIncreasing(1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)

• 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])
• (x0[2] ≥ 0∧x1[2] ≥ 0∧x2[2] ≥ 0∧[1] + x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])), ≥)∧0 = 0∧[(-1)Bound*bni_32 + bni_32] + [bni_32]x2[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 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(1534_0_MAIN_GE(x1, x2, x3, x4, x5, x6)) = [-1] + [-1]x2 + [-1]x4
POL(java.lang.Object(x1)) = x1
POL(ARRAY(x1, x2)) = [-1] + [-1]x1
POL(COND_1533_0_MAIN_GE(x1, x2, x3, x4, x5, x6, x7)) = [-1] + [-1]x3 + [-1]x5
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(1) = [1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(COND_1441_0_MAIN_GE2(x1, x2, x3, x4, x5)) = [-1] + [-1]x4 + [-1]x3
POL(1441_0_MAIN_GE(x1, x2, x3, x4)) = [-1] + [-1]x3 + [-1]x2
POL(+(x1, x2)) = x1 + x2
POL(1533_0_MAIN_GE(x1, x2, x3, x4, x5, x6)) = [-1] + [-1]x2 + [-1]x4
POL(<=(x1, x2)) = [-1]
POL(COND_1441_0_MAIN_GE1(x1, x2, x3, x4, x5)) = [-1] + [-1]x4 + [-1]x3

The following pairs are in P>:

COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), +(x1[7], 1), x2[7])

The following pairs are in Pbound:

1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])
1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])

The following pairs are in P:

1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(&&(&&(&&(&&(>(x5[8], x4[8]), >(x2[8], x1[8])), >(x2[8], x0[8])), >(x1[8], 1)), >=(x0[8], 0)), x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])
COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(&&(&&(&&(>(x2[4], x1[4]), >(x2[4], x0[4])), >=(x1[4], 1)), >=(x0[4], 0)), x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(&&(<=(x5[6], x4[6]), >(x1[6], 0)), x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(&&(&&(&&(>(x2[2], x1[2]), >(x2[2], x0[2])), >=(x1[2], 1)), >=(x0[2], 0)), x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])

There are no usable rules.

### (22) 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): 1534_0_MAIN_GE(x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8]) → COND_1533_0_MAIN_GE(x5[8] > x4[8] && x2[8] > x1[8] && x2[8] > x0[8] && x1[8] > 1 && x0[8] >= 0, x0[8], x1[8], x2[8], java.lang.Object(ARRAY(x2[8], x3[8])), x4[8], x5[8])
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(4): 1441_0_MAIN_GE(x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4]) → COND_1441_0_MAIN_GE2(x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0, x0[4], java.lang.Object(ARRAY(x2[4], x3[4])), x1[4], x2[4])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
(2): 1441_0_MAIN_GE(x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2]) → COND_1441_0_MAIN_GE1(x2[2] > x1[2] && x2[2] > x0[2] && x1[2] >= 1 && x0[2] >= 0, x0[2], java.lang.Object(ARRAY(x2[2], x3[2])), x1[2], x2[2])

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

(4) -> (5), if ((x2[4] > x1[4] && x2[4] > x0[4] && x1[4] >= 1 && x0[4] >= 0* TRUE)∧(x0[4]* x0[5])∧(java.lang.Object(ARRAY(x2[4], x3[4])) →* java.lang.Object(ARRAY(x2[5], x3[5])))∧(x1[4]* x1[5])∧(x2[4]* x2[5]))

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

(5) -> (8), if ((x0[5]* x0[8])∧(x1[5]* x1[8])∧(x2[5]* x2[8])∧(java.lang.Object(ARRAY(x2[5], x3[5])) →* java.lang.Object(ARRAY(x2[8], x3[8])))∧(x4[5]* x4[8])∧(x5[5]* x5[8]))

The set Q is empty.

### (23) IDependencyGraphProof (EQUIVALENT transformation)

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

### (25) 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:
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(7): COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), x1[7] + 1, x2[7])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])

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

(6) -> (7), if ((x5[6] <= x4[6] && x1[6] > 0* TRUE)∧(x0[6]* x0[7])∧(x1[6]* x1[7])∧(x2[6]* x2[7])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[6]* x4[7])∧(x5[6]* x5[7]))

The set Q is empty.

### (26) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

### (28) 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:
(1): COND_1441_0_MAIN_GE(TRUE, x0[1], java.lang.Object(ARRAY(x2[1], x3[1])), x1[1], x2[1]) → 1441_0_MAIN_GE(x0[1] + 1, java.lang.Object(ARRAY(x2[1], x3[1])), x0[1] + 1 + 1, x2[1])
(3): COND_1441_0_MAIN_GE1(TRUE, x0[3], java.lang.Object(ARRAY(x2[3], x3[3])), x1[3], x2[3]) → 1533_0_MAIN_GE(x0[3], x1[3], x2[3], java.lang.Object(ARRAY(x2[3], x3[3])), x4[3], x5[3])
(5): COND_1441_0_MAIN_GE2(TRUE, x0[5], java.lang.Object(ARRAY(x2[5], x3[5])), x1[5], x2[5]) → 1534_0_MAIN_GE(x0[5], x1[5], x2[5], java.lang.Object(ARRAY(x2[5], x3[5])), x4[5], x5[5])
(6): 1533_0_MAIN_GE(x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6]) → COND_1533_0_MAIN_GE(x5[6] <= x4[6] && x1[6] > 0, x0[6], x1[6], x2[6], java.lang.Object(ARRAY(x2[6], x3[6])), x4[6], x5[6])
(7): COND_1533_0_MAIN_GE(TRUE, x0[7], x1[7], x2[7], java.lang.Object(ARRAY(x2[7], x3[7])), x4[7], x5[7]) → 1441_0_MAIN_GE(x0[7], java.lang.Object(ARRAY(x2[7], x3[7])), x1[7] + 1, x2[7])

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

(6) -> (7), if ((x5[6] <= x4[6] && x1[6] > 0* TRUE)∧(x0[6]* x0[7])∧(x1[6]* x1[7])∧(x2[6]* x2[7])∧(java.lang.Object(ARRAY(x2[6], x3[6])) →* java.lang.Object(ARRAY(x2[7], x3[7])))∧(x4[6]* x4[7])∧(x5[6]* x5[7]))

The set Q is empty.

### (29) IDependencyGraphProof (EQUIVALENT transformation)

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

### (31) 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): 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0]) → COND_555_0_MAIN_LOAD(x2[0] >= 0 && x2[0] < x0[0] && x2[0] < x0[0] - 1 && x0[0] >= 0, java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])
(1): COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1]) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1] + 1)

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

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

The set Q is empty.

### (32) 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 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2) → COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2, 0), <(x2, x0)), <(x2, -(x0, 1))), >=(x0, 0)), java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2) the following chains were created:
• We consider the chain 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0]) → COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0]), COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1]) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1)) which results in the following constraint:

(1)    (&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0))=TRUEjava.lang.Object(ARRAY(x0[0], x1[0]))=java.lang.Object(ARRAY(x0[1], x1[1]))∧x0[0]=x0[1]java.lang.Object(ARRAY(x0[0], x3[0]))=java.lang.Object(ARRAY(x0[1], x3[1]))∧x2[0]=x2[1]555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])≥NonInfC∧555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])≥COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])∧(UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥))

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

(2)    (>=(x0[0], 0)=TRUE<(x2[0], -(x0[0], 1))=TRUE>=(x2[0], 0)=TRUE<(x2[0], x0[0])=TRUE555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])≥NonInfC∧555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])≥COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])∧(UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥))

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

(3)    (x0[0] ≥ 0∧x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧[(-1)Bound*bni_15] + [(-1)bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(4)    (x0[0] ≥ 0∧x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧[(-1)Bound*bni_15] + [(-1)bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(5)    (x0[0] ≥ 0∧x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧[(-1)Bound*bni_15] + [(-1)bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(6)    (x0[0] ≥ 0∧x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [(-1)bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

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

(7)    ([2] + x2[0] + x0[0] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧[1] + x0[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15 + (4)bni_15] + [bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

For Pair COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), +(x2, 1)) the following chains were created:
• We consider the chain COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1]) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1)) which results in the following constraint:

(8)    (COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1])≥NonInfC∧COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1])≥555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))∧(UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(9)    ((UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥)∧[(-1)bso_18] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(10)    ((UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥)∧[(-1)bso_18] ≥ 0)

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

(11)    ((UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥)∧[(-1)bso_18] ≥ 0)

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

(12)    ((UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2) → COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2, 0), <(x2, x0)), <(x2, -(x0, 1))), >=(x0, 0)), java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2)
• ([2] + x2[0] + x0[0] ≥ 0∧x0[0] ≥ 0∧x2[0] ≥ 0∧[1] + x0[0] ≥ 0 ⇒ (UIncreasing(COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15 + (4)bni_15] + [bni_15]x2[0] + [(2)bni_15]x0[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

• COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), x2) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0, x1)), x0, java.lang.Object(ARRAY(x0, x3)), +(x2, 1))
• ((UIncreasing(555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 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(555_0_MAIN_LOAD(x1, x2, x3, x4)) = [-1]x4 + [-1]x3 + [-1]x1
POL(java.lang.Object(x1)) = x1
POL(ARRAY(x1, x2)) = [-1]x1
POL(COND_555_0_MAIN_LOAD(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(+(x1, x2)) = x1 + x2

The following pairs are in P>:

555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0]) → COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])

The following pairs are in Pbound:

555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0]) → COND_555_0_MAIN_LOAD(&&(&&(&&(>=(x2[0], 0), <(x2[0], x0[0])), <(x2[0], -(x0[0], 1))), >=(x0[0], 0)), java.lang.Object(ARRAY(x0[0], x1[0])), x0[0], java.lang.Object(ARRAY(x0[0], x3[0])), x2[0])

The following pairs are in P:

COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1]) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), +(x2[1], 1))

There are no usable rules.

### (33) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_555_0_MAIN_LOAD(TRUE, java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1]) → 555_0_MAIN_LOAD(java.lang.Object(ARRAY(x0[1], x1[1])), x0[1], java.lang.Object(ARRAY(x0[1], x3[1])), x2[1] + 1)

The set Q is empty.

### (34) IDependencyGraphProof (EQUIVALENT transformation)

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