Termination proof of /tmp/tmpU4mYdu/PastaB13.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 IDP

↳5 IDPNonInfProof (⇒)

↳6 IDP

↳7 IDependencyGraphProof (⇔)

↳8 IDP

↳9 IDPNonInfProof (⇒)

↳10 IDP

↳11 IDependencyGraphProof (⇔)

↳12 IDP

↳13 IDPNonInfProof (⇒)

↳14 IDP

↳15 IDependencyGraphProof (⇔)

↳16 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaB13

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

public class PastaB13 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();
        int z = Random.random();

        while (x > z || y > z) {
            if (x > z) {
                x--;
            } else if (y > z) {
                y--;
            } else {
                continue;
            }
        }
    }
}


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

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
PastaB13.main([Ljava/lang/String;)V: Graph of 246 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 30 rules for P and 2 rules for R.

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

Filtered ground terms:

1497_0_main_LE(x1, x2, x3, x4, x5, x6) → 1497_0_main_LE(x2, x3, x4, x5, x6)
Cond_1482_0_main_Load1(x1, x2, x3, x4, x5, x6) → Cond_1482_0_main_Load1(x1, x3, x4, x5, x6)
1482_0_main_Load(x1, x2, x3, x4, x5) → 1482_0_main_Load(x2, x3, x4, x5)
Cond_1497_0_main_LE2(x1, x2, x3, x4, x5, x6, x7) → Cond_1497_0_main_LE2(x1, x3, x4, x5, x6, x7)
Cond_1497_0_main_LE1(x1, x2, x3, x4, x5, x6, x7) → Cond_1497_0_main_LE1(x1, x3, x4, x5, x6, x7)
Cond_1497_0_main_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_1497_0_main_LE(x1, x3, x4, x5, x6, x7)
Cond_1482_0_main_Load(x1, x2, x3, x4, x5, x6) → Cond_1482_0_main_Load(x1, x3, x4, x5, x6)

Filtered duplicate args:

1497_0_main_LE(x1, x2, x3, x4, x5) → 1497_0_main_LE(x2, x4, x5)
Cond_1482_0_main_Load1(x1, x2, x3, x4, x5) → Cond_1482_0_main_Load1(x1, x3, x4, x5)
1482_0_main_Load(x1, x2, x3, x4) → 1482_0_main_Load(x2, x3, x4)
Cond_1497_0_main_LE2(x1, x2, x3, x4, x5, x6) → Cond_1497_0_main_LE2(x1, x3, x5, x6)
Cond_1497_0_main_LE1(x1, x2, x3, x4, x5, x6) → Cond_1497_0_main_LE1(x1, x3, x5, x6)
Cond_1497_0_main_LE(x1, x2, x3, x4, x5, x6) → Cond_1497_0_main_LE(x1, x3, x5, x6)
Cond_1482_0_main_Load(x1, x2, x3, x4, x5) → Cond_1482_0_main_Load(x1, 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.

(4) Obligation:

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

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])
(2): 1497_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(3): COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(4): 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(x2[4] >= x0[4] && x2[4] < x1[4], x1[4], x0[4], x2[4])
(5): COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(x1[5] + -1, x2[5], x0[5])
(6): 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(x2[6] < x0[6], x1[6], x0[6], x2[6])
(7): COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], x0[7] + -1)
(8): 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])

(0) -> (1), if ((x2[0] < x0[0] →^* TRUE)∧(x1[0] →^* x1[1])∧(x2[0] →^* x2[1])∧(x0[0] →^* x0[1]))

(1) -> (2), if ((x1[1] →^* x1[2])∧(x0[1] →^* x0[2])∧(x2[1] →^* x2[2]))

(1) -> (4), if ((x1[1] →^* x1[4])∧(x0[1] →^* x0[4])∧(x2[1] →^* x2[4]))

(1) -> (6), if ((x1[1] →^* x1[6])∧(x0[1] →^* x0[6])∧(x2[1] →^* x2[6]))

(2) -> (3), if ((x2[2] >= x1[2] && x2[2] >= x0[2] →^* TRUE)∧(x1[2] →^* x1[3])∧(x0[2] →^* x0[3])∧(x2[2] →^* x2[3]))

(3) -> (0), if ((x1[3] →^* x1[0])∧(x2[3] →^* x2[0])∧(x0[3] →^* x0[0]))

(3) -> (8), if ((x1[3] →^* x1[8])∧(x2[3] →^* x2[8])∧(x0[3] →^* x0[8]))

(4) -> (5), if ((x2[4] >= x0[4] && x2[4] < x1[4] →^* TRUE)∧(x1[4] →^* x1[5])∧(x0[4] →^* x0[5])∧(x2[4] →^* x2[5]))

(5) -> (0), if ((x1[5] + -1 →^* x1[0])∧(x2[5] →^* x2[0])∧(x0[5] →^* x0[0]))

(5) -> (8), if ((x1[5] + -1 →^* x1[8])∧(x2[5] →^* x2[8])∧(x0[5] →^* x0[8]))

(6) -> (7), if ((x2[6] < x0[6] →^* TRUE)∧(x1[6] →^* x1[7])∧(x0[6] →^* x0[7])∧(x2[6] →^* x2[7]))

(7) -> (0), if ((x1[7] →^* x1[0])∧(x2[7] →^* x2[0])∧(x0[7] + -1 →^* x0[0]))

(7) -> (8), if ((x1[7] →^* x1[8])∧(x2[7] →^* x2[8])∧(x0[7] + -1 →^* x0[8]))

(8) -> (1), if ((x2[8] >= x0[8] && x2[8] < x1[8] →^* TRUE)∧(x1[8] →^* x1[1])∧(x2[8] →^* x2[1])∧(x0[8] →^* x0[1]))

The set Q is empty.

(5) IDPNonInfProof (SOUND transformation)

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

For Pair 1482_0_MAIN_LOAD(x1, x2, x0) → COND_1482_0_MAIN_LOAD(<(x2, x0), x1, x2, x0) the following chains were created:

We consider the chain 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:
(1)    (<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧1482_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (<(x2[0], x0[0])=TRUE ⇒ 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧1482_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] + [bni_34]x1[0] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] + [bni_34]x1[0] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] + [bni_34]x1[0] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(8)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

(9)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)

For Pair COND_1482_0_MAIN_LOAD(TRUE, x1, x2, x0) → 1497_0_MAIN_LE(x1, x0, x2) the following chains were created:

We consider the chain COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]), 1497_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:
(10)    (x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2] ⇒ COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (10) using rule (IV) which results in the following new constraint:
(11)    (COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(12)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (12) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(13)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (13) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(14)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (14) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(15)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
We consider the chain COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]), 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) which results in the following constraint:
(16)    (x1[1]=x1[4]∧x0[1]=x0[4]∧x2[1]=x2[4] ⇒ COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (16) using rule (IV) which results in the following new constraint:
(17)    (COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(18)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(19)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(20)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (20) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(21)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
We consider the chain COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]), 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]) which results in the following constraint:
(22)    (x1[1]=x1[6]∧x0[1]=x0[6]∧x2[1]=x2[6] ⇒ COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (22) using rule (IV) which results in the following new constraint:
(23)    (COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥1497_0_MAIN_LE(x1[1], x0[1], x2[1])∧(U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (23) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(24)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(25)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (25) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(26)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_37] ≥ 0)

We simplified constraint (26) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(27)    ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)

For Pair 1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE(&&(>=(x2, x1), >=(x2, x0)), x1, x0, x2) the following chains were created:

We consider the chain 1497_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3]) which results in the following constraint:
(28)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3] ⇒ 1497_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧1497_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

We simplified constraint (28) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(29)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ 1497_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧1497_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

We simplified constraint (29) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(30)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] + [bni_38]x1[2] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(31)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] + [bni_38]x1[2] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(32)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] + [bni_38]x1[2] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(33)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(35)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)

(36)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)

For Pair COND_1497_0_MAIN_LE(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(x1, x2, x0) the following chains were created:

We consider the chain COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:
(37)    (x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0] ⇒ COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (37) using rule (IV) which results in the following new constraint:
(38)    (COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(42)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
We consider the chain COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:
(43)    (x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8] ⇒ COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (43) using rule (IV) which results in the following new constraint:
(44)    (COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_41] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)

For Pair 1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE1(&&(>=(x2, x0), <(x2, x1)), x1, x0, x2) the following chains were created:

We consider the chain 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]) which results in the following constraint:
(49)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5] ⇒ 1497_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧1497_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))

We simplified constraint (49) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(50)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ 1497_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧1497_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))

We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(51)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x2[4] + [bni_42]x1[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x2[4] + [bni_42]x1[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x2[4] + [bni_42]x1[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(54)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x0[4] + [(-1)bni_42]x2[4] + [bni_42]x1[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(55)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(56)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

(57)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

For Pair COND_1497_0_MAIN_LE1(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(+(x1, -1), x2, x0) the following chains were created:

We consider the chain 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:
(58)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[0]∧x2[5]=x2[0]∧x0[5]=x0[0] ⇒ COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))

We simplified constraint (58) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(59)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_1497_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_1497_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥1482_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))

We simplified constraint (59) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(60)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(61)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(62)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(63)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x0[4] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(64)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(65)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

(66)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)
We consider the chain 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:
(67)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[8]∧x2[5]=x2[8]∧x0[5]=x0[8] ⇒ COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))

We simplified constraint (67) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(68)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_1497_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_1497_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥1482_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(69)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(71)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(72)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x0[4] + [(-1)bni_44]x2[4] + [bni_44]x1[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (72) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(73)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (73) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(74)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

(75)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)

For Pair 1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE2(<(x2, x0), x1, x0, x2) the following chains were created:

We consider the chain 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)) which results in the following constraint:
(76)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7] ⇒ 1497_0_MAIN_LE(x1[6], x0[6], x2[6])≥NonInfC∧1497_0_MAIN_LE(x1[6], x0[6], x2[6])≥COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])∧(U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))

We simplified constraint (76) using rule (IV) which results in the following new constraint:
(77)    (<(x2[6], x0[6])=TRUE ⇒ 1497_0_MAIN_LE(x1[6], x0[6], x2[6])≥NonInfC∧1497_0_MAIN_LE(x1[6], x0[6], x2[6])≥COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])∧(U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(78)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] + [bni_46]x1[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (78) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(79)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] + [bni_46]x1[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (79) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(80)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] + [bni_46]x1[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (80) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(81)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(82)    (x0[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (82) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(83)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

(84)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

For Pair COND_1497_0_MAIN_LE2(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(x1, x2, +(x0, -1)) the following chains were created:

We consider the chain 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)), 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:
(85)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7]∧x1[7]=x1[0]∧x2[7]=x2[0]∧+(x0[7], -1)=x0[0] ⇒ COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥NonInfC∧COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))∧(U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

We simplified constraint (85) using rules (III), (IV) which results in the following new constraint:
(86)    (<(x2[6], x0[6])=TRUE ⇒ COND_1497_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥NonInfC∧COND_1497_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥1482_0_MAIN_LOAD(x1[6], x2[6], +(x0[6], -1))∧(U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

We simplified constraint (86) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(87)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(88)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(89)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(90)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (90) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(91)    (x0[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (91) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(92)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

(93)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
We consider the chain 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)), 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:
(94)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7]∧x1[7]=x1[8]∧x2[7]=x2[8]∧+(x0[7], -1)=x0[8] ⇒ COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥NonInfC∧COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))∧(U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

We simplified constraint (94) using rules (III), (IV) which results in the following new constraint:
(95)    (<(x2[6], x0[6])=TRUE ⇒ COND_1497_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥NonInfC∧COND_1497_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥1482_0_MAIN_LOAD(x1[6], x2[6], +(x0[6], -1))∧(U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

We simplified constraint (95) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(96)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (96) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(97)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (97) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(98)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] + [bni_48]x1[6] ≥ 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (98) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(99)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (99) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(100)    (x0[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (100) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(101)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

(102)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

For Pair 1482_0_MAIN_LOAD(x1, x2, x0) → COND_1482_0_MAIN_LOAD(&&(>=(x2, x0), <(x2, x1)), x1, x2, x0) the following chains were created:

We consider the chain 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:
(103)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[1]∧x2[8]=x2[1]∧x0[8]=x0[1] ⇒ 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧1482_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))

We simplified constraint (103) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(104)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE ⇒ 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧1482_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))

We simplified constraint (104) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(105)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x2[8] + [bni_50]x1[8] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(106)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x2[8] + [bni_50]x1[8] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (106) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(107)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x2[8] + [bni_50]x1[8] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (107) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(108)    (x2[8] ≥ 0∧x1[8] + [-1] + [-1]x0[8] + [-1]x2[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x0[8] + [(-1)bni_50]x2[8] + [bni_50]x1[8] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (108) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(109)    (x2[8] ≥ 0∧x0[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_50] + [bni_50]x0[8] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (109) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(110)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_50] + [bni_50]x0[8] ≥ 0∧[(-1)bso_51] ≥ 0)

(111)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_50] + [bni_50]x0[8] ≥ 0∧[(-1)bso_51] ≥ 0)

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

1482_0_MAIN_LOAD(x1, x2, x0) → COND_1482_0_MAIN_LOAD(<(x2, x0), x1, x2, x0)
- (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)
- (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[bni_34] = 0∧[(-1)bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[0] ≥ 0∧0 = 0∧[(-1)bso_35] ≥ 0)
COND_1482_0_MAIN_LOAD(TRUE, x1, x2, x0) → 1497_0_MAIN_LE(x1, x0, x2)
- ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
- ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
- ((U^Increasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE(&&(>=(x2, x1), >=(x2, x0)), x1, x0, x2)
- (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)
- (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x2[2] ≥ 0∧[(-1)bso_39] ≥ 0)
COND_1497_0_MAIN_LE(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(x1, x2, x0)
- ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
- ((U^Increasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE1(&&(>=(x2, x0), <(x2, x1)), x1, x0, x2)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)
COND_1497_0_MAIN_LE1(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(+(x1, -1), x2, x0)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)
- (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[4] ≥ 0∧[1 + (-1)bso_45] ≥ 0)
1497_0_MAIN_LE(x1, x0, x2) → COND_1497_0_MAIN_LE2(<(x2, x0), x1, x0, x2)
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x2[6] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)
COND_1497_0_MAIN_LE2(TRUE, x1, x0, x2) → 1482_0_MAIN_LOAD(x1, x2, +(x0, -1))
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
- (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (U^Increasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[bni_48] = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [bni_48]x2[6] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
1482_0_MAIN_LOAD(x1, x2, x0) → COND_1482_0_MAIN_LOAD(&&(>=(x2, x0), <(x2, x1)), x1, x2, x0)
- (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_50] + [bni_50]x0[8] ≥ 0∧[(-1)bso_51] ≥ 0)
- (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_50] + [bni_50]x0[8] ≥ 0∧[(-1)bso_51] ≥ 0)

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0
POL(FALSE) = [3]
POL(1482_0_MAIN_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₂ + x₁
POL(COND_1482_0_MAIN_LOAD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + x₂
POL(<(x₁, x₂)) = [-1]
POL(1497_0_MAIN_LE(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₁
POL(COND_1497_0_MAIN_LE(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(COND_1497_0_MAIN_LE1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(COND_1497_0_MAIN_LE2(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₂

The following pairs are in P_>:

COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])

The following pairs are in P_bound:

1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])
COND_1497_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 1482_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])
1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])

The following pairs are in P_≥:

1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])
COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])
1497_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])
1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])
COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))
1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])

At least the following rules have been oriented under context sensitive arithmetic replacement:

FALSE¹ → &&(FALSE, FALSE)¹

(6) 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:
(0): 1482_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])
(2): 1497_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(3): COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(4): 1497_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_1497_0_MAIN_LE1(x2[4] >= x0[4] && x2[4] < x1[4], x1[4], x0[4], x2[4])
(6): 1497_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_1497_0_MAIN_LE2(x2[6] < x0[6], x1[6], x0[6], x2[6])
(7): COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], x0[7] + -1)
(8): 1482_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_1482_0_MAIN_LOAD(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])