### (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)
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_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)

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:
(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:

We simplified constraint (1) using rule (IV) which results in the following new constraint:

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

(3)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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]))=TRUEx1[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])∧(UIncreasing(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])=TRUE1497_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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]))=TRUEx1[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])∧(UIncreasing(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])=TRUE1497_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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]))=TRUEx1[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])∧(UIncreasing(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])=TRUECOND_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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]))=TRUEx1[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])∧(UIncreasing(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])=TRUECOND_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])=TRUEx1[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])∧(UIncreasing(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])=TRUE1497_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])=TRUEx1[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))∧(UIncreasing(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])=TRUECOND_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))∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])=TRUEx1[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))∧(UIncreasing(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])=TRUECOND_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))∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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:

We simplified constraint (103) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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.
• (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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)
• ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
• ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_37] ≥ 0)
• ((UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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)
• ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_41] ≥ 0)
• ((UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 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) = [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 Pbound:

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])

The following pairs are in P:

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))

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:
(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])

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

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

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

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

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

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

(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]))

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

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

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

The set Q is empty.

### (7) IDependencyGraphProof (EQUIVALENT transformation)

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

### (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:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(7): COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], x0[7] + -1)
(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])
(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])
(3): COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(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])
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])

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

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

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

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

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

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

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

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

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

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

The set Q is empty.

### (9) IDPNonInfProof (SOUND transformation)

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

For Pair COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -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:

(1)    (<(x2[6], x0[6])=TRUEx1[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))∧(UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

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

(2)    (<(x2[6], x0[6])=TRUECOND_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))∧(UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

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

(3)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(4)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(5)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(6)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

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

(7)    (x0[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

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

(8)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

(9)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 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:

(10)    (<(x2[6], x0[6])=TRUEx1[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))∧(UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

We simplified constraint (10) using rules (III), (IV) which results in the following new constraint:

(11)    (<(x2[6], x0[6])=TRUECOND_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))∧(UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))

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

(12)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(13)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(14)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(15)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x2[6] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

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

(16)    (x0[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

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

(17)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

(18)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

For Pair 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]) 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:

(19)    (<(x2[6], x0[6])=TRUEx1[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])∧(UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))

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

(20)    (<(x2[6], x0[6])=TRUE1497_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])∧(UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))

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

(21)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x2[6] + [bni_31]x0[6] ≥ 0∧[(-1)bso_32] ≥ 0)

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

(22)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x2[6] + [bni_31]x0[6] ≥ 0∧[(-1)bso_32] ≥ 0)

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

(23)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x2[6] + [bni_31]x0[6] ≥ 0∧[(-1)bso_32] ≥ 0)

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

(24)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x2[6] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)

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

(25)    (x0[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_31] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)

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

(26)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_31] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)

(27)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_31] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)

For Pair 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 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:

We simplified constraint (28) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(30)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x0[8] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(31)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x0[8] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(32)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]x0[8] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(33)    (x2[8] ≥ 0∧x1[8] + [-1] + [-1]x0[8] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(34)    (x2[8] ≥ 0∧x0[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(35)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

(36)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

For Pair COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3]) 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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(40)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

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

(41)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

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

(42)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 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])∧(UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

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

(46)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

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

(47)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bso_36] ≥ 0)

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

(48)    ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

For Pair 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]) 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:

(49)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[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])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

We simplified constraint (49) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(50)    (>=(x2[2], x1[2])=TRUE>=(x2[2], x0[2])=TRUE1497_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])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

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

(51)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x2[2] + [bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(52)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x2[2] + [bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(53)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x2[2] + [bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(54)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x1[2] + [(-1)bni_37]x2[2] + [bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(55)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(56)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

(57)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

For Pair COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]) 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:

(58)    (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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

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

(59)    (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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

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

(60)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

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

(61)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

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

(62)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

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

(63)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 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:

(64)    (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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

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

(65)    (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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(66)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

We simplified constraint (66) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(67)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

We simplified constraint (67) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(68)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bso_40] ≥ 0)

We simplified constraint (68) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(69)    ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)

For Pair 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]) 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:

We simplified constraint (70) using rule (IV) which results in the following new constraint:

We simplified constraint (71) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(72)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x0[0] + [(-1)bni_41]x2[0] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (72) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(73)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x0[0] + [(-1)bni_41]x2[0] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (73) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(74)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x0[0] + [(-1)bni_41]x2[0] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (74) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(75)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x0[0] + [(-1)bni_41]x2[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (75) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(76)    (x0[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]x0[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (76) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(77)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]x0[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

(78)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]x0[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_29] + [bni_29]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_30] ≥ 0)

• 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])
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_31] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)
• (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_31] + [bni_31]x0[6] ≥ 0∧0 = 0∧[(-1)bso_32] ≥ 0)

• 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])
• (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)
• (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] ≥ 0∧[(-1)bso_34] ≥ 0)

• COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
• ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)
• ((UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

• 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])
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] ≥ 0∧[(-1)bso_38] ≥ 0)

• COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])
• ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)
• ((UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)

• (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]x0[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)
• (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]x0[0] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

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

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

The following pairs are in P>:

COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))

The following pairs are in Pbound:

COND_1497_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 1482_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -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])

The following pairs are in P:

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_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
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_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])

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

TRUE1&&(TRUE, TRUE)1
FALSE1&&(TRUE, FALSE)1
FALSE1&&(FALSE, TRUE)1
FALSE1&&(FALSE, FALSE)1

### (10) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(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])
(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])
(3): COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(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])
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])

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

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

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

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

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

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

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

The set Q is empty.

### (11) IDependencyGraphProof (EQUIVALENT transformation)

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

### (12) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(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])
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[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])

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

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

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

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

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

The set Q is empty.

### (13) 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[0], x2[0], x0[0]) → COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) 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]), 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:

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

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

(3)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_13] + [(2)bni_13]x2[2] + [(-1)bni_13]x0[2] + [(-1)bni_13]x1[2] ≥ 0∧[-1 + (-1)bso_14] ≥ 0)

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

(4)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_13] + [(2)bni_13]x2[2] + [(-1)bni_13]x0[2] + [(-1)bni_13]x1[2] ≥ 0∧[-1 + (-1)bso_14] ≥ 0)

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

(5)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_13] + [(2)bni_13]x2[2] + [(-1)bni_13]x0[2] + [(-1)bni_13]x1[2] ≥ 0∧[-1 + (-1)bso_14] ≥ 0)

We solved constraint (5) using rule (IDP_SMT_SPLIT).

For Pair COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3]) 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]), 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:

(6)    (x1[1]=x1[2]x0[1]=x0[2]x2[1]=x2[2]&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[2]=x1[3]x0[2]=x0[3]x2[2]=x2[3]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])∧(UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (6) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(7)    (>=(x2[2], x1[2])=TRUE>=(x2[2], x0[2])=TRUECOND_1497_0_MAIN_LE(TRUE, x1[2], x0[2], x2[2])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[2], x0[2], x2[2])≥1482_0_MAIN_LOAD(x1[2], x2[2], x0[2])∧(UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

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

(8)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(9)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(10)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(11)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x1[2] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(12)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(13)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(14)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 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[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]), 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:

(15)    (x1[1]=x1[2]x0[1]=x0[2]x2[1]=x2[2]&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[2]=x1[3]x0[2]=x0[3]x2[2]=x2[3]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])∧(UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

We simplified constraint (15) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(16)    (>=(x2[2], x1[2])=TRUE>=(x2[2], x0[2])=TRUECOND_1497_0_MAIN_LE(TRUE, x1[2], x0[2], x2[2])≥NonInfC∧COND_1497_0_MAIN_LE(TRUE, x1[2], x0[2], x2[2])≥1482_0_MAIN_LOAD(x1[2], x2[2], x0[2])∧(UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))

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

(17)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(18)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(19)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] + [(-1)bni_15]x1[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(20)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x1[2] + [(2)bni_15]x2[2] + [(-1)bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(21)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(22)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(23)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

For Pair 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]) 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]), 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:

(24)    (<(x2[0], x0[0])=TRUEx1[0]=x1[1]x2[0]=x2[1]x0[0]=x0[1]x1[1]=x1[2]x0[1]=x0[2]x2[1]=x2[2]&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[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])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

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

(25)    (<(x2[0], x0[0])=TRUE>=(x2[0], x1[2])=TRUE>=(x2[0], x0[0])=TRUE1497_0_MAIN_LE(x1[2], x0[0], x2[0])≥NonInfC∧1497_0_MAIN_LE(x1[2], x0[0], x2[0])≥COND_1497_0_MAIN_LE(&&(>=(x2[0], x1[2]), >=(x2[0], x0[0])), x1[2], x0[0], x2[0])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

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

(26)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[0] + [(-1)bni_17]x0[0] + [(-1)bni_17]x1[2] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

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

(27)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[0] + [(-1)bni_17]x0[0] + [(-1)bni_17]x1[2] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

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

(28)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[0] + [(-1)bni_17]x0[0] + [(-1)bni_17]x1[2] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

We solved constraint (28) using rule (IDP_SMT_SPLIT).
• 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]), 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:

(29)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUEx1[8]=x1[1]x2[8]=x2[1]x0[8]=x0[1]x1[1]=x1[2]x0[1]=x0[2]x2[1]=x2[2]&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[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])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

We simplified constraint (29) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(30)    (>=(x2[8], x0[8])=TRUE<(x2[8], x1[8])=TRUE>=(x2[8], x1[8])=TRUE1497_0_MAIN_LE(x1[8], x0[8], x2[8])≥NonInfC∧1497_0_MAIN_LE(x1[8], x0[8], x2[8])≥COND_1497_0_MAIN_LE(&&(>=(x2[8], x1[8]), >=(x2[8], x0[8])), x1[8], x0[8], x2[8])∧(UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))

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

(31)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[8] + [(-1)bni_17]x0[8] + [(-1)bni_17]x1[8] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

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

(32)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[8] + [(-1)bni_17]x0[8] + [(-1)bni_17]x1[8] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

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

(33)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]x2[8] + [(-1)bni_17]x0[8] + [(-1)bni_17]x1[8] ≥ 0∧[-2 + (-1)bso_18] ≥ 0)

We solved constraint (33) using rule (IDP_SMT_SPLIT).

For Pair COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1]) 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]), 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:

(34)    (x1[3]=x1[0]x2[3]=x2[0]x0[3]=x0[0]<(x2[0], x0[0])=TRUEx1[0]=x1[1]x2[0]=x2[1]x0[0]=x0[1]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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (34) using rules (III), (IV) which results in the following new constraint:

(35)    (<(x2[0], x0[0])=TRUECOND_1482_0_MAIN_LOAD(TRUE, x1[3], x2[0], x0[0])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[3], x2[0], x0[0])≥1497_0_MAIN_LE(x1[3], x0[0], x2[0])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

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

(36)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[0] + [(-1)bni_19]x0[0] + [(-1)bni_19]x1[3] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(37)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[0] + [(-1)bni_19]x0[0] + [(-1)bni_19]x1[3] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(38)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[0] + [(-1)bni_19]x0[0] + [(-1)bni_19]x1[3] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(39)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 0)

We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(40)    (x0[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[(-1)Bound*bni_19] + [bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 0)

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

(41)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[(-1)Bound*bni_19] + [(-1)bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 0)

(42)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[(-1)Bound*bni_19] + [bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 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]), 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:

(43)    (x1[3]=x1[8]x2[3]=x2[8]x0[3]=x0[8]&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUEx1[8]=x1[1]x2[8]=x2[1]x0[8]=x0[1]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])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

We simplified constraint (43) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

(44)    (>=(x2[8], x0[8])=TRUE<(x2[8], x1[8])=TRUECOND_1482_0_MAIN_LOAD(TRUE, x1[8], x2[8], x0[8])≥NonInfC∧COND_1482_0_MAIN_LOAD(TRUE, x1[8], x2[8], x0[8])≥1497_0_MAIN_LE(x1[8], x0[8], x2[8])∧(UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))

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

(45)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[8] + [(-1)bni_19]x0[8] + [(-1)bni_19]x1[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(46)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[8] + [(-1)bni_19]x0[8] + [(-1)bni_19]x1[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(47)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x2[8] + [(-1)bni_19]x0[8] + [(-1)bni_19]x1[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(48)    (x2[8] ≥ 0∧x1[8] + [-1] + [-1]x0[8] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_19 + (-1)Bound*bni_19] + [bni_19]x0[8] + [(2)bni_19]x2[8] + [(-1)bni_19]x1[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(49)    (x2[8] ≥ 0∧x0[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)Bound*bni_19] + [bni_19]x2[8] + [(-1)bni_19]x0[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

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

(50)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)Bound*bni_19] + [bni_19]x2[8] + [(-1)bni_19]x0[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

(51)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)Bound*bni_19] + [bni_19]x2[8] + [(-1)bni_19]x0[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

For Pair 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 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]), 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:

(52)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUEx1[2]=x1[3]x0[2]=x0[3]x2[2]=x2[3]x1[3]=x1[8]x2[3]=x2[8]x0[3]=x0[8]&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUEx1[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])∧(UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))

We simplified constraint (52) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(54)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_21] + [(2)bni_21]x2[2] + [(-1)bni_21]x0[2] + [(-1)bni_21]x1[2] ≥ 0∧[-1 + (-1)bso_22] ≥ 0)

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

(55)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_21] + [(2)bni_21]x2[2] + [(-1)bni_21]x0[2] + [(-1)bni_21]x1[2] ≥ 0∧[-1 + (-1)bso_22] ≥ 0)

We simplified constraint (55) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(56)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_1482_0_MAIN_LOAD(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)Bound*bni_21] + [(2)bni_21]x2[2] + [(-1)bni_21]x0[2] + [(-1)bni_21]x1[2] ≥ 0∧[-1 + (-1)bso_22] ≥ 0)

We solved constraint (56) using rule (IDP_SMT_SPLIT).

To summarize, we get the following constraints P for the following pairs.

• COND_1497_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
• (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(1482_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[2] + [bni_15]x0[2] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

• 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_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])
• (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[(-1)Bound*bni_19] + [(-1)bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 0)
• (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_19] = 0∧[(-1)Bound*bni_19] + [bni_19]x2[0] + [(-1)bni_19]x0[0] ≥ 0∧0 = 0∧[2 + (-1)bso_20] ≥ 0)
• (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)Bound*bni_19] + [bni_19]x2[8] + [(-1)bni_19]x0[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)
• (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(1497_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)Bound*bni_19] + [bni_19]x2[8] + [(-1)bni_19]x0[8] ≥ 0∧[2 + (-1)bso_20] ≥ 0)

• 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 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(1482_0_MAIN_LOAD(x1, x2, x3)) = [2]x2 + [-1]x3 + [-1]x1
POL(COND_1482_0_MAIN_LOAD(x1, x2, x3, x4)) = [1] + [2]x3 + [-1]x4 + [-1]x2
POL(<(x1, x2)) = [-1]
POL(COND_1497_0_MAIN_LE(x1, x2, x3, x4)) = [1] + [2]x4 + [-1]x3 + [-1]x2
POL(1497_0_MAIN_LE(x1, x2, x3)) = [-1] + [2]x3 + [-1]x2 + [-1]x1
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]

The following pairs are in P>:

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[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_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])

The following pairs are in Pbound:

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[2], x0[2], x2[2]) → COND_1497_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])

The following pairs are in P:
none

There are no usable rules.

### (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:
none

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_1482_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 1497_0_MAIN_LE(x1[1], x0[1], x2[1])

The set Q is empty.

### (15) IDependencyGraphProof (EQUIVALENT transformation)

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