### (0) Obligation:

JBC Problem based on JBC Program:
`No human-readable program information known.`

Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: Test10

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 157 nodes with 1 SCC.

### (3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

### (4) Obligation:

ITRS 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 TRS R consists of the following rules:
Load1100(i5, i7, i7, 0) → Load83(i5, i7 + 1)
Load949(i5, i7, i7, i7, i7, 0) → Load1100(i5, i7, i7, i7)
Load1100(i5, i7, i7, i696) → Cond_Load1100(i696 > 0, i5, i7, i7, i696)
Cond_Load1100(TRUE, i5, i7, i7, i696) → Load1100(i5, i7, i7, i696 - 1)
Load768(i5, i7, i7, i7, i7, 0) → Load949(i5, i7, i7, i7, i7, i7)
Load949(i5, i7, i7, i7, i7, i605) → Cond_Load949(i605 > 0, i5, i7, i7, i7, i7, i605)
Cond_Load949(TRUE, i5, i7, i7, i7, i7, i605) → Load949(i5, i7, i7, i7, i7, i605 - 1)
Load608(i5, i7, i7, i7, i7, 0) → Load768(i5, i7, i7, i7, i7, i7)
Load768(i5, i7, i7, i7, i7, i436) → Cond_Load768(i436 > 0, i5, i7, i7, i7, i7, i436)
Cond_Load768(TRUE, i5, i7, i7, i7, i7, i436) → Load768(i5, i7, i7, i7, i7, i436 - 1)
Load484(i5, i7, i7, i7, i7, 0) → Load608(i5, i7, i7, i7, i7, i7)
Load608(i5, i7, i7, i7, i7, i296) → Cond_Load608(i296 > 0, i5, i7, i7, i7, i7, i296)
Cond_Load608(TRUE, i5, i7, i7, i7, i7, i296) → Load608(i5, i7, i7, i7, i7, i296 - 1)
Load363(i5, i7, i7, i7, i7, 0) → Load484(i5, i7, i7, i7, i7, i7)
Load484(i5, i7, i7, i7, i7, i187) → Cond_Load484(i187 > 0, i5, i7, i7, i7, i7, i187)
Cond_Load484(TRUE, i5, i7, i7, i7, i7, i187) → Load484(i5, i7, i7, i7, i7, i187 - 1)
Load258(i5, i7, i7, i7, i7, 0) → Load363(i5, i7, i7, i7, i7, i7)
Load363(i5, i7, i7, i7, i7, i104) → Cond_Load363(i104 > 0, i5, i7, i7, i7, i7, i104)
Cond_Load363(TRUE, i5, i7, i7, i7, i7, i104) → Load363(i5, i7, i7, i7, i7, i104 - 1)
Load175(i5, i7, i7, i7, i7, 0) → Load258(i5, i7, i7, i7, i7, i7)
Load258(i5, i7, i7, i7, i7, i49) → Cond_Load258(i49 > 0, i5, i7, i7, i7, i7, i49)
Cond_Load258(TRUE, i5, i7, i7, i7, i7, i49) → Load258(i5, i7, i7, i7, i7, i49 - 1)
Load83(i5, i7) → Cond_Load83(i7 > 0 && i7 < 100, i5, i7)
Cond_Load83(TRUE, i5, i7) → Load175(i5, i7, i7, i7, i7, i7)
Load55(i5) → Cond_Load55(i5 > 0 && i5 < 100, i5)
Cond_Load55(TRUE, i5) → Load175(i5, i5, i5, i5, i5, i5)
Load175(i5, i7, i7, i7, i7, i20) → Cond_Load175(i20 > 0, i5, i7, i7, i7, i7, i20)
Cond_Load175(TRUE, i5, i7, i7, i7, i7, i20) → Load175(i5, i7, i7, i7, i7, i20 - 1)
Load83(i5, i7) → Cond_Load831(i7 >= 100 && i5 > 0, i5, i7)
Cond_Load831(TRUE, i5, i7) → Load55(i5 - 1)
The set Q consists of the following terms:
Load1100(x0, x1, x1, x2)
Cond_Load1100(TRUE, x0, x1, x1, x2)
Load949(x0, x1, x1, x1, x1, x2)
Cond_Load949(TRUE, x0, x1, x1, x1, x1, x2)
Load768(x0, x1, x1, x1, x1, x2)
Cond_Load768(TRUE, x0, x1, x1, x1, x1, x2)
Load608(x0, x1, x1, x1, x1, x2)
Cond_Load608(TRUE, x0, x1, x1, x1, x1, x2)
Load484(x0, x1, x1, x1, x1, x2)
Cond_Load484(TRUE, x0, x1, x1, x1, x1, x2)
Load363(x0, x1, x1, x1, x1, x2)
Cond_Load363(TRUE, x0, x1, x1, x1, x1, x2)
Load258(x0, x1, x1, x1, x1, x2)
Cond_Load258(TRUE, x0, x1, x1, x1, x1, x2)
Load175(x0, x1, x1, x1, x1, x2)
Cond_Load175(TRUE, x0, x1, x1, x1, x1, x2)

### (5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

Some arguments are removed because they only appear as duplicates.
We removed arguments according to the following replacements:

Load175(x1, x2, x3, x4, x5, x6) → Load175(x1, x5, x6)
Cond_Load175(x1, x2, x3, x4, x5, x6, x7) → Cond_Load175(x1, x2, x6, x7)
Load258(x1, x2, x3, x4, x5, x6) → Load258(x1, x5, x6)
Cond_Load258(x1, x2, x3, x4, x5, x6, x7) → Cond_Load258(x1, x2, x6, x7)
Load363(x1, x2, x3, x4, x5, x6) → Load363(x1, x5, x6)
Cond_Load363(x1, x2, x3, x4, x5, x6, x7) → Cond_Load363(x1, x2, x6, x7)
Load484(x1, x2, x3, x4, x5, x6) → Load484(x1, x5, x6)
Cond_Load484(x1, x2, x3, x4, x5, x6, x7) → Cond_Load484(x1, x2, x6, x7)
Load608(x1, x2, x3, x4, x5, x6) → Load608(x1, x5, x6)
Cond_Load608(x1, x2, x3, x4, x5, x6, x7) → Cond_Load608(x1, x2, x6, x7)
Load768(x1, x2, x3, x4, x5, x6) → Load768(x1, x5, x6)
Cond_Load768(x1, x2, x3, x4, x5, x6, x7) → Cond_Load768(x1, x2, x6, x7)
Load949(x1, x2, x3, x4, x5, x6) → Load949(x1, x5, x6)
Cond_Load949(x1, x2, x3, x4, x5, x6, x7) → Cond_Load949(x1, x2, x6, x7)
Load1100(x1, x2, x3, x4) → Load1100(x1, x3, x4)
Cond_Load1100(x1, x2, x3, x4, x5) → Cond_Load1100(x1, x2, x4, x5)

### (6) Obligation:

ITRS 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 TRS R consists of the following rules:
Load1100(i5, i7, 0) → Load83(i5, i7 + 1)
Load949(i5, i7, 0) → Load1100(i5, i7, i7)
Load1100(i5, i7, i696) → Cond_Load1100(i696 > 0, i5, i7, i696)
Cond_Load1100(TRUE, i5, i7, i696) → Load1100(i5, i7, i696 - 1)
Load768(i5, i7, 0) → Load949(i5, i7, i7)
Load949(i5, i7, i605) → Cond_Load949(i605 > 0, i5, i7, i605)
Cond_Load949(TRUE, i5, i7, i605) → Load949(i5, i7, i605 - 1)
Load608(i5, i7, 0) → Load768(i5, i7, i7)
Load768(i5, i7, i436) → Cond_Load768(i436 > 0, i5, i7, i436)
Cond_Load768(TRUE, i5, i7, i436) → Load768(i5, i7, i436 - 1)
Load484(i5, i7, 0) → Load608(i5, i7, i7)
Load608(i5, i7, i296) → Cond_Load608(i296 > 0, i5, i7, i296)
Cond_Load608(TRUE, i5, i7, i296) → Load608(i5, i7, i296 - 1)
Load363(i5, i7, 0) → Load484(i5, i7, i7)
Load484(i5, i7, i187) → Cond_Load484(i187 > 0, i5, i7, i187)
Cond_Load484(TRUE, i5, i7, i187) → Load484(i5, i7, i187 - 1)
Load258(i5, i7, 0) → Load363(i5, i7, i7)
Load363(i5, i7, i104) → Cond_Load363(i104 > 0, i5, i7, i104)
Cond_Load363(TRUE, i5, i7, i104) → Load363(i5, i7, i104 - 1)
Load175(i5, i7, 0) → Load258(i5, i7, i7)
Load258(i5, i7, i49) → Cond_Load258(i49 > 0, i5, i7, i49)
Cond_Load258(TRUE, i5, i7, i49) → Load258(i5, i7, i49 - 1)
Load83(i5, i7) → Cond_Load83(i7 > 0 && i7 < 100, i5, i7)
Cond_Load83(TRUE, i5, i7) → Load175(i5, i7, i7)
Load55(i5) → Cond_Load55(i5 > 0 && i5 < 100, i5)
Load175(i5, i7, i20) → Cond_Load175(i20 > 0, i5, i7, i20)
Cond_Load175(TRUE, i5, i7, i20) → Load175(i5, i7, i20 - 1)
Load83(i5, i7) → Cond_Load831(i7 >= 100 && i5 > 0, i5, i7)
Cond_Load831(TRUE, i5, i7) → Load55(i5 - 1)
The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (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

The ITRS R consists of the following rules:
Load1100(i5, i7, 0) → Load83(i5, i7 + 1)
Load949(i5, i7, 0) → Load1100(i5, i7, i7)
Load1100(i5, i7, i696) → Cond_Load1100(i696 > 0, i5, i7, i696)
Cond_Load1100(TRUE, i5, i7, i696) → Load1100(i5, i7, i696 - 1)
Load768(i5, i7, 0) → Load949(i5, i7, i7)
Load949(i5, i7, i605) → Cond_Load949(i605 > 0, i5, i7, i605)
Cond_Load949(TRUE, i5, i7, i605) → Load949(i5, i7, i605 - 1)
Load608(i5, i7, 0) → Load768(i5, i7, i7)
Load768(i5, i7, i436) → Cond_Load768(i436 > 0, i5, i7, i436)
Cond_Load768(TRUE, i5, i7, i436) → Load768(i5, i7, i436 - 1)
Load484(i5, i7, 0) → Load608(i5, i7, i7)
Load608(i5, i7, i296) → Cond_Load608(i296 > 0, i5, i7, i296)
Cond_Load608(TRUE, i5, i7, i296) → Load608(i5, i7, i296 - 1)
Load363(i5, i7, 0) → Load484(i5, i7, i7)
Load484(i5, i7, i187) → Cond_Load484(i187 > 0, i5, i7, i187)
Cond_Load484(TRUE, i5, i7, i187) → Load484(i5, i7, i187 - 1)
Load258(i5, i7, 0) → Load363(i5, i7, i7)
Load363(i5, i7, i104) → Cond_Load363(i104 > 0, i5, i7, i104)
Cond_Load363(TRUE, i5, i7, i104) → Load363(i5, i7, i104 - 1)
Load175(i5, i7, 0) → Load258(i5, i7, i7)
Load258(i5, i7, i49) → Cond_Load258(i49 > 0, i5, i7, i49)
Cond_Load258(TRUE, i5, i7, i49) → Load258(i5, i7, i49 - 1)
Load83(i5, i7) → Cond_Load83(i7 > 0 && i7 < 100, i5, i7)
Cond_Load83(TRUE, i5, i7) → Load175(i5, i7, i7)
Load55(i5) → Cond_Load55(i5 > 0 && i5 < 100, i5)
Load175(i5, i7, i20) → Cond_Load175(i20 > 0, i5, i7, i20)
Cond_Load175(TRUE, i5, i7, i20) → Load175(i5, i7, i20 - 1)
Load83(i5, i7) → Cond_Load831(i7 >= 100 && i5 > 0, i5, i7)
Cond_Load831(TRUE, i5, i7) → Load55(i5 - 1)

The integer pair graph contains the following rules and edges:
(0): LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], i7[0] + 1)
(1): LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(4): LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(7): LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(10): LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
(11): LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(i296[11] > 0, i5[11], i7[11], i296[11])
(12): COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], i296[12] - 1)
(13): LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
(14): LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(i187[14] > 0, i5[14], i7[14], i187[14])
(15): COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], i187[15] - 1)
(16): LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
(17): LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(i104[17] > 0, i5[17], i7[17], i104[17])
(18): COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], i104[18] - 1)
(19): LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
(20): LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(i49[20] > 0, i5[20], i7[20], i49[20])
(21): COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], i49[21] - 1)
(22): LOAD83(i5[22], i7[22]) → COND_LOAD83(i7[22] > 0 && i7[22] < 100, i5[22], i7[22])
(23): COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
(24): LOAD55(i5[24]) → COND_LOAD55(i5[24] > 0 && i5[24] < 100, i5[24])
(25): COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25])
(26): LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(i20[26] > 0, i5[26], i7[26], i20[26])
(27): COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], i20[27] - 1)
(28): LOAD83(i5[28], i7[28]) → COND_LOAD831(i7[28] >= 100 && i5[28] > 0, i5[28], i7[28])
(29): COND_LOAD831(TRUE, i5[29], i7[29]) → LOAD55(i5[29] - 1)
(30): LOAD55(i5[30]) → COND_LOAD551(i5[30] >= 100, i5[30])
(31): COND_LOAD551(TRUE, i5[31]) → LOAD55(i5[31] - 1)

(0) -> (22), if ((i5[0]* i5[22])∧(i7[0] + 1* i7[22]))

(0) -> (28), if ((i5[0]* i5[28])∧(i7[0] + 1* i7[28]))

(1) -> (0), if ((i7[1]* 0)∧(i5[1]* i5[0])∧(i7[1]* i7[0]))

(1) -> (2), if ((i5[1]* i5[2])∧(i7[1]* i7[2])∧(i7[1]* i696[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

(3) -> (0), if ((i7[3]* i7[0])∧(i5[3]* i5[0])∧(i696[3] - 1* 0))

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(4) -> (1), if ((i5[4]* i5[1])∧(i7[4]* 0)∧(i7[4]* i7[1]))

(4) -> (5), if ((i7[4]* i7[5])∧(i7[4]* i605[5])∧(i5[4]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

(6) -> (1), if ((i605[6] - 1* 0)∧(i5[6]* i5[1])∧(i7[6]* i7[1]))

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(7) -> (4), if ((i7[7]* 0)∧(i7[7]* i7[4])∧(i5[7]* i5[4]))

(7) -> (8), if ((i5[7]* i5[8])∧(i7[7]* i436[8])∧(i7[7]* i7[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

(9) -> (4), if ((i7[9]* i7[4])∧(i436[9] - 1* 0)∧(i5[9]* i5[4]))

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(10) -> (7), if ((i5[10]* i5[7])∧(i7[10]* i7[7])∧(i7[10]* 0))

(10) -> (11), if ((i7[10]* i7[11])∧(i5[10]* i5[11])∧(i7[10]* i296[11]))

(11) -> (12), if ((i296[11] > 0* TRUE)∧(i7[11]* i7[12])∧(i296[11]* i296[12])∧(i5[11]* i5[12]))

(12) -> (7), if ((i296[12] - 1* 0)∧(i7[12]* i7[7])∧(i5[12]* i5[7]))

(12) -> (11), if ((i296[12] - 1* i296[11])∧(i5[12]* i5[11])∧(i7[12]* i7[11]))

(13) -> (10), if ((i5[13]* i5[10])∧(i7[13]* 0)∧(i7[13]* i7[10]))

(13) -> (14), if ((i7[13]* i187[14])∧(i5[13]* i5[14])∧(i7[13]* i7[14]))

(14) -> (15), if ((i7[14]* i7[15])∧(i5[14]* i5[15])∧(i187[14]* i187[15])∧(i187[14] > 0* TRUE))

(15) -> (10), if ((i7[15]* i7[10])∧(i187[15] - 1* 0)∧(i5[15]* i5[10]))

(15) -> (14), if ((i187[15] - 1* i187[14])∧(i5[15]* i5[14])∧(i7[15]* i7[14]))

(16) -> (13), if ((i7[16]* i7[13])∧(i7[16]* 0)∧(i5[16]* i5[13]))

(16) -> (17), if ((i7[16]* i104[17])∧(i5[16]* i5[17])∧(i7[16]* i7[17]))

(17) -> (18), if ((i7[17]* i7[18])∧(i5[17]* i5[18])∧(i104[17]* i104[18])∧(i104[17] > 0* TRUE))

(18) -> (13), if ((i5[18]* i5[13])∧(i104[18] - 1* 0)∧(i7[18]* i7[13]))

(18) -> (17), if ((i104[18] - 1* i104[17])∧(i5[18]* i5[17])∧(i7[18]* i7[17]))

(19) -> (16), if ((i7[19]* 0)∧(i5[19]* i5[16])∧(i7[19]* i7[16]))

(19) -> (20), if ((i7[19]* i49[20])∧(i7[19]* i7[20])∧(i5[19]* i5[20]))

(20) -> (21), if ((i7[20]* i7[21])∧(i49[20] > 0* TRUE)∧(i5[20]* i5[21])∧(i49[20]* i49[21]))

(21) -> (16), if ((i7[21]* i7[16])∧(i49[21] - 1* 0)∧(i5[21]* i5[16]))

(21) -> (20), if ((i7[21]* i7[20])∧(i49[21] - 1* i49[20])∧(i5[21]* i5[20]))

(22) -> (23), if ((i5[22]* i5[23])∧(i7[22] > 0 && i7[22] < 100* TRUE)∧(i7[22]* i7[23]))

(23) -> (19), if ((i5[23]* i5[19])∧(i7[23]* i7[19])∧(i7[23]* 0))

(23) -> (26), if ((i7[23]* i7[26])∧(i5[23]* i5[26])∧(i7[23]* i20[26]))

(24) -> (25), if ((i5[24] > 0 && i5[24] < 100* TRUE)∧(i5[24]* i5[25]))

(25) -> (19), if ((i5[25]* i5[19])∧(i5[25]* i7[19])∧(i5[25]* 0))

(25) -> (26), if ((i5[25]* i5[26])∧(i5[25]* i7[26])∧(i5[25]* i20[26]))

(26) -> (27), if ((i20[26] > 0* TRUE)∧(i7[26]* i7[27])∧(i20[26]* i20[27])∧(i5[26]* i5[27]))

(27) -> (19), if ((i7[27]* i7[19])∧(i5[27]* i5[19])∧(i20[27] - 1* 0))

(27) -> (26), if ((i20[27] - 1* i20[26])∧(i7[27]* i7[26])∧(i5[27]* i5[26]))

(28) -> (29), if ((i7[28] >= 100 && i5[28] > 0* TRUE)∧(i5[28]* i5[29])∧(i7[28]* i7[29]))

(29) -> (24), if ((i5[29] - 1* i5[24]))

(29) -> (30), if ((i5[29] - 1* i5[30]))

(30) -> (31), if ((i5[30]* i5[31])∧(i5[30] >= 100* TRUE))

(31) -> (24), if ((i5[31] - 1* i5[24]))

(31) -> (30), if ((i5[31] - 1* i5[30]))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (9) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

### (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:
(0): LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], i7[0] + 1)
(1): LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(4): LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(7): LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(10): LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
(11): LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(i296[11] > 0, i5[11], i7[11], i296[11])
(12): COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], i296[12] - 1)
(13): LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
(14): LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(i187[14] > 0, i5[14], i7[14], i187[14])
(15): COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], i187[15] - 1)
(16): LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
(17): LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(i104[17] > 0, i5[17], i7[17], i104[17])
(18): COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], i104[18] - 1)
(19): LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
(20): LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(i49[20] > 0, i5[20], i7[20], i49[20])
(21): COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], i49[21] - 1)
(22): LOAD83(i5[22], i7[22]) → COND_LOAD83(i7[22] > 0 && i7[22] < 100, i5[22], i7[22])
(23): COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
(24): LOAD55(i5[24]) → COND_LOAD55(i5[24] > 0 && i5[24] < 100, i5[24])
(25): COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25])
(26): LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(i20[26] > 0, i5[26], i7[26], i20[26])
(27): COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], i20[27] - 1)
(28): LOAD83(i5[28], i7[28]) → COND_LOAD831(i7[28] >= 100 && i5[28] > 0, i5[28], i7[28])
(29): COND_LOAD831(TRUE, i5[29], i7[29]) → LOAD55(i5[29] - 1)
(30): LOAD55(i5[30]) → COND_LOAD551(i5[30] >= 100, i5[30])
(31): COND_LOAD551(TRUE, i5[31]) → LOAD55(i5[31] - 1)

(0) -> (22), if ((i5[0]* i5[22])∧(i7[0] + 1* i7[22]))

(0) -> (28), if ((i5[0]* i5[28])∧(i7[0] + 1* i7[28]))

(1) -> (0), if ((i7[1]* 0)∧(i5[1]* i5[0])∧(i7[1]* i7[0]))

(1) -> (2), if ((i5[1]* i5[2])∧(i7[1]* i7[2])∧(i7[1]* i696[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

(3) -> (0), if ((i7[3]* i7[0])∧(i5[3]* i5[0])∧(i696[3] - 1* 0))

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(4) -> (1), if ((i5[4]* i5[1])∧(i7[4]* 0)∧(i7[4]* i7[1]))

(4) -> (5), if ((i7[4]* i7[5])∧(i7[4]* i605[5])∧(i5[4]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

(6) -> (1), if ((i605[6] - 1* 0)∧(i5[6]* i5[1])∧(i7[6]* i7[1]))

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(7) -> (4), if ((i7[7]* 0)∧(i7[7]* i7[4])∧(i5[7]* i5[4]))

(7) -> (8), if ((i5[7]* i5[8])∧(i7[7]* i436[8])∧(i7[7]* i7[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

(9) -> (4), if ((i7[9]* i7[4])∧(i436[9] - 1* 0)∧(i5[9]* i5[4]))

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(10) -> (7), if ((i5[10]* i5[7])∧(i7[10]* i7[7])∧(i7[10]* 0))

(10) -> (11), if ((i7[10]* i7[11])∧(i5[10]* i5[11])∧(i7[10]* i296[11]))

(11) -> (12), if ((i296[11] > 0* TRUE)∧(i7[11]* i7[12])∧(i296[11]* i296[12])∧(i5[11]* i5[12]))

(12) -> (7), if ((i296[12] - 1* 0)∧(i7[12]* i7[7])∧(i5[12]* i5[7]))

(12) -> (11), if ((i296[12] - 1* i296[11])∧(i5[12]* i5[11])∧(i7[12]* i7[11]))

(13) -> (10), if ((i5[13]* i5[10])∧(i7[13]* 0)∧(i7[13]* i7[10]))

(13) -> (14), if ((i7[13]* i187[14])∧(i5[13]* i5[14])∧(i7[13]* i7[14]))

(14) -> (15), if ((i7[14]* i7[15])∧(i5[14]* i5[15])∧(i187[14]* i187[15])∧(i187[14] > 0* TRUE))

(15) -> (10), if ((i7[15]* i7[10])∧(i187[15] - 1* 0)∧(i5[15]* i5[10]))

(15) -> (14), if ((i187[15] - 1* i187[14])∧(i5[15]* i5[14])∧(i7[15]* i7[14]))

(16) -> (13), if ((i7[16]* i7[13])∧(i7[16]* 0)∧(i5[16]* i5[13]))

(16) -> (17), if ((i7[16]* i104[17])∧(i5[16]* i5[17])∧(i7[16]* i7[17]))

(17) -> (18), if ((i7[17]* i7[18])∧(i5[17]* i5[18])∧(i104[17]* i104[18])∧(i104[17] > 0* TRUE))

(18) -> (13), if ((i5[18]* i5[13])∧(i104[18] - 1* 0)∧(i7[18]* i7[13]))

(18) -> (17), if ((i104[18] - 1* i104[17])∧(i5[18]* i5[17])∧(i7[18]* i7[17]))

(19) -> (16), if ((i7[19]* 0)∧(i5[19]* i5[16])∧(i7[19]* i7[16]))

(19) -> (20), if ((i7[19]* i49[20])∧(i7[19]* i7[20])∧(i5[19]* i5[20]))

(20) -> (21), if ((i7[20]* i7[21])∧(i49[20] > 0* TRUE)∧(i5[20]* i5[21])∧(i49[20]* i49[21]))

(21) -> (16), if ((i7[21]* i7[16])∧(i49[21] - 1* 0)∧(i5[21]* i5[16]))

(21) -> (20), if ((i7[21]* i7[20])∧(i49[21] - 1* i49[20])∧(i5[21]* i5[20]))

(22) -> (23), if ((i5[22]* i5[23])∧(i7[22] > 0 && i7[22] < 100* TRUE)∧(i7[22]* i7[23]))

(23) -> (19), if ((i5[23]* i5[19])∧(i7[23]* i7[19])∧(i7[23]* 0))

(23) -> (26), if ((i7[23]* i7[26])∧(i5[23]* i5[26])∧(i7[23]* i20[26]))

(24) -> (25), if ((i5[24] > 0 && i5[24] < 100* TRUE)∧(i5[24]* i5[25]))

(25) -> (19), if ((i5[25]* i5[19])∧(i5[25]* i7[19])∧(i5[25]* 0))

(25) -> (26), if ((i5[25]* i5[26])∧(i5[25]* i7[26])∧(i5[25]* i20[26]))

(26) -> (27), if ((i20[26] > 0* TRUE)∧(i7[26]* i7[27])∧(i20[26]* i20[27])∧(i5[26]* i5[27]))

(27) -> (19), if ((i7[27]* i7[19])∧(i5[27]* i5[19])∧(i20[27] - 1* 0))

(27) -> (26), if ((i20[27] - 1* i20[26])∧(i7[27]* i7[26])∧(i5[27]* i5[26]))

(28) -> (29), if ((i7[28] >= 100 && i5[28] > 0* TRUE)∧(i5[28]* i5[29])∧(i7[28]* i7[29]))

(29) -> (24), if ((i5[29] - 1* i5[24]))

(29) -> (30), if ((i5[29] - 1* i5[30]))

(30) -> (31), if ((i5[30]* i5[31])∧(i5[30] >= 100* TRUE))

(31) -> (24), if ((i5[31] - 1* i5[24]))

(31) -> (30), if ((i5[31] - 1* i5[30]))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (11) 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 LOAD1100(i5, i7, 0) → LOAD83(i5, +(i7, 1)) the following chains were created:
• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]) which results in the following constraint:

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

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

(3)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(4)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(5)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(6)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[(-1)bso_99] ≥ 0)

• We consider the chain COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]) which results in the following constraint:

We simplified constraint (7) using rules (III), (IV) which results in the following new constraint:

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

(9)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(10)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(11)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(12)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_99] ≥ 0)

• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28]) which results in the following constraint:

We simplified constraint (13) using rules (III), (IV) which results in the following new constraint:

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

(15)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(16)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(17)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[(-1)bso_99] ≥ 0)

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

(18)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[(-1)bso_99] ≥ 0)

• We consider the chain COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28]) which results in the following constraint:

We simplified constraint (19) using rules (III), (IV) which results in the following new constraint:

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

(21)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(22)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(23)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[(-1)bso_99] ≥ 0)

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

(24)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_99] ≥ 0)

For Pair LOAD949(i5, i7, 0) → LOAD1100(i5, i7, i7) the following chains were created:
• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)) which results in the following constraint:

We simplified constraint (25) using rules (III), (IV) which results in the following new constraint:

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

(27)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(28)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(29)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(30)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧[(-1)bso_101] ≥ 0)

• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) which results in the following constraint:

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

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

(33)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(34)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(35)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_101] ≥ 0)

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

(36)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_101] ≥ 0)

For Pair LOAD1100(i5, i7, i696) → COND_LOAD1100(>(i696, 0), i5, i7, i696) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)) which results in the following constraint:

(37)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

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

(38)    (>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

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

(39)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_102 + (-1)Bound*bni_102] + [bni_102]i5[2] ≥ 0∧[(-1)bso_103] ≥ 0)

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

(40)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_102 + (-1)Bound*bni_102] + [bni_102]i5[2] ≥ 0∧[(-1)bso_103] ≥ 0)

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

(41)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_102 + (-1)Bound*bni_102] + [bni_102]i5[2] ≥ 0∧[(-1)bso_103] ≥ 0)

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

(42)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧[bni_102] = 0∧[(-1)bni_102 + (-1)Bound*bni_102] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_103] ≥ 0)

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

(43)    (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧[bni_102] = 0∧[(-1)bni_102 + (-1)Bound*bni_102] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_103] ≥ 0)

For Pair COND_LOAD1100(TRUE, i5, i7, i696) → LOAD1100(i5, i7, -(i696, 1)) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)) which results in the following constraint:

(44)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUEi7[3]=i7[0]i5[3]=i5[0]-(i696[3], 1)=0COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥NonInfC∧COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥LOAD1100(i5[3], i7[3], -(i696[3], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (44) using rules (III), (IV) which results in the following new constraint:

(45)    (>(i696[2], 0)=TRUE-(i696[2], 1)=0COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥NonInfC∧COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥LOAD1100(i5[2], i7[2], -(i696[2], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

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

(46)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(47)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(48)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(49)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)

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

(50)    (i696[2] ≥ 0∧i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)

• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) which results in the following constraint:

(51)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUEi7[3]=i7[2]1-(i696[3], 1)=i696[2]1i5[3]=i5[2]1COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥NonInfC∧COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥LOAD1100(i5[3], i7[3], -(i696[3], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (51) using rules (III), (IV) which results in the following new constraint:

(52)    (>(i696[2], 0)=TRUECOND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥NonInfC∧COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥LOAD1100(i5[2], i7[2], -(i696[2], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

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

(53)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(54)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(55)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]i5[2] ≥ 0∧[(-1)bso_105] ≥ 0)

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

(56)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)

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

(57)    (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)

For Pair LOAD768(i5, i7, 0) → LOAD949(i5, i7, i7) the following chains were created:
• We consider the chain LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]), LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]) which results in the following constraint:

We simplified constraint (58) using rules (III), (IV) which results in the following new constraint:

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

(60)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(61)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(62)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(63)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧[(-1)bso_107] ≥ 0)

• We consider the chain LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]), LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) which results in the following constraint:

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

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

(66)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(67)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(68)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_107] ≥ 0)

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

(69)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_107] ≥ 0)

For Pair LOAD949(i5, i7, i605) → COND_LOAD949(>(i605, 0), i5, i7, i605) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)) which results in the following constraint:

(70)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

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

(71)    (>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

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

(72)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_108 + (-1)Bound*bni_108] + [bni_108]i5[5] ≥ 0∧[(-1)bso_109] ≥ 0)

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

(73)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_108 + (-1)Bound*bni_108] + [bni_108]i5[5] ≥ 0∧[(-1)bso_109] ≥ 0)

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

(74)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_108 + (-1)Bound*bni_108] + [bni_108]i5[5] ≥ 0∧[(-1)bso_109] ≥ 0)

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

(75)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧[bni_108] = 0∧[(-1)bni_108 + (-1)Bound*bni_108] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_109] ≥ 0)

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

(76)    (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧[bni_108] = 0∧[(-1)bni_108 + (-1)Bound*bni_108] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_109] ≥ 0)

For Pair COND_LOAD949(TRUE, i5, i7, i605) → LOAD949(i5, i7, -(i605, 1)) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)), LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]) which results in the following constraint:

(77)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUE-(i605[6], 1)=0i5[6]=i5[1]i7[6]=i7[1]COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥NonInfC∧COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥LOAD949(i5[6], i7[6], -(i605[6], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (77) using rules (III), (IV) which results in the following new constraint:

(78)    (>(i605[5], 0)=TRUE-(i605[5], 1)=0COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥NonInfC∧COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥LOAD949(i5[5], i7[5], -(i605[5], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (78) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(79)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (79) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(80)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (80) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(81)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (81) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(82)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (82) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(83)    (i605[5] ≥ 0∧i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)

• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)), LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) which results in the following constraint:

(84)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUEi7[6]=i7[5]1-(i605[6], 1)=i605[5]1i5[6]=i5[5]1COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥NonInfC∧COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥LOAD949(i5[6], i7[6], -(i605[6], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (84) using rules (III), (IV) which results in the following new constraint:

(85)    (>(i605[5], 0)=TRUECOND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥NonInfC∧COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥LOAD949(i5[5], i7[5], -(i605[5], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(86)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (86) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(87)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (87) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(88)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]i5[5] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (88) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(89)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (89) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(90)    (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)

For Pair LOAD608(i5, i7, 0) → LOAD768(i5, i7, i7) the following chains were created:
• We consider the chain LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]), LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]) which results in the following constraint:

We simplified constraint (91) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (92) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(93)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (93) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(94)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (94) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(95)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (95) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(96)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧[(-1)bso_113] ≥ 0)

• We consider the chain LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]), LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) which results in the following constraint:

We simplified constraint (97) using rule (IV) which results in the following new constraint:

We simplified constraint (98) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(99)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (99) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(100)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (100) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(101)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_113] ≥ 0)

We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(102)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_113] ≥ 0)

For Pair LOAD768(i5, i7, i436) → COND_LOAD768(>(i436, 0), i5, i7, i436) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)) which results in the following constraint:

(103)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

We simplified constraint (103) using rule (IV) which results in the following new constraint:

(104)    (>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

We simplified constraint (104) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(105)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_114 + (-1)Bound*bni_114] + [bni_114]i5[8] ≥ 0∧[(-1)bso_115] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(106)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_114 + (-1)Bound*bni_114] + [bni_114]i5[8] ≥ 0∧[(-1)bso_115] ≥ 0)

We simplified constraint (106) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(107)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_114 + (-1)Bound*bni_114] + [bni_114]i5[8] ≥ 0∧[(-1)bso_115] ≥ 0)

We simplified constraint (107) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(108)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧[bni_114] = 0∧[(-1)bni_114 + (-1)Bound*bni_114] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_115] ≥ 0)

We simplified constraint (108) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(109)    (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧[bni_114] = 0∧[(-1)bni_114 + (-1)Bound*bni_114] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_115] ≥ 0)

For Pair COND_LOAD768(TRUE, i5, i7, i436) → LOAD768(i5, i7, -(i436, 1)) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)), LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]) which results in the following constraint:

(110)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUEi7[9]=i7[4]-(i436[9], 1)=0i5[9]=i5[4]COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥NonInfC∧COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥LOAD768(i5[9], i7[9], -(i436[9], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (110) using rules (III), (IV) which results in the following new constraint:

(111)    (>(i436[8], 0)=TRUE-(i436[8], 1)=0COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥NonInfC∧COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥LOAD768(i5[8], i7[8], -(i436[8], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (111) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(112)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (112) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(113)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (113) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(114)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (114) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(115)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (115) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(116)    (i436[8] ≥ 0∧i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)

• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)), LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) which results in the following constraint:

(117)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUE-(i436[9], 1)=i436[8]1i7[9]=i7[8]1i5[9]=i5[8]1COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥NonInfC∧COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥LOAD768(i5[9], i7[9], -(i436[9], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (117) using rules (III), (IV) which results in the following new constraint:

(118)    (>(i436[8], 0)=TRUECOND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥NonInfC∧COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥LOAD768(i5[8], i7[8], -(i436[8], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (118) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(119)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (119) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(120)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (120) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(121)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]i5[8] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (121) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(122)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (122) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(123)    (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)

For Pair LOAD484(i5, i7, 0) → LOAD608(i5, i7, i7) the following chains were created:
• We consider the chain LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]), LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]) which results in the following constraint:

We simplified constraint (124) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (125) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(126)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (126) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(127)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (127) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(128)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (128) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(129)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧[(-1)bso_119] ≥ 0)

• We consider the chain LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]), LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]) which results in the following constraint:

We simplified constraint (130) using rule (IV) which results in the following new constraint:

We simplified constraint (131) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(132)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (132) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(133)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (133) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(134)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_119] ≥ 0)

We simplified constraint (134) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(135)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_119] ≥ 0)

For Pair LOAD608(i5, i7, i296) → COND_LOAD608(>(i296, 0), i5, i7, i296) the following chains were created:
• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)) which results in the following constraint:

(136)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]LOAD608(i5[11], i7[11], i296[11])≥NonInfC∧LOAD608(i5[11], i7[11], i296[11])≥COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])∧(UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥))

We simplified constraint (136) using rule (IV) which results in the following new constraint:

(137)    (>(i296[11], 0)=TRUELOAD608(i5[11], i7[11], i296[11])≥NonInfC∧LOAD608(i5[11], i7[11], i296[11])≥COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])∧(UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥))

We simplified constraint (137) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(138)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]i5[11] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (138) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(139)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]i5[11] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (139) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(140)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]i5[11] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (140) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(141)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧0 = 0∧[bni_120] = 0∧[(-1)bni_120 + (-1)Bound*bni_120] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (141) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(142)    (i296[11] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧0 = 0∧[bni_120] = 0∧[(-1)bni_120 + (-1)Bound*bni_120] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_121] ≥ 0)

For Pair COND_LOAD608(TRUE, i5, i7, i296) → LOAD608(i5, i7, -(i296, 1)) the following chains were created:
• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)), LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]) which results in the following constraint:

(143)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]-(i296[12], 1)=0i7[12]=i7[7]i5[12]=i5[7]COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥NonInfC∧COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥LOAD608(i5[12], i7[12], -(i296[12], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (143) using rules (III), (IV) which results in the following new constraint:

(144)    (>(i296[11], 0)=TRUE-(i296[11], 1)=0COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥NonInfC∧COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥LOAD608(i5[11], i7[11], -(i296[11], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (144) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(145)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (145) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(146)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (146) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(147)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (147) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(148)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (148) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(149)    (i296[11] ≥ 0∧i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)

• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)), LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]) which results in the following constraint:

(150)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]-(i296[12], 1)=i296[11]1i5[12]=i5[11]1i7[12]=i7[11]1COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥NonInfC∧COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥LOAD608(i5[12], i7[12], -(i296[12], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (150) using rules (III), (IV) which results in the following new constraint:

(151)    (>(i296[11], 0)=TRUECOND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥NonInfC∧COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥LOAD608(i5[11], i7[11], -(i296[11], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (151) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(152)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (152) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(153)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (153) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(154)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_122 + (-1)Bound*bni_122] + [bni_122]i5[11] ≥ 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (154) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(155)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)

We simplified constraint (155) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(156)    (i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)

For Pair LOAD363(i5, i7, 0) → LOAD484(i5, i7, i7) the following chains were created:
• We consider the chain LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]), LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]) which results in the following constraint:

We simplified constraint (157) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (158) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(159)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (159) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(160)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (160) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(161)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (161) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(162)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧[(-1)bso_125] ≥ 0)

• We consider the chain LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]), LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]) which results in the following constraint:

We simplified constraint (163) using rule (IV) which results in the following new constraint:

We simplified constraint (164) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(165)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (165) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(166)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (166) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(167)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_125] ≥ 0)

We simplified constraint (167) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(168)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_125] ≥ 0)

For Pair LOAD484(i5, i7, i187) → COND_LOAD484(>(i187, 0), i5, i7, i187) the following chains were created:
• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)) which results in the following constraint:

(169)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUELOAD484(i5[14], i7[14], i187[14])≥NonInfC∧LOAD484(i5[14], i7[14], i187[14])≥COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])∧(UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥))

We simplified constraint (169) using rule (IV) which results in the following new constraint:

(170)    (>(i187[14], 0)=TRUELOAD484(i5[14], i7[14], i187[14])≥NonInfC∧LOAD484(i5[14], i7[14], i187[14])≥COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])∧(UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥))

We simplified constraint (170) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(171)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_126 + (-1)Bound*bni_126] + [bni_126]i5[14] ≥ 0∧[(-1)bso_127] ≥ 0)

We simplified constraint (171) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(172)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_126 + (-1)Bound*bni_126] + [bni_126]i5[14] ≥ 0∧[(-1)bso_127] ≥ 0)

We simplified constraint (172) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(173)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_126 + (-1)Bound*bni_126] + [bni_126]i5[14] ≥ 0∧[(-1)bso_127] ≥ 0)

We simplified constraint (173) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(174)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧0 = 0∧[bni_126] = 0∧[(-1)bni_126 + (-1)Bound*bni_126] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_127] ≥ 0)

We simplified constraint (174) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(175)    (i187[14] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧0 = 0∧[bni_126] = 0∧[(-1)bni_126 + (-1)Bound*bni_126] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_127] ≥ 0)

For Pair COND_LOAD484(TRUE, i5, i7, i187) → LOAD484(i5, i7, -(i187, 1)) the following chains were created:
• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)), LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]) which results in the following constraint:

(176)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUEi7[15]=i7[10]-(i187[15], 1)=0i5[15]=i5[10]COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥NonInfC∧COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥LOAD484(i5[15], i7[15], -(i187[15], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (176) using rules (III), (IV) which results in the following new constraint:

(177)    (>(i187[14], 0)=TRUE-(i187[14], 1)=0COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥NonInfC∧COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥LOAD484(i5[14], i7[14], -(i187[14], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (177) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(178)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (178) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(179)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (179) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(180)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (180) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(181)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (181) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(182)    (i187[14] ≥ 0∧i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)

• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)), LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]) which results in the following constraint:

(183)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUE-(i187[15], 1)=i187[14]1i5[15]=i5[14]1i7[15]=i7[14]1COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥NonInfC∧COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥LOAD484(i5[15], i7[15], -(i187[15], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (183) using rules (III), (IV) which results in the following new constraint:

(184)    (>(i187[14], 0)=TRUECOND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥NonInfC∧COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥LOAD484(i5[14], i7[14], -(i187[14], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (184) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(185)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (185) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(186)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (186) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(187)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_128 + (-1)Bound*bni_128] + [bni_128]i5[14] ≥ 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (187) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(188)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)

We simplified constraint (188) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(189)    (i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)

For Pair LOAD258(i5, i7, 0) → LOAD363(i5, i7, i7) the following chains were created:
• We consider the chain LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]), LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]) which results in the following constraint:

We simplified constraint (190) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (191) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(192)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (192) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(193)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (193) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(194)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (194) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(195)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧[(-1)bso_131] ≥ 0)

• We consider the chain LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]), LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]) which results in the following constraint:

We simplified constraint (196) using rule (IV) which results in the following new constraint:

We simplified constraint (197) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(198)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (198) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(199)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (199) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(200)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_131] ≥ 0)

We simplified constraint (200) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(201)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_131] ≥ 0)

For Pair LOAD363(i5, i7, i104) → COND_LOAD363(>(i104, 0), i5, i7, i104) the following chains were created:
• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)) which results in the following constraint:

(202)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUELOAD363(i5[17], i7[17], i104[17])≥NonInfC∧LOAD363(i5[17], i7[17], i104[17])≥COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])∧(UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥))

We simplified constraint (202) using rule (IV) which results in the following new constraint:

(203)    (>(i104[17], 0)=TRUELOAD363(i5[17], i7[17], i104[17])≥NonInfC∧LOAD363(i5[17], i7[17], i104[17])≥COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])∧(UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥))

We simplified constraint (203) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(204)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_132 + (-1)Bound*bni_132] + [bni_132]i5[17] ≥ 0∧[(-1)bso_133] ≥ 0)

We simplified constraint (204) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(205)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_132 + (-1)Bound*bni_132] + [bni_132]i5[17] ≥ 0∧[(-1)bso_133] ≥ 0)

We simplified constraint (205) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(206)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_132 + (-1)Bound*bni_132] + [bni_132]i5[17] ≥ 0∧[(-1)bso_133] ≥ 0)

We simplified constraint (206) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(207)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧0 = 0∧[bni_132] = 0∧[(-1)bni_132 + (-1)Bound*bni_132] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_133] ≥ 0)

We simplified constraint (207) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(208)    (i104[17] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧0 = 0∧[bni_132] = 0∧[(-1)bni_132 + (-1)Bound*bni_132] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_133] ≥ 0)

For Pair COND_LOAD363(TRUE, i5, i7, i104) → LOAD363(i5, i7, -(i104, 1)) the following chains were created:
• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)), LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]) which results in the following constraint:

(209)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUEi5[18]=i5[13]-(i104[18], 1)=0i7[18]=i7[13]COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥NonInfC∧COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥LOAD363(i5[18], i7[18], -(i104[18], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

We simplified constraint (209) using rules (III), (IV) which results in the following new constraint:

(210)    (>(i104[17], 0)=TRUE-(i104[17], 1)=0COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥NonInfC∧COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥LOAD363(i5[17], i7[17], -(i104[17], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

We simplified constraint (210) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(211)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (211) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(212)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (212) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(213)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (213) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(214)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (214) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(215)    (i104[17] ≥ 0∧i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)

• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)), LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]) which results in the following constraint:

(216)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUE-(i104[18], 1)=i104[17]1i5[18]=i5[17]1i7[18]=i7[17]1COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥NonInfC∧COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥LOAD363(i5[18], i7[18], -(i104[18], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

We simplified constraint (216) using rules (III), (IV) which results in the following new constraint:

(217)    (>(i104[17], 0)=TRUECOND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥NonInfC∧COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥LOAD363(i5[17], i7[17], -(i104[17], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

We simplified constraint (217) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(218)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (218) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(219)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (219) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(220)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_134 + (-1)Bound*bni_134] + [bni_134]i5[17] ≥ 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (220) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(221)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)

We simplified constraint (221) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(222)    (i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)

For Pair LOAD175(i5, i7, 0) → LOAD258(i5, i7, i7) the following chains were created:
• We consider the chain LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]), LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]) which results in the following constraint:

We simplified constraint (223) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (224) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(225)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (225) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(226)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (226) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(227)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (227) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(228)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧[(-1)bso_137] ≥ 0)

• We consider the chain LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]), LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]) which results in the following constraint:

We simplified constraint (229) using rule (IV) which results in the following new constraint:

We simplified constraint (230) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(231)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (231) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(232)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (232) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(233)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_137] ≥ 0)

We simplified constraint (233) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(234)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_137] ≥ 0)

For Pair LOAD258(i5, i7, i49) → COND_LOAD258(>(i49, 0), i5, i7, i49) the following chains were created:
• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)) which results in the following constraint:

(235)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]LOAD258(i5[20], i7[20], i49[20])≥NonInfC∧LOAD258(i5[20], i7[20], i49[20])≥COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])∧(UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥))

We simplified constraint (235) using rule (IV) which results in the following new constraint:

(236)    (>(i49[20], 0)=TRUELOAD258(i5[20], i7[20], i49[20])≥NonInfC∧LOAD258(i5[20], i7[20], i49[20])≥COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])∧(UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥))

We simplified constraint (236) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(237)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_138 + (-1)Bound*bni_138] + [bni_138]i5[20] ≥ 0∧[(-1)bso_139] ≥ 0)

We simplified constraint (237) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(238)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_138 + (-1)Bound*bni_138] + [bni_138]i5[20] ≥ 0∧[(-1)bso_139] ≥ 0)

We simplified constraint (238) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(239)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_138 + (-1)Bound*bni_138] + [bni_138]i5[20] ≥ 0∧[(-1)bso_139] ≥ 0)

We simplified constraint (239) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(240)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧0 = 0∧[bni_138] = 0∧[(-1)bni_138 + (-1)Bound*bni_138] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_139] ≥ 0)

We simplified constraint (240) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(241)    (i49[20] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧0 = 0∧[bni_138] = 0∧[(-1)bni_138 + (-1)Bound*bni_138] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_139] ≥ 0)

For Pair COND_LOAD258(TRUE, i5, i7, i49) → LOAD258(i5, i7, -(i49, 1)) the following chains were created:
• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)), LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]) which results in the following constraint:

(242)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]i7[21]=i7[16]-(i49[21], 1)=0i5[21]=i5[16]COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥NonInfC∧COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥LOAD258(i5[21], i7[21], -(i49[21], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

We simplified constraint (242) using rules (III), (IV) which results in the following new constraint:

(243)    (>(i49[20], 0)=TRUE-(i49[20], 1)=0COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥NonInfC∧COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥LOAD258(i5[20], i7[20], -(i49[20], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

We simplified constraint (243) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(244)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (244) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(245)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (245) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(246)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (246) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(247)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (247) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(248)    (i49[20] ≥ 0∧i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)

• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)), LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]) which results in the following constraint:

(249)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]i7[21]=i7[20]1-(i49[21], 1)=i49[20]1i5[21]=i5[20]1COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥NonInfC∧COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥LOAD258(i5[21], i7[21], -(i49[21], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

We simplified constraint (249) using rules (III), (IV) which results in the following new constraint:

(250)    (>(i49[20], 0)=TRUECOND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥NonInfC∧COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥LOAD258(i5[20], i7[20], -(i49[20], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

We simplified constraint (250) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(251)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (251) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(252)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (252) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(253)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_140 + (-1)Bound*bni_140] + [bni_140]i5[20] ≥ 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (253) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(254)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)

We simplified constraint (254) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(255)    (i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)

For Pair LOAD83(i5, i7) → COND_LOAD83(&&(>(i7, 0), <(i7, 100)), i5, i7) the following chains were created:
• We consider the chain LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]), COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]) which results in the following constraint:

(256)    (i5[22]=i5[23]&&(>(i7[22], 0), <(i7[22], 100))=TRUEi7[22]=i7[23]LOAD83(i5[22], i7[22])≥NonInfC∧LOAD83(i5[22], i7[22])≥COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])∧(UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥))

We simplified constraint (256) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(257)    (>(i7[22], 0)=TRUE<(i7[22], 100)=TRUELOAD83(i5[22], i7[22])≥NonInfC∧LOAD83(i5[22], i7[22])≥COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])∧(UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥))

We simplified constraint (257) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(258)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_142 + (-1)Bound*bni_142] + [bni_142]i5[22] ≥ 0∧[(-1)bso_143] ≥ 0)

We simplified constraint (258) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(259)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_142 + (-1)Bound*bni_142] + [bni_142]i5[22] ≥ 0∧[(-1)bso_143] ≥ 0)

We simplified constraint (259) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(260)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_142 + (-1)Bound*bni_142] + [bni_142]i5[22] ≥ 0∧[(-1)bso_143] ≥ 0)

We simplified constraint (260) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(261)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[bni_142] = 0∧[(-1)bni_142 + (-1)Bound*bni_142] ≥ 0∧0 = 0∧[(-1)bso_143] ≥ 0)

We simplified constraint (261) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(262)    (i7[22] ≥ 0∧[98] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[bni_142] = 0∧[(-1)bni_142 + (-1)Bound*bni_142] ≥ 0∧0 = 0∧[(-1)bso_143] ≥ 0)

For Pair COND_LOAD83(TRUE, i5, i7) → LOAD175(i5, i7, i7) the following chains were created:
• We consider the chain COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]), LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) which results in the following constraint:

We simplified constraint (263) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (264) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(265)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (265) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(266)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (266) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(267)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (267) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(268)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧[(-1)bso_145] ≥ 0)

• We consider the chain COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]), LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) which results in the following constraint:

We simplified constraint (269) using rule (IV) which results in the following new constraint:

We simplified constraint (270) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(271)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (271) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(272)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (272) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(273)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_145] ≥ 0)

We simplified constraint (273) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(274)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_145] ≥ 0)

For Pair LOAD55(i5) → COND_LOAD55(&&(>(i5, 0), <(i5, 100)), i5) the following chains were created:
• We consider the chain LOAD55(i5[24]) → COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24]), COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25]) which results in the following constraint:

(275)    (&&(>(i5[24], 0), <(i5[24], 100))=TRUEi5[24]=i5[25]LOAD55(i5[24])≥NonInfC∧LOAD55(i5[24])≥COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])∧(UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥))

We simplified constraint (275) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (276) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(277)    (i5[24] + [-1] ≥ 0∧[99] + [-1]i5[24] ≥ 0 ⇒ (UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥)∧[(-1)bni_146 + (-1)Bound*bni_146] + [bni_146]i5[24] ≥ 0∧[(-1)bso_147] ≥ 0)

We simplified constraint (277) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(278)    (i5[24] + [-1] ≥ 0∧[99] + [-1]i5[24] ≥ 0 ⇒ (UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥)∧[(-1)bni_146 + (-1)Bound*bni_146] + [bni_146]i5[24] ≥ 0∧[(-1)bso_147] ≥ 0)

We simplified constraint (278) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(279)    (i5[24] + [-1] ≥ 0∧[99] + [-1]i5[24] ≥ 0 ⇒ (UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥)∧[(-1)bni_146 + (-1)Bound*bni_146] + [bni_146]i5[24] ≥ 0∧[(-1)bso_147] ≥ 0)

We simplified constraint (279) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(280)    (i5[24] ≥ 0∧[98] + [-1]i5[24] ≥ 0 ⇒ (UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥)∧[(-1)Bound*bni_146] + [bni_146]i5[24] ≥ 0∧[(-1)bso_147] ≥ 0)

For Pair COND_LOAD55(TRUE, i5) → LOAD175(i5, i5, i5) the following chains were created:
• We consider the chain COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25]), LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) which results in the following constraint:

We simplified constraint (281) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (282) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(283)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

We simplified constraint (283) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(284)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

We simplified constraint (284) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(285)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

• We consider the chain COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25]), LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) which results in the following constraint:

We simplified constraint (286) using rule (IV) which results in the following new constraint:

We simplified constraint (287) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(288)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

We simplified constraint (288) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(289)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

We simplified constraint (289) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(290)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)

We simplified constraint (290) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(291)    ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧0 = 0∧[(-1)bso_149] ≥ 0)

For Pair LOAD175(i5, i7, i20) → COND_LOAD175(>(i20, 0), i5, i7, i20) the following chains were created:
• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)) which results in the following constraint:

(292)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]LOAD175(i5[26], i7[26], i20[26])≥NonInfC∧LOAD175(i5[26], i7[26], i20[26])≥COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])∧(UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥))

We simplified constraint (292) using rule (IV) which results in the following new constraint:

(293)    (>(i20[26], 0)=TRUELOAD175(i5[26], i7[26], i20[26])≥NonInfC∧LOAD175(i5[26], i7[26], i20[26])≥COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])∧(UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥))

We simplified constraint (293) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(294)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_150 + (-1)Bound*bni_150] + [bni_150]i5[26] ≥ 0∧[(-1)bso_151] ≥ 0)

We simplified constraint (294) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(295)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_150 + (-1)Bound*bni_150] + [bni_150]i5[26] ≥ 0∧[(-1)bso_151] ≥ 0)

We simplified constraint (295) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(296)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_150 + (-1)Bound*bni_150] + [bni_150]i5[26] ≥ 0∧[(-1)bso_151] ≥ 0)

We simplified constraint (296) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(297)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧0 = 0∧[bni_150] = 0∧[(-1)bni_150 + (-1)Bound*bni_150] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_151] ≥ 0)

We simplified constraint (297) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(298)    (i20[26] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧0 = 0∧[bni_150] = 0∧[(-1)bni_150 + (-1)Bound*bni_150] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_151] ≥ 0)

For Pair COND_LOAD175(TRUE, i5, i7, i20) → LOAD175(i5, i7, -(i20, 1)) the following chains were created:
• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)), LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) which results in the following constraint:

(299)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]i7[27]=i7[19]i5[27]=i5[19]-(i20[27], 1)=0COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥NonInfC∧COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥LOAD175(i5[27], i7[27], -(i20[27], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

We simplified constraint (299) using rules (III), (IV) which results in the following new constraint:

(300)    (>(i20[26], 0)=TRUE-(i20[26], 1)=0COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥NonInfC∧COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥LOAD175(i5[26], i7[26], -(i20[26], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

We simplified constraint (300) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(301)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (301) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(302)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (302) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(303)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (303) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(304)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (304) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(305)    (i20[26] ≥ 0∧i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)

• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)), LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) which results in the following constraint:

(306)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]-(i20[27], 1)=i20[26]1i7[27]=i7[26]1i5[27]=i5[26]1COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥NonInfC∧COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥LOAD175(i5[27], i7[27], -(i20[27], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

We simplified constraint (306) using rules (III), (IV) which results in the following new constraint:

(307)    (>(i20[26], 0)=TRUECOND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥NonInfC∧COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥LOAD175(i5[26], i7[26], -(i20[26], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

We simplified constraint (307) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(308)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (308) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(309)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (309) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(310)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_152 + (-1)Bound*bni_152] + [bni_152]i5[26] ≥ 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (310) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(311)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)

We simplified constraint (311) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(312)    (i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)

For Pair LOAD83(i5, i7) → COND_LOAD831(&&(>=(i7, 100), >(i5, 0)), i5, i7) the following chains were created:
• We consider the chain LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28]), COND_LOAD831(TRUE, i5[29], i7[29]) → LOAD55(-(i5[29], 1)) which results in the following constraint:

(313)    (&&(>=(i7[28], 100), >(i5[28], 0))=TRUEi5[28]=i5[29]i7[28]=i7[29]LOAD83(i5[28], i7[28])≥NonInfC∧LOAD83(i5[28], i7[28])≥COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])∧(UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥))

We simplified constraint (313) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(314)    (>=(i7[28], 100)=TRUE>(i5[28], 0)=TRUELOAD83(i5[28], i7[28])≥NonInfC∧LOAD83(i5[28], i7[28])≥COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])∧(UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥))

We simplified constraint (314) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(315)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)bni_154 + (-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

We simplified constraint (315) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(316)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)bni_154 + (-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

We simplified constraint (316) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(317)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)bni_154 + (-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

We simplified constraint (317) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(318)    (i7[28] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)bni_154 + (-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

We simplified constraint (318) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(319)    (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

For Pair COND_LOAD831(TRUE, i5, i7) → LOAD55(-(i5, 1)) the following chains were created:
• We consider the chain LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28]), COND_LOAD831(TRUE, i5[29], i7[29]) → LOAD55(-(i5[29], 1)), LOAD55(i5[24]) → COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24]) which results in the following constraint:

We simplified constraint (320) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (321) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(322)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (322) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(323)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (323) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(324)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (324) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(325)    (i7[28] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (325) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(326)    (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

• We consider the chain LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28]), COND_LOAD831(TRUE, i5[29], i7[29]) → LOAD55(-(i5[29], 1)), LOAD55(i5[30]) → COND_LOAD551(>=(i5[30], 100), i5[30]) which results in the following constraint:

We simplified constraint (327) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (328) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(329)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (329) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(330)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (330) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(331)    (i7[28] + [-100] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (331) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(332)    (i7[28] ≥ 0∧i5[28] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)bni_156 + (-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

We simplified constraint (332) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(333)    (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

For Pair LOAD55(i5) → COND_LOAD551(>=(i5, 100), i5) the following chains were created:
• We consider the chain LOAD55(i5[30]) → COND_LOAD551(>=(i5[30], 100), i5[30]), COND_LOAD551(TRUE, i5[31]) → LOAD55(-(i5[31], 1)) which results in the following constraint:

We simplified constraint (334) using rule (IV) which results in the following new constraint:

We simplified constraint (335) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(336)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(COND_LOAD551(>=(i5[30], 100), i5[30])), ≥)∧[(-1)bni_158 + (-1)Bound*bni_158] + [bni_158]i5[30] ≥ 0∧[(-1)bso_159] ≥ 0)

We simplified constraint (336) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(337)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(COND_LOAD551(>=(i5[30], 100), i5[30])), ≥)∧[(-1)bni_158 + (-1)Bound*bni_158] + [bni_158]i5[30] ≥ 0∧[(-1)bso_159] ≥ 0)

We simplified constraint (337) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(338)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(COND_LOAD551(>=(i5[30], 100), i5[30])), ≥)∧[(-1)bni_158 + (-1)Bound*bni_158] + [bni_158]i5[30] ≥ 0∧[(-1)bso_159] ≥ 0)

We simplified constraint (338) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(339)    (i5[30] ≥ 0 ⇒ (UIncreasing(COND_LOAD551(>=(i5[30], 100), i5[30])), ≥)∧[(99)bni_158 + (-1)Bound*bni_158] + [bni_158]i5[30] ≥ 0∧[(-1)bso_159] ≥ 0)

For Pair COND_LOAD551(TRUE, i5) → LOAD55(-(i5, 1)) the following chains were created:
• We consider the chain LOAD55(i5[30]) → COND_LOAD551(>=(i5[30], 100), i5[30]), COND_LOAD551(TRUE, i5[31]) → LOAD55(-(i5[31], 1)), LOAD55(i5[24]) → COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24]) which results in the following constraint:

We simplified constraint (340) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (341) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(342)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (342) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(343)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (343) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(344)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (344) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(345)    (i5[30] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(99)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

• We consider the chain LOAD55(i5[30]) → COND_LOAD551(>=(i5[30], 100), i5[30]), COND_LOAD551(TRUE, i5[31]) → LOAD55(-(i5[31], 1)), LOAD55(i5[30]) → COND_LOAD551(>=(i5[30], 100), i5[30]) which results in the following constraint:

We simplified constraint (346) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (347) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(348)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (348) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(349)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (349) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(350)    (i5[30] + [-100] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(-1)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

We simplified constraint (350) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(351)    (i5[30] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(99)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD1100(i5, i7, 0) → LOAD83(i5, +(i7, 1))
• ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[(-1)bso_99] ≥ 0)
• (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_99] ≥ 0)
• ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[(-1)bso_99] ≥ 0)
• (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_99] ≥ 0)

• LOAD949(i5, i7, 0) → LOAD1100(i5, i7, i7)
• ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧[(-1)bso_101] ≥ 0)
• ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_101] ≥ 0)

• LOAD1100(i5, i7, i696) → COND_LOAD1100(>(i696, 0), i5, i7, i696)
• (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧[bni_102] = 0∧[(-1)bni_102 + (-1)Bound*bni_102] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_103] ≥ 0)

• COND_LOAD1100(TRUE, i5, i7, i696) → LOAD1100(i5, i7, -(i696, 1))
• (i696[2] ≥ 0∧i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)
• (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧[bni_104] = 0∧[(-1)bni_104 + (-1)Bound*bni_104] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_105] ≥ 0)

• LOAD768(i5, i7, 0) → LOAD949(i5, i7, i7)
• ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧[(-1)bso_107] ≥ 0)
• ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_107] ≥ 0)

• LOAD949(i5, i7, i605) → COND_LOAD949(>(i605, 0), i5, i7, i605)
• (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧[bni_108] = 0∧[(-1)bni_108 + (-1)Bound*bni_108] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_109] ≥ 0)

• COND_LOAD949(TRUE, i5, i7, i605) → LOAD949(i5, i7, -(i605, 1))
• (i605[5] ≥ 0∧i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)
• (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧[bni_110] = 0∧[(-1)bni_110 + (-1)Bound*bni_110] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_111] ≥ 0)

• LOAD608(i5, i7, 0) → LOAD768(i5, i7, i7)
• ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧[(-1)bso_113] ≥ 0)
• ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_113] ≥ 0)

• LOAD768(i5, i7, i436) → COND_LOAD768(>(i436, 0), i5, i7, i436)
• (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧[bni_114] = 0∧[(-1)bni_114 + (-1)Bound*bni_114] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_115] ≥ 0)

• COND_LOAD768(TRUE, i5, i7, i436) → LOAD768(i5, i7, -(i436, 1))
• (i436[8] ≥ 0∧i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)
• (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧[bni_116] = 0∧[(-1)bni_116 + (-1)Bound*bni_116] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_117] ≥ 0)

• LOAD484(i5, i7, 0) → LOAD608(i5, i7, i7)
• ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧[(-1)bso_119] ≥ 0)
• ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_119] ≥ 0)

• LOAD608(i5, i7, i296) → COND_LOAD608(>(i296, 0), i5, i7, i296)
• (i296[11] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧0 = 0∧[bni_120] = 0∧[(-1)bni_120 + (-1)Bound*bni_120] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_121] ≥ 0)

• COND_LOAD608(TRUE, i5, i7, i296) → LOAD608(i5, i7, -(i296, 1))
• (i296[11] ≥ 0∧i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)
• (i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧0 = 0∧[bni_122] = 0∧[(-1)bni_122 + (-1)Bound*bni_122] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_123] ≥ 0)

• LOAD363(i5, i7, 0) → LOAD484(i5, i7, i7)
• ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧[(-1)bso_125] ≥ 0)
• ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_125] ≥ 0)

• LOAD484(i5, i7, i187) → COND_LOAD484(>(i187, 0), i5, i7, i187)
• (i187[14] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧0 = 0∧[bni_126] = 0∧[(-1)bni_126 + (-1)Bound*bni_126] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_127] ≥ 0)

• COND_LOAD484(TRUE, i5, i7, i187) → LOAD484(i5, i7, -(i187, 1))
• (i187[14] ≥ 0∧i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)
• (i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧0 = 0∧[bni_128] = 0∧[(-1)bni_128 + (-1)Bound*bni_128] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_129] ≥ 0)

• LOAD258(i5, i7, 0) → LOAD363(i5, i7, i7)
• ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧[(-1)bso_131] ≥ 0)
• ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_131] ≥ 0)

• LOAD363(i5, i7, i104) → COND_LOAD363(>(i104, 0), i5, i7, i104)
• (i104[17] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧0 = 0∧[bni_132] = 0∧[(-1)bni_132 + (-1)Bound*bni_132] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_133] ≥ 0)

• COND_LOAD363(TRUE, i5, i7, i104) → LOAD363(i5, i7, -(i104, 1))
• (i104[17] ≥ 0∧i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)
• (i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧0 = 0∧[bni_134] = 0∧[(-1)bni_134 + (-1)Bound*bni_134] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_135] ≥ 0)

• LOAD175(i5, i7, 0) → LOAD258(i5, i7, i7)
• ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧[(-1)bso_137] ≥ 0)
• ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_137] ≥ 0)

• LOAD258(i5, i7, i49) → COND_LOAD258(>(i49, 0), i5, i7, i49)
• (i49[20] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧0 = 0∧[bni_138] = 0∧[(-1)bni_138 + (-1)Bound*bni_138] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_139] ≥ 0)

• COND_LOAD258(TRUE, i5, i7, i49) → LOAD258(i5, i7, -(i49, 1))
• (i49[20] ≥ 0∧i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)
• (i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧0 = 0∧[bni_140] = 0∧[(-1)bni_140 + (-1)Bound*bni_140] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_141] ≥ 0)

• LOAD83(i5, i7) → COND_LOAD83(&&(>(i7, 0), <(i7, 100)), i5, i7)
• (i7[22] ≥ 0∧[98] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[bni_142] = 0∧[(-1)bni_142 + (-1)Bound*bni_142] ≥ 0∧0 = 0∧[(-1)bso_143] ≥ 0)

• COND_LOAD83(TRUE, i5, i7) → LOAD175(i5, i7, i7)
• ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧[(-1)bso_145] ≥ 0)
• ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_145] ≥ 0)

• LOAD55(i5) → COND_LOAD55(&&(>(i5, 0), <(i5, 100)), i5)
• (i5[24] ≥ 0∧[98] + [-1]i5[24] ≥ 0 ⇒ (UIncreasing(COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])), ≥)∧[(-1)Bound*bni_146] + [bni_146]i5[24] ≥ 0∧[(-1)bso_147] ≥ 0)

• COND_LOAD55(TRUE, i5) → LOAD175(i5, i5, i5)
• ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧[(-1)bso_149] ≥ 0)
• ((UIncreasing(LOAD175(i5[25], i5[25], i5[25])), ≥)∧0 = 0∧[(-1)bso_149] ≥ 0)

• LOAD175(i5, i7, i20) → COND_LOAD175(>(i20, 0), i5, i7, i20)
• (i20[26] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧0 = 0∧[bni_150] = 0∧[(-1)bni_150 + (-1)Bound*bni_150] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_151] ≥ 0)

• COND_LOAD175(TRUE, i5, i7, i20) → LOAD175(i5, i7, -(i20, 1))
• (i20[26] ≥ 0∧i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)
• (i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧0 = 0∧[bni_152] = 0∧[(-1)bni_152 + (-1)Bound*bni_152] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_153] ≥ 0)

• LOAD83(i5, i7) → COND_LOAD831(&&(>=(i7, 100), >(i5, 0)), i5, i7)
• (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])), ≥)∧[(-1)Bound*bni_154] + [bni_154]i5[28] ≥ 0∧[(-1)bso_155] ≥ 0)

• COND_LOAD831(TRUE, i5, i7) → LOAD55(-(i5, 1))
• (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)
• (i7[28] ≥ 0∧i5[28] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[29], 1))), ≥)∧[(-1)Bound*bni_156] + [bni_156]i5[28] ≥ 0∧[1 + (-1)bso_157] ≥ 0)

• (i5[30] ≥ 0 ⇒ (UIncreasing(COND_LOAD551(>=(i5[30], 100), i5[30])), ≥)∧[(99)bni_158 + (-1)Bound*bni_158] + [bni_158]i5[30] ≥ 0∧[(-1)bso_159] ≥ 0)

• (i5[30] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(99)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 0)
• (i5[30] ≥ 0 ⇒ (UIncreasing(LOAD55(-(i5[31], 1))), ≥)∧[(99)bni_160 + (-1)Bound*bni_160] + [bni_160]i5[30] ≥ 0∧[1 + (-1)bso_161] ≥ 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(LOAD1100(x1, x2, x3)) = [-1] + x1
POL(0) = 0
POL(LOAD83(x1, x2)) = [-1] + x1
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]
POL(LOAD949(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD1100(x1, x2, x3, x4)) = [-1] + x2
POL(>(x1, x2)) = [-1]
POL(-(x1, x2)) = x1 + [-1]x2
POL(LOAD768(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD949(x1, x2, x3, x4)) = [-1] + x2
POL(LOAD608(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD768(x1, x2, x3, x4)) = [-1] + x2
POL(LOAD484(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD608(x1, x2, x3, x4)) = [-1] + x2
POL(LOAD363(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD484(x1, x2, x3, x4)) = [-1] + x2
POL(LOAD258(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD363(x1, x2, x3, x4)) = [-1] + x2
POL(LOAD175(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD258(x1, x2, x3, x4)) = [-1] + x2
POL(COND_LOAD83(x1, x2, x3)) = [-1] + x2
POL(&&(x1, x2)) = [-1]
POL(<(x1, x2)) = [-1]
POL(100) = [100]
POL(LOAD55(x1)) = [-1] + x1
POL(COND_LOAD55(x1, x2)) = [-1] + x2
POL(COND_LOAD175(x1, x2, x3, x4)) = [-1] + x2
POL(COND_LOAD831(x1, x2, x3)) = [-1] + x2
POL(>=(x1, x2)) = [-1]
POL(COND_LOAD551(x1, x2)) = [-1] + x2

The following pairs are in P>:

The following pairs are in Pbound:

LOAD55(i5[24]) → COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])
LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])

The following pairs are in P:

LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1))
LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])
COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))
LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])
COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))
LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])
COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))
LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])
COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1))
LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])
COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1))
LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])
COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1))
LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])
COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1))
LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])
COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
LOAD55(i5[24]) → COND_LOAD55(&&(>(i5[24], 0), <(i5[24], 100)), i5[24])
LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])
COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1))
LOAD83(i5[28], i7[28]) → COND_LOAD831(&&(>=(i7[28], 100), >(i5[28], 0)), i5[28], i7[28])

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

### (13) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], i7[0] + 1)
(1): LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(4): LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(7): LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(10): LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
(11): LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(i296[11] > 0, i5[11], i7[11], i296[11])
(12): COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], i296[12] - 1)
(13): LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
(14): LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(i187[14] > 0, i5[14], i7[14], i187[14])
(15): COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], i187[15] - 1)
(16): LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
(17): LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(i104[17] > 0, i5[17], i7[17], i104[17])
(18): COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], i104[18] - 1)
(19): LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
(20): LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(i49[20] > 0, i5[20], i7[20], i49[20])
(21): COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], i49[21] - 1)
(22): LOAD83(i5[22], i7[22]) → COND_LOAD83(i7[22] > 0 && i7[22] < 100, i5[22], i7[22])
(23): COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
(24): LOAD55(i5[24]) → COND_LOAD55(i5[24] > 0 && i5[24] < 100, i5[24])
(25): COND_LOAD55(TRUE, i5[25]) → LOAD175(i5[25], i5[25], i5[25])
(26): LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(i20[26] > 0, i5[26], i7[26], i20[26])
(27): COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], i20[27] - 1)
(28): LOAD83(i5[28], i7[28]) → COND_LOAD831(i7[28] >= 100 && i5[28] > 0, i5[28], i7[28])
(30): LOAD55(i5[30]) → COND_LOAD551(i5[30] >= 100, i5[30])

(1) -> (0), if ((i7[1]* 0)∧(i5[1]* i5[0])∧(i7[1]* i7[0]))

(3) -> (0), if ((i7[3]* i7[0])∧(i5[3]* i5[0])∧(i696[3] - 1* 0))

(4) -> (1), if ((i5[4]* i5[1])∧(i7[4]* 0)∧(i7[4]* i7[1]))

(6) -> (1), if ((i605[6] - 1* 0)∧(i5[6]* i5[1])∧(i7[6]* i7[1]))

(1) -> (2), if ((i5[1]* i5[2])∧(i7[1]* i7[2])∧(i7[1]* i696[2]))

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

(7) -> (4), if ((i7[7]* 0)∧(i7[7]* i7[4])∧(i5[7]* i5[4]))

(9) -> (4), if ((i7[9]* i7[4])∧(i436[9] - 1* 0)∧(i5[9]* i5[4]))

(4) -> (5), if ((i7[4]* i7[5])∧(i7[4]* i605[5])∧(i5[4]* i5[5]))

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

(10) -> (7), if ((i5[10]* i5[7])∧(i7[10]* i7[7])∧(i7[10]* 0))

(12) -> (7), if ((i296[12] - 1* 0)∧(i7[12]* i7[7])∧(i5[12]* i5[7]))

(7) -> (8), if ((i5[7]* i5[8])∧(i7[7]* i436[8])∧(i7[7]* i7[8]))

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

(13) -> (10), if ((i5[13]* i5[10])∧(i7[13]* 0)∧(i7[13]* i7[10]))

(15) -> (10), if ((i7[15]* i7[10])∧(i187[15] - 1* 0)∧(i5[15]* i5[10]))

(10) -> (11), if ((i7[10]* i7[11])∧(i5[10]* i5[11])∧(i7[10]* i296[11]))

(12) -> (11), if ((i296[12] - 1* i296[11])∧(i5[12]* i5[11])∧(i7[12]* i7[11]))

(11) -> (12), if ((i296[11] > 0* TRUE)∧(i7[11]* i7[12])∧(i296[11]* i296[12])∧(i5[11]* i5[12]))

(16) -> (13), if ((i7[16]* i7[13])∧(i7[16]* 0)∧(i5[16]* i5[13]))

(18) -> (13), if ((i5[18]* i5[13])∧(i104[18] - 1* 0)∧(i7[18]* i7[13]))

(13) -> (14), if ((i7[13]* i187[14])∧(i5[13]* i5[14])∧(i7[13]* i7[14]))

(15) -> (14), if ((i187[15] - 1* i187[14])∧(i5[15]* i5[14])∧(i7[15]* i7[14]))

(14) -> (15), if ((i7[14]* i7[15])∧(i5[14]* i5[15])∧(i187[14]* i187[15])∧(i187[14] > 0* TRUE))

(19) -> (16), if ((i7[19]* 0)∧(i5[19]* i5[16])∧(i7[19]* i7[16]))

(21) -> (16), if ((i7[21]* i7[16])∧(i49[21] - 1* 0)∧(i5[21]* i5[16]))

(16) -> (17), if ((i7[16]* i104[17])∧(i5[16]* i5[17])∧(i7[16]* i7[17]))

(18) -> (17), if ((i104[18] - 1* i104[17])∧(i5[18]* i5[17])∧(i7[18]* i7[17]))

(17) -> (18), if ((i7[17]* i7[18])∧(i5[17]* i5[18])∧(i104[17]* i104[18])∧(i104[17] > 0* TRUE))

(23) -> (19), if ((i5[23]* i5[19])∧(i7[23]* i7[19])∧(i7[23]* 0))

(25) -> (19), if ((i5[25]* i5[19])∧(i5[25]* i7[19])∧(i5[25]* 0))

(27) -> (19), if ((i7[27]* i7[19])∧(i5[27]* i5[19])∧(i20[27] - 1* 0))

(19) -> (20), if ((i7[19]* i49[20])∧(i7[19]* i7[20])∧(i5[19]* i5[20]))

(21) -> (20), if ((i7[21]* i7[20])∧(i49[21] - 1* i49[20])∧(i5[21]* i5[20]))

(20) -> (21), if ((i7[20]* i7[21])∧(i49[20] > 0* TRUE)∧(i5[20]* i5[21])∧(i49[20]* i49[21]))

(0) -> (22), if ((i5[0]* i5[22])∧(i7[0] + 1* i7[22]))

(22) -> (23), if ((i5[22]* i5[23])∧(i7[22] > 0 && i7[22] < 100* TRUE)∧(i7[22]* i7[23]))

(24) -> (25), if ((i5[24] > 0 && i5[24] < 100* TRUE)∧(i5[24]* i5[25]))

(23) -> (26), if ((i7[23]* i7[26])∧(i5[23]* i5[26])∧(i7[23]* i20[26]))

(25) -> (26), if ((i5[25]* i5[26])∧(i5[25]* i7[26])∧(i5[25]* i20[26]))

(27) -> (26), if ((i20[27] - 1* i20[26])∧(i7[27]* i7[26])∧(i5[27]* i5[26]))

(26) -> (27), if ((i20[26] > 0* TRUE)∧(i7[26]* i7[27])∧(i20[26]* i20[27])∧(i5[26]* i5[27]))

(0) -> (28), if ((i5[0]* i5[28])∧(i7[0] + 1* i7[28]))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.

### (15) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(27): COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], i20[27] - 1)
(26): LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(i20[26] > 0, i5[26], i7[26], i20[26])
(21): COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], i49[21] - 1)
(20): LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(i49[20] > 0, i5[20], i7[20], i49[20])
(18): COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], i104[18] - 1)
(17): LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(i104[17] > 0, i5[17], i7[17], i104[17])
(15): COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], i187[15] - 1)
(14): LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(i187[14] > 0, i5[14], i7[14], i187[14])
(12): COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], i296[12] - 1)
(11): LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(i296[11] > 0, i5[11], i7[11], i296[11])
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])
(1): LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
(4): LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
(7): LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
(10): LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
(13): LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
(16): LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
(19): LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
(23): COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
(22): LOAD83(i5[22], i7[22]) → COND_LOAD83(i7[22] > 0 && i7[22] < 100, i5[22], i7[22])
(0): LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], i7[0] + 1)

(1) -> (0), if ((i7[1]* 0)∧(i5[1]* i5[0])∧(i7[1]* i7[0]))

(3) -> (0), if ((i7[3]* i7[0])∧(i5[3]* i5[0])∧(i696[3] - 1* 0))

(4) -> (1), if ((i5[4]* i5[1])∧(i7[4]* 0)∧(i7[4]* i7[1]))

(6) -> (1), if ((i605[6] - 1* 0)∧(i5[6]* i5[1])∧(i7[6]* i7[1]))

(1) -> (2), if ((i5[1]* i5[2])∧(i7[1]* i7[2])∧(i7[1]* i696[2]))

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

(7) -> (4), if ((i7[7]* 0)∧(i7[7]* i7[4])∧(i5[7]* i5[4]))

(9) -> (4), if ((i7[9]* i7[4])∧(i436[9] - 1* 0)∧(i5[9]* i5[4]))

(4) -> (5), if ((i7[4]* i7[5])∧(i7[4]* i605[5])∧(i5[4]* i5[5]))

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

(10) -> (7), if ((i5[10]* i5[7])∧(i7[10]* i7[7])∧(i7[10]* 0))

(12) -> (7), if ((i296[12] - 1* 0)∧(i7[12]* i7[7])∧(i5[12]* i5[7]))

(7) -> (8), if ((i5[7]* i5[8])∧(i7[7]* i436[8])∧(i7[7]* i7[8]))

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

(13) -> (10), if ((i5[13]* i5[10])∧(i7[13]* 0)∧(i7[13]* i7[10]))

(15) -> (10), if ((i7[15]* i7[10])∧(i187[15] - 1* 0)∧(i5[15]* i5[10]))

(10) -> (11), if ((i7[10]* i7[11])∧(i5[10]* i5[11])∧(i7[10]* i296[11]))

(12) -> (11), if ((i296[12] - 1* i296[11])∧(i5[12]* i5[11])∧(i7[12]* i7[11]))

(11) -> (12), if ((i296[11] > 0* TRUE)∧(i7[11]* i7[12])∧(i296[11]* i296[12])∧(i5[11]* i5[12]))

(16) -> (13), if ((i7[16]* i7[13])∧(i7[16]* 0)∧(i5[16]* i5[13]))

(18) -> (13), if ((i5[18]* i5[13])∧(i104[18] - 1* 0)∧(i7[18]* i7[13]))

(13) -> (14), if ((i7[13]* i187[14])∧(i5[13]* i5[14])∧(i7[13]* i7[14]))

(15) -> (14), if ((i187[15] - 1* i187[14])∧(i5[15]* i5[14])∧(i7[15]* i7[14]))

(14) -> (15), if ((i7[14]* i7[15])∧(i5[14]* i5[15])∧(i187[14]* i187[15])∧(i187[14] > 0* TRUE))

(19) -> (16), if ((i7[19]* 0)∧(i5[19]* i5[16])∧(i7[19]* i7[16]))

(21) -> (16), if ((i7[21]* i7[16])∧(i49[21] - 1* 0)∧(i5[21]* i5[16]))

(16) -> (17), if ((i7[16]* i104[17])∧(i5[16]* i5[17])∧(i7[16]* i7[17]))

(18) -> (17), if ((i104[18] - 1* i104[17])∧(i5[18]* i5[17])∧(i7[18]* i7[17]))

(17) -> (18), if ((i7[17]* i7[18])∧(i5[17]* i5[18])∧(i104[17]* i104[18])∧(i104[17] > 0* TRUE))

(23) -> (19), if ((i5[23]* i5[19])∧(i7[23]* i7[19])∧(i7[23]* 0))

(27) -> (19), if ((i7[27]* i7[19])∧(i5[27]* i5[19])∧(i20[27] - 1* 0))

(19) -> (20), if ((i7[19]* i49[20])∧(i7[19]* i7[20])∧(i5[19]* i5[20]))

(21) -> (20), if ((i7[21]* i7[20])∧(i49[21] - 1* i49[20])∧(i5[21]* i5[20]))

(20) -> (21), if ((i7[20]* i7[21])∧(i49[20] > 0* TRUE)∧(i5[20]* i5[21])∧(i49[20]* i49[21]))

(0) -> (22), if ((i5[0]* i5[22])∧(i7[0] + 1* i7[22]))

(22) -> (23), if ((i5[22]* i5[23])∧(i7[22] > 0 && i7[22] < 100* TRUE)∧(i7[22]* i7[23]))

(23) -> (26), if ((i7[23]* i7[26])∧(i5[23]* i5[26])∧(i7[23]* i20[26]))

(27) -> (26), if ((i20[27] - 1* i20[26])∧(i7[27]* i7[26])∧(i5[27]* i5[26]))

(26) -> (27), if ((i20[26] > 0* TRUE)∧(i7[26]* i7[27])∧(i20[26]* i20[27])∧(i5[26]* i5[27]))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (16) 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_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)) the following chains were created:
• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)), LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) which results in the following constraint:

(1)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]i7[27]=i7[19]i5[27]=i5[19]-(i20[27], 1)=0COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥NonInfC∧COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥LOAD175(i5[27], i7[27], -(i20[27], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

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

(2)    (>(i20[26], 0)=TRUE-(i20[26], 1)=0COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥NonInfC∧COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥LOAD175(i5[26], i7[26], -(i20[26], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

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

(3)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(4)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(5)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(6)    (i20[26] + [-1] ≥ 0∧i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

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

(7)    (i20[26] ≥ 0∧i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)), LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) which results in the following constraint:

(8)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]-(i20[27], 1)=i20[26]1i7[27]=i7[26]1i5[27]=i5[26]1COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥NonInfC∧COND_LOAD175(TRUE, i5[27], i7[27], i20[27])≥LOAD175(i5[27], i7[27], -(i20[27], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

We simplified constraint (8) using rules (III), (IV) which results in the following new constraint:

(9)    (>(i20[26], 0)=TRUECOND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥NonInfC∧COND_LOAD175(TRUE, i5[26], i7[26], i20[26])≥LOAD175(i5[26], i7[26], -(i20[26], 1))∧(UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥))

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

(10)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(11)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(12)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85 + (-1)Bound*bni_85] + [(-1)bni_85]i7[26] ≥ 0∧[(-1)bso_86] ≥ 0)

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

(13)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

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

(14)    (i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

For Pair LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) the following chains were created:
• We consider the chain LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]), COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1)) which results in the following constraint:

(15)    (>(i20[26], 0)=TRUEi7[26]=i7[27]i20[26]=i20[27]i5[26]=i5[27]LOAD175(i5[26], i7[26], i20[26])≥NonInfC∧LOAD175(i5[26], i7[26], i20[26])≥COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])∧(UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥))

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

(16)    (>(i20[26], 0)=TRUELOAD175(i5[26], i7[26], i20[26])≥NonInfC∧LOAD175(i5[26], i7[26], i20[26])≥COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])∧(UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥))

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

(17)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87 + (-1)Bound*bni_87] + [(-1)bni_87]i7[26] ≥ 0∧[(-1)bso_88] ≥ 0)

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

(18)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87 + (-1)Bound*bni_87] + [(-1)bni_87]i7[26] ≥ 0∧[(-1)bso_88] ≥ 0)

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

(19)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87 + (-1)Bound*bni_87] + [(-1)bni_87]i7[26] ≥ 0∧[(-1)bso_88] ≥ 0)

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

(20)    (i20[26] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87] = 0∧0 = 0∧[(-1)bni_87 + (-1)Bound*bni_87] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_88] ≥ 0)

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

(21)    (i20[26] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87] = 0∧0 = 0∧[(-1)bni_87 + (-1)Bound*bni_87] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_88] ≥ 0)

For Pair COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)) the following chains were created:
• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)), LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]) which results in the following constraint:

(22)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]i7[21]=i7[16]-(i49[21], 1)=0i5[21]=i5[16]COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥NonInfC∧COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥LOAD258(i5[21], i7[21], -(i49[21], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

We simplified constraint (22) using rules (III), (IV) which results in the following new constraint:

(23)    (>(i49[20], 0)=TRUE-(i49[20], 1)=0COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥NonInfC∧COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥LOAD258(i5[20], i7[20], -(i49[20], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

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

(24)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(25)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(26)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(27)    (i49[20] + [-1] ≥ 0∧i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

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

(28)    (i49[20] ≥ 0∧i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)), LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]) which results in the following constraint:

(29)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]i7[21]=i7[20]1-(i49[21], 1)=i49[20]1i5[21]=i5[20]1COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥NonInfC∧COND_LOAD258(TRUE, i5[21], i7[21], i49[21])≥LOAD258(i5[21], i7[21], -(i49[21], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

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

(30)    (>(i49[20], 0)=TRUECOND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥NonInfC∧COND_LOAD258(TRUE, i5[20], i7[20], i49[20])≥LOAD258(i5[20], i7[20], -(i49[20], 1))∧(UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥))

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

(31)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(32)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(33)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89 + (-1)Bound*bni_89] + [(-1)bni_89]i7[20] ≥ 0∧[(-1)bso_90] ≥ 0)

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

(34)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

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

(35)    (i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

For Pair LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]) the following chains were created:
• We consider the chain LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]), COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1)) which results in the following constraint:

(36)    (i7[20]=i7[21]>(i49[20], 0)=TRUEi5[20]=i5[21]i49[20]=i49[21]LOAD258(i5[20], i7[20], i49[20])≥NonInfC∧LOAD258(i5[20], i7[20], i49[20])≥COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])∧(UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥))

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

(37)    (>(i49[20], 0)=TRUELOAD258(i5[20], i7[20], i49[20])≥NonInfC∧LOAD258(i5[20], i7[20], i49[20])≥COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])∧(UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥))

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

(38)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91 + (-1)Bound*bni_91] + [(-1)bni_91]i7[20] ≥ 0∧[(-1)bso_92] ≥ 0)

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

(39)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91 + (-1)Bound*bni_91] + [(-1)bni_91]i7[20] ≥ 0∧[(-1)bso_92] ≥ 0)

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

(40)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91 + (-1)Bound*bni_91] + [(-1)bni_91]i7[20] ≥ 0∧[(-1)bso_92] ≥ 0)

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

(41)    (i49[20] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91] = 0∧0 = 0∧[(-1)bni_91 + (-1)Bound*bni_91] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_92] ≥ 0)

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

(42)    (i49[20] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91] = 0∧0 = 0∧[(-1)bni_91 + (-1)Bound*bni_91] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_92] ≥ 0)

For Pair COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)) the following chains were created:
• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)), LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]) which results in the following constraint:

(43)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUEi5[18]=i5[13]-(i104[18], 1)=0i7[18]=i7[13]COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥NonInfC∧COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥LOAD363(i5[18], i7[18], -(i104[18], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

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

(44)    (>(i104[17], 0)=TRUE-(i104[17], 1)=0COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥NonInfC∧COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥LOAD363(i5[17], i7[17], -(i104[17], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

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

(45)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(46)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(47)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(48)    (i104[17] + [-1] ≥ 0∧i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)

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

(49)    (i104[17] ≥ 0∧i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)

• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)), LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]) which results in the following constraint:

(50)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUE-(i104[18], 1)=i104[17]1i5[18]=i5[17]1i7[18]=i7[17]1COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥NonInfC∧COND_LOAD363(TRUE, i5[18], i7[18], i104[18])≥LOAD363(i5[18], i7[18], -(i104[18], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

We simplified constraint (50) using rules (III), (IV) which results in the following new constraint:

(51)    (>(i104[17], 0)=TRUECOND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥NonInfC∧COND_LOAD363(TRUE, i5[17], i7[17], i104[17])≥LOAD363(i5[17], i7[17], -(i104[17], 1))∧(UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥))

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

(52)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(53)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(54)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(-1)bni_93]i7[17] ≥ 0∧[(-1)bso_94] ≥ 0)

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

(55)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)

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

(56)    (i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)

For Pair LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]) the following chains were created:
• We consider the chain LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]), COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1)) which results in the following constraint:

(57)    (i7[17]=i7[18]i5[17]=i5[18]i104[17]=i104[18]>(i104[17], 0)=TRUELOAD363(i5[17], i7[17], i104[17])≥NonInfC∧LOAD363(i5[17], i7[17], i104[17])≥COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])∧(UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥))

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

(58)    (>(i104[17], 0)=TRUELOAD363(i5[17], i7[17], i104[17])≥NonInfC∧LOAD363(i5[17], i7[17], i104[17])≥COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])∧(UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥))

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

(59)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95 + (-1)Bound*bni_95] + [(-1)bni_95]i7[17] ≥ 0∧[(-1)bso_96] ≥ 0)

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

(60)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95 + (-1)Bound*bni_95] + [(-1)bni_95]i7[17] ≥ 0∧[(-1)bso_96] ≥ 0)

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

(61)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95 + (-1)Bound*bni_95] + [(-1)bni_95]i7[17] ≥ 0∧[(-1)bso_96] ≥ 0)

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

(62)    (i104[17] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95] = 0∧0 = 0∧[(-1)bni_95 + (-1)Bound*bni_95] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_96] ≥ 0)

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

(63)    (i104[17] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95] = 0∧0 = 0∧[(-1)bni_95 + (-1)Bound*bni_95] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_96] ≥ 0)

For Pair COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)) the following chains were created:
• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)), LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]) which results in the following constraint:

(64)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUEi7[15]=i7[10]-(i187[15], 1)=0i5[15]=i5[10]COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥NonInfC∧COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥LOAD484(i5[15], i7[15], -(i187[15], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (64) using rules (III), (IV) which results in the following new constraint:

(65)    (>(i187[14], 0)=TRUE-(i187[14], 1)=0COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥NonInfC∧COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥LOAD484(i5[14], i7[14], -(i187[14], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

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

(66)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(67)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(68)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(69)    (i187[14] + [-1] ≥ 0∧i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(70)    (i187[14] ≥ 0∧i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)

• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)), LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]) which results in the following constraint:

(71)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUE-(i187[15], 1)=i187[14]1i5[15]=i5[14]1i7[15]=i7[14]1COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥NonInfC∧COND_LOAD484(TRUE, i5[15], i7[15], i187[15])≥LOAD484(i5[15], i7[15], -(i187[15], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

We simplified constraint (71) using rules (III), (IV) which results in the following new constraint:

(72)    (>(i187[14], 0)=TRUECOND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥NonInfC∧COND_LOAD484(TRUE, i5[14], i7[14], i187[14])≥LOAD484(i5[14], i7[14], -(i187[14], 1))∧(UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥))

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

(73)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(74)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(75)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(-1)bni_97]i7[14] ≥ 0∧[(-1)bso_98] ≥ 0)

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

(76)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)

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

(77)    (i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)

For Pair LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]) the following chains were created:
• We consider the chain LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]), COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1)) which results in the following constraint:

(78)    (i7[14]=i7[15]i5[14]=i5[15]i187[14]=i187[15]>(i187[14], 0)=TRUELOAD484(i5[14], i7[14], i187[14])≥NonInfC∧LOAD484(i5[14], i7[14], i187[14])≥COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])∧(UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥))

We simplified constraint (78) using rule (IV) which results in the following new constraint:

(79)    (>(i187[14], 0)=TRUELOAD484(i5[14], i7[14], i187[14])≥NonInfC∧LOAD484(i5[14], i7[14], i187[14])≥COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])∧(UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥))

We simplified constraint (79) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(80)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99 + (-1)Bound*bni_99] + [(-1)bni_99]i7[14] ≥ 0∧[(-1)bso_100] ≥ 0)

We simplified constraint (80) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(81)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99 + (-1)Bound*bni_99] + [(-1)bni_99]i7[14] ≥ 0∧[(-1)bso_100] ≥ 0)

We simplified constraint (81) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(82)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99 + (-1)Bound*bni_99] + [(-1)bni_99]i7[14] ≥ 0∧[(-1)bso_100] ≥ 0)

We simplified constraint (82) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(83)    (i187[14] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99] = 0∧0 = 0∧[(-1)bni_99 + (-1)Bound*bni_99] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_100] ≥ 0)

We simplified constraint (83) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(84)    (i187[14] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99] = 0∧0 = 0∧[(-1)bni_99 + (-1)Bound*bni_99] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_100] ≥ 0)

For Pair COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)) the following chains were created:
• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)), LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]) which results in the following constraint:

(85)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]-(i296[12], 1)=0i7[12]=i7[7]i5[12]=i5[7]COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥NonInfC∧COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥LOAD608(i5[12], i7[12], -(i296[12], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (85) using rules (III), (IV) which results in the following new constraint:

(86)    (>(i296[11], 0)=TRUE-(i296[11], 1)=0COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥NonInfC∧COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥LOAD608(i5[11], i7[11], -(i296[11], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (86) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(87)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(88)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(89)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(90)    (i296[11] + [-1] ≥ 0∧i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (90) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(91)    (i296[11] ≥ 0∧i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)

• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)), LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]) which results in the following constraint:

(92)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]-(i296[12], 1)=i296[11]1i5[12]=i5[11]1i7[12]=i7[11]1COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥NonInfC∧COND_LOAD608(TRUE, i5[12], i7[12], i296[12])≥LOAD608(i5[12], i7[12], -(i296[12], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (92) using rules (III), (IV) which results in the following new constraint:

(93)    (>(i296[11], 0)=TRUECOND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥NonInfC∧COND_LOAD608(TRUE, i5[11], i7[11], i296[11])≥LOAD608(i5[11], i7[11], -(i296[11], 1))∧(UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥))

We simplified constraint (93) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(94)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (94) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(95)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (95) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(96)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101 + (-1)Bound*bni_101] + [(-1)bni_101]i7[11] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (96) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(97)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (97) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(98)    (i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)

For Pair LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]) the following chains were created:
• We consider the chain LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]), COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1)) which results in the following constraint:

(99)    (>(i296[11], 0)=TRUEi7[11]=i7[12]i296[11]=i296[12]i5[11]=i5[12]LOAD608(i5[11], i7[11], i296[11])≥NonInfC∧LOAD608(i5[11], i7[11], i296[11])≥COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])∧(UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥))

We simplified constraint (99) using rule (IV) which results in the following new constraint:

(100)    (>(i296[11], 0)=TRUELOAD608(i5[11], i7[11], i296[11])≥NonInfC∧LOAD608(i5[11], i7[11], i296[11])≥COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])∧(UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥))

We simplified constraint (100) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(101)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [(-1)bni_103]i7[11] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (101) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(102)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [(-1)bni_103]i7[11] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (102) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(103)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [(-1)bni_103]i7[11] ≥ 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (103) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(104)    (i296[11] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103] = 0∧0 = 0∧[(-1)bni_103 + (-1)Bound*bni_103] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_104] ≥ 0)

We simplified constraint (104) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(105)    (i296[11] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103] = 0∧0 = 0∧[(-1)bni_103 + (-1)Bound*bni_103] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_104] ≥ 0)

For Pair COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)), LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]) which results in the following constraint:

(106)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUEi7[9]=i7[4]-(i436[9], 1)=0i5[9]=i5[4]COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥NonInfC∧COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥LOAD768(i5[9], i7[9], -(i436[9], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (106) using rules (III), (IV) which results in the following new constraint:

(107)    (>(i436[8], 0)=TRUE-(i436[8], 1)=0COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥NonInfC∧COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥LOAD768(i5[8], i7[8], -(i436[8], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (107) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(108)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (108) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(109)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (109) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(110)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (110) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(111)    (i436[8] + [-1] ≥ 0∧i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (111) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(112)    (i436[8] ≥ 0∧i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)

• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)), LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) which results in the following constraint:

(113)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUE-(i436[9], 1)=i436[8]1i7[9]=i7[8]1i5[9]=i5[8]1COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥NonInfC∧COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥LOAD768(i5[9], i7[9], -(i436[9], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (113) using rules (III), (IV) which results in the following new constraint:

(114)    (>(i436[8], 0)=TRUECOND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥NonInfC∧COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥LOAD768(i5[8], i7[8], -(i436[8], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

We simplified constraint (114) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(115)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (115) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(116)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (116) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(117)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105 + (-1)Bound*bni_105] + [(-1)bni_105]i7[8] ≥ 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (117) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(118)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)

We simplified constraint (118) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(119)    (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)

For Pair LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)) which results in the following constraint:

(120)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

We simplified constraint (120) using rule (IV) which results in the following new constraint:

(121)    (>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

We simplified constraint (121) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(122)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107 + (-1)Bound*bni_107] + [(-1)bni_107]i7[8] ≥ 0∧[(-1)bso_108] ≥ 0)

We simplified constraint (122) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(123)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107 + (-1)Bound*bni_107] + [(-1)bni_107]i7[8] ≥ 0∧[(-1)bso_108] ≥ 0)

We simplified constraint (123) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(124)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107 + (-1)Bound*bni_107] + [(-1)bni_107]i7[8] ≥ 0∧[(-1)bso_108] ≥ 0)

We simplified constraint (124) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(125)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107] = 0∧0 = 0∧[(-1)bni_107 + (-1)Bound*bni_107] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_108] ≥ 0)

We simplified constraint (125) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(126)    (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107] = 0∧0 = 0∧[(-1)bni_107 + (-1)Bound*bni_107] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_108] ≥ 0)

For Pair COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)), LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]) which results in the following constraint:

(127)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUE-(i605[6], 1)=0i5[6]=i5[1]i7[6]=i7[1]COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥NonInfC∧COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥LOAD949(i5[6], i7[6], -(i605[6], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (127) using rules (III), (IV) which results in the following new constraint:

(128)    (>(i605[5], 0)=TRUE-(i605[5], 1)=0COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥NonInfC∧COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥LOAD949(i5[5], i7[5], -(i605[5], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (128) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(129)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (129) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(130)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (130) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(131)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (131) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(132)    (i605[5] + [-1] ≥ 0∧i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (132) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(133)    (i605[5] ≥ 0∧i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)

• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)), LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) which results in the following constraint:

(134)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUEi7[6]=i7[5]1-(i605[6], 1)=i605[5]1i5[6]=i5[5]1COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥NonInfC∧COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥LOAD949(i5[6], i7[6], -(i605[6], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (134) using rules (III), (IV) which results in the following new constraint:

(135)    (>(i605[5], 0)=TRUECOND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥NonInfC∧COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥LOAD949(i5[5], i7[5], -(i605[5], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

We simplified constraint (135) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(136)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (136) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(137)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (137) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(138)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109 + (-1)Bound*bni_109] + [(-1)bni_109]i7[5] ≥ 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (138) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(139)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)

We simplified constraint (139) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(140)    (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)

For Pair LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)) which results in the following constraint:

(141)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

We simplified constraint (141) using rule (IV) which results in the following new constraint:

(142)    (>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

We simplified constraint (142) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(143)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [(-1)bni_111]i7[5] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (143) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(144)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [(-1)bni_111]i7[5] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (144) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(145)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [(-1)bni_111]i7[5] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (145) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(146)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111] = 0∧0 = 0∧[(-1)bni_111 + (-1)Bound*bni_111] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (146) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(147)    (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111] = 0∧0 = 0∧[(-1)bni_111 + (-1)Bound*bni_111] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_112] ≥ 0)

For Pair COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)) which results in the following constraint:

(148)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUEi7[3]=i7[0]i5[3]=i5[0]-(i696[3], 1)=0COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥NonInfC∧COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥LOAD1100(i5[3], i7[3], -(i696[3], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (148) using rules (III), (IV) which results in the following new constraint:

(149)    (>(i696[2], 0)=TRUE-(i696[2], 1)=0COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥NonInfC∧COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥LOAD1100(i5[2], i7[2], -(i696[2], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (149) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(150)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (150) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(151)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (151) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(152)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (152) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(153)    (i696[2] + [-1] ≥ 0∧i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (153) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(154)    (i696[2] ≥ 0∧i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)

• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) which results in the following constraint:

(155)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUEi7[3]=i7[2]1-(i696[3], 1)=i696[2]1i5[3]=i5[2]1COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥NonInfC∧COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥LOAD1100(i5[3], i7[3], -(i696[3], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (155) using rules (III), (IV) which results in the following new constraint:

(156)    (>(i696[2], 0)=TRUECOND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥NonInfC∧COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥LOAD1100(i5[2], i7[2], -(i696[2], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

We simplified constraint (156) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(157)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (157) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(158)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (158) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(159)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [(-1)bni_113]i7[2] ≥ 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (159) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(160)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)

We simplified constraint (160) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(161)    (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)

For Pair LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)) which results in the following constraint:

(162)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

We simplified constraint (162) using rule (IV) which results in the following new constraint:

(163)    (>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

We simplified constraint (163) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(164)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [(-1)bni_115]i7[2] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (164) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(165)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [(-1)bni_115]i7[2] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (165) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(166)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [(-1)bni_115]i7[2] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (166) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(167)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115] = 0∧0 = 0∧[(-1)bni_115 + (-1)Bound*bni_115] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (167) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(168)    (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115] = 0∧0 = 0∧[(-1)bni_115 + (-1)Bound*bni_115] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_116] ≥ 0)

For Pair LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]) the following chains were created:
• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)) which results in the following constraint:

We simplified constraint (169) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (170) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(171)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (171) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(172)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (172) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(173)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (173) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(174)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧[(-1)bso_118] ≥ 0)

• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) which results in the following constraint:

We simplified constraint (175) using rule (IV) which results in the following new constraint:

We simplified constraint (176) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(177)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (177) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(178)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (178) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(179)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧[(-1)bso_118] ≥ 0)

We simplified constraint (179) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(180)    ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_118] ≥ 0)

For Pair LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]) the following chains were created:
• We consider the chain LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]), LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]) which results in the following constraint:

We simplified constraint (181) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (182) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(183)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (183) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(184)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (184) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(185)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (185) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(186)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧[(-1)bso_120] ≥ 0)

• We consider the chain LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]), LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) which results in the following constraint:

We simplified constraint (187) using rule (IV) which results in the following new constraint:

We simplified constraint (188) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(189)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (189) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(190)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (190) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(191)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧[(-1)bso_120] ≥ 0)

We simplified constraint (191) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(192)    ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_120] ≥ 0)

For Pair LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]) the following chains were created:
• We consider the chain LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]), LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4]) which results in the following constraint:

We simplified constraint (193) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (194) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(195)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (195) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(196)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (196) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(197)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (197) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(198)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧[(-1)bso_122] ≥ 0)

• We consider the chain LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]), LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) which results in the following constraint:

We simplified constraint (199) using rule (IV) which results in the following new constraint:

We simplified constraint (200) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(201)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (201) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(202)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (202) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(203)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧[(-1)bso_122] ≥ 0)

We simplified constraint (203) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(204)    ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_122] ≥ 0)

For Pair LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]) the following chains were created:
• We consider the chain LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]), LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7]) which results in the following constraint:

We simplified constraint (205) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (206) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(207)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (207) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(208)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (208) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(209)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (209) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(210)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧[(-1)bso_124] ≥ 0)

• We consider the chain LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]), LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11]) which results in the following constraint:

We simplified constraint (211) using rule (IV) which results in the following new constraint:

We simplified constraint (212) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(213)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (213) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(214)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (214) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(215)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧[(-1)bso_124] ≥ 0)

We simplified constraint (215) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(216)    ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_124] ≥ 0)

For Pair LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]) the following chains were created:
• We consider the chain LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]), LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10]) which results in the following constraint:

We simplified constraint (217) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (218) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(219)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (219) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(220)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (220) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(221)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (221) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(222)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧[(-1)bso_126] ≥ 0)

• We consider the chain LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]), LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14]) which results in the following constraint:

We simplified constraint (223) using rule (IV) which results in the following new constraint:

We simplified constraint (224) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(225)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (225) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(226)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (226) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(227)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧[(-1)bso_126] ≥ 0)

We simplified constraint (227) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(228)    ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_126] ≥ 0)

For Pair LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]) the following chains were created:
• We consider the chain LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]), LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13]) which results in the following constraint:

We simplified constraint (229) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (230) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(231)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (231) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(232)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (232) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(233)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (233) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(234)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧[(-1)bso_128] ≥ 0)

• We consider the chain LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]), LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17]) which results in the following constraint:

We simplified constraint (235) using rule (IV) which results in the following new constraint:

We simplified constraint (236) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(237)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (237) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(238)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (238) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(239)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧[(-1)bso_128] ≥ 0)

We simplified constraint (239) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(240)    ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_128] ≥ 0)

For Pair LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) the following chains were created:
• We consider the chain LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]), LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16]) which results in the following constraint:

We simplified constraint (241) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (242) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(243)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (243) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(244)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (244) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(245)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (245) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(246)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧[(-1)bso_130] ≥ 0)

• We consider the chain LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]), LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20]) which results in the following constraint:

We simplified constraint (247) using rule (IV) which results in the following new constraint:

We simplified constraint (248) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(249)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (249) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(250)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (250) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(251)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧[(-1)bso_130] ≥ 0)

We simplified constraint (251) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(252)    ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_130] ≥ 0)

For Pair COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]) the following chains were created:
• We consider the chain COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]), LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19]) which results in the following constraint:

We simplified constraint (253) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (254) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(255)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (255) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(256)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (256) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(257)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (257) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(258)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧[(-1)bso_132] ≥ 0)

• We consider the chain COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]), LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26]) which results in the following constraint:

We simplified constraint (259) using rule (IV) which results in the following new constraint:

We simplified constraint (260) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(261)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (261) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(262)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (262) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(263)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧[(-1)bso_132] ≥ 0)

We simplified constraint (263) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(264)    ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_132] ≥ 0)

For Pair LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]) the following chains were created:
• We consider the chain LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]), COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23]) which results in the following constraint:

(265)    (i5[22]=i5[23]&&(>(i7[22], 0), <(i7[22], 100))=TRUEi7[22]=i7[23]LOAD83(i5[22], i7[22])≥NonInfC∧LOAD83(i5[22], i7[22])≥COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])∧(UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥))

We simplified constraint (265) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(266)    (>(i7[22], 0)=TRUE<(i7[22], 100)=TRUELOAD83(i5[22], i7[22])≥NonInfC∧LOAD83(i5[22], i7[22])≥COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])∧(UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥))

We simplified constraint (266) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(267)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧[(-1)bso_134] ≥ 0)

We simplified constraint (267) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(268)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧[(-1)bso_134] ≥ 0)

We simplified constraint (268) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(269)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧[(-1)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧[(-1)bso_134] ≥ 0)

We simplified constraint (269) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(270)    (i7[22] + [-1] ≥ 0∧[99] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧0 = 0∧[(-1)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧0 = 0∧[(-1)bso_134] ≥ 0)

We simplified constraint (270) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(271)    (i7[22] ≥ 0∧[98] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧0 = 0∧[(-2)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧0 = 0∧[(-1)bso_134] ≥ 0)

For Pair LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)) the following chains were created:
• We consider the chain LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1]), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]) which results in the following constraint:

We simplified constraint (272) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (273) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(274)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (274) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(275)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (275) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(276)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (276) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(277)    ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[1 + (-1)bso_136] ≥ 0)

• We consider the chain COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1)), LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22]) which results in the following constraint:

We simplified constraint (278) using rules (III), (IV) which results in the following new constraint:

We simplified constraint (279) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(280)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (280) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(281)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (281) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(282)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 ≥ 0∧[1 + (-1)bso_136] ≥ 0)

We simplified constraint (282) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(283)    (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_136] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1))
• (i20[26] ≥ 0∧i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)
• (i20[26] ≥ 0 ⇒ (UIncreasing(LOAD175(i5[27], i7[27], -(i20[27], 1))), ≥)∧[(-1)bni_85] = 0∧0 = 0∧[(-1)bni_85 + (-1)Bound*bni_85] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

• LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])
• (i20[26] ≥ 0 ⇒ (UIncreasing(COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])), ≥)∧[(-1)bni_87] = 0∧0 = 0∧[(-1)bni_87 + (-1)Bound*bni_87] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_88] ≥ 0)

• COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1))
• (i49[20] ≥ 0∧i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)
• (i49[20] ≥ 0 ⇒ (UIncreasing(LOAD258(i5[21], i7[21], -(i49[21], 1))), ≥)∧[(-1)bni_89] = 0∧0 = 0∧[(-1)bni_89 + (-1)Bound*bni_89] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

• LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])
• (i49[20] ≥ 0 ⇒ (UIncreasing(COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])), ≥)∧[(-1)bni_91] = 0∧0 = 0∧[(-1)bni_91 + (-1)Bound*bni_91] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_92] ≥ 0)

• COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1))
• (i104[17] ≥ 0∧i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)
• (i104[17] ≥ 0 ⇒ (UIncreasing(LOAD363(i5[18], i7[18], -(i104[18], 1))), ≥)∧[(-1)bni_93] = 0∧0 = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_94] ≥ 0)

• LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])
• (i104[17] ≥ 0 ⇒ (UIncreasing(COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])), ≥)∧[(-1)bni_95] = 0∧0 = 0∧[(-1)bni_95 + (-1)Bound*bni_95] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_96] ≥ 0)

• COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1))
• (i187[14] ≥ 0∧i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)
• (i187[14] ≥ 0 ⇒ (UIncreasing(LOAD484(i5[15], i7[15], -(i187[15], 1))), ≥)∧[(-1)bni_97] = 0∧0 = 0∧[(-1)bni_97 + (-1)Bound*bni_97] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_98] ≥ 0)

• LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])
• (i187[14] ≥ 0 ⇒ (UIncreasing(COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])), ≥)∧[(-1)bni_99] = 0∧0 = 0∧[(-1)bni_99 + (-1)Bound*bni_99] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_100] ≥ 0)

• COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1))
• (i296[11] ≥ 0∧i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)
• (i296[11] ≥ 0 ⇒ (UIncreasing(LOAD608(i5[12], i7[12], -(i296[12], 1))), ≥)∧[(-1)bni_101] = 0∧0 = 0∧[(-1)bni_101 + (-1)Bound*bni_101] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_102] ≥ 0)

• LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])
• (i296[11] ≥ 0 ⇒ (UIncreasing(COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])), ≥)∧[(-1)bni_103] = 0∧0 = 0∧[(-1)bni_103 + (-1)Bound*bni_103] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_104] ≥ 0)

• COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))
• (i436[8] ≥ 0∧i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)
• (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_105] = 0∧0 = 0∧[(-1)bni_105 + (-1)Bound*bni_105] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_106] ≥ 0)

• LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])
• (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_107] = 0∧0 = 0∧[(-1)bni_107 + (-1)Bound*bni_107] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_108] ≥ 0)

• COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))
• (i605[5] ≥ 0∧i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)
• (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_109] = 0∧0 = 0∧[(-1)bni_109 + (-1)Bound*bni_109] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_110] ≥ 0)

• LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])
• (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_111] = 0∧0 = 0∧[(-1)bni_111 + (-1)Bound*bni_111] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_112] ≥ 0)

• COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))
• (i696[2] ≥ 0∧i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)
• (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_113] = 0∧0 = 0∧[(-1)bni_113 + (-1)Bound*bni_113] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_114] ≥ 0)

• LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])
• (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_115] = 0∧0 = 0∧[(-1)bni_115 + (-1)Bound*bni_115] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_116] ≥ 0)

• LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
• ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧[(-1)bso_118] ≥ 0)
• ((UIncreasing(LOAD1100(i5[1], i7[1], i7[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_118] ≥ 0)

• LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
• ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧[(-1)bso_120] ≥ 0)
• ((UIncreasing(LOAD949(i5[4], i7[4], i7[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_120] ≥ 0)

• LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
• ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧[(-1)bso_122] ≥ 0)
• ((UIncreasing(LOAD768(i5[7], i7[7], i7[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_122] ≥ 0)

• LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
• ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧[(-1)bso_124] ≥ 0)
• ((UIncreasing(LOAD608(i5[10], i7[10], i7[10])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_124] ≥ 0)

• LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
• ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧[(-1)bso_126] ≥ 0)
• ((UIncreasing(LOAD484(i5[13], i7[13], i7[13])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_126] ≥ 0)

• LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
• ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧[(-1)bso_128] ≥ 0)
• ((UIncreasing(LOAD363(i5[16], i7[16], i7[16])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_128] ≥ 0)

• LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
• ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧[(-1)bso_130] ≥ 0)
• ((UIncreasing(LOAD258(i5[19], i7[19], i7[19])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_130] ≥ 0)

• COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
• ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧[(-1)bso_132] ≥ 0)
• ((UIncreasing(LOAD175(i5[23], i7[23], i7[23])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_132] ≥ 0)

• LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])
• (i7[22] ≥ 0∧[98] + [-1]i7[22] ≥ 0 ⇒ (UIncreasing(COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])), ≥)∧0 = 0∧[(-2)bni_133 + (-1)Bound*bni_133] + [(-1)bni_133]i7[22] ≥ 0∧0 = 0∧[(-1)bso_134] ≥ 0)

• LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1))
• ((UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧[1 + (-1)bso_136] ≥ 0)
• (i696[3] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD83(i5[0], +(i7[0], 1))), ≥)∧0 = 0∧0 = 0∧0 ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_136] ≥ 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) = [3]
POL(FALSE) = 0
POL(COND_LOAD175(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD175(x1, x2, x3)) = [-1] + [-1]x2
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(>(x1, x2)) = [-1]
POL(0) = 0
POL(COND_LOAD258(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD258(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD363(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD363(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD484(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD484(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD608(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD608(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD768(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD768(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD949(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD949(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD1100(x1, x2, x3, x4)) = [-1] + [-1]x3
POL(LOAD1100(x1, x2, x3)) = [-1] + [-1]x2
POL(COND_LOAD83(x1, x2, x3)) = [-1] + [-1]x3
POL(LOAD83(x1, x2)) = [-1] + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(<(x1, x2)) = [-1]
POL(100) = [100]
POL(+(x1, x2)) = x1 + x2

The following pairs are in P>:

LOAD1100(i5[0], i7[0], 0) → LOAD83(i5[0], +(i7[0], 1))

The following pairs are in Pbound:

LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])

The following pairs are in P:

COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], -(i20[27], 1))
LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(>(i20[26], 0), i5[26], i7[26], i20[26])
COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], -(i49[21], 1))
LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(>(i49[20], 0), i5[20], i7[20], i49[20])
COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], -(i104[18], 1))
LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(>(i104[17], 0), i5[17], i7[17], i104[17])
COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], -(i187[15], 1))
LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(>(i187[14], 0), i5[14], i7[14], i187[14])
COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], -(i296[12], 1))
LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(>(i296[11], 0), i5[11], i7[11], i296[11])
COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))
LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])
COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))
LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])
COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))
LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])
LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
LOAD83(i5[22], i7[22]) → COND_LOAD83(&&(>(i7[22], 0), <(i7[22], 100)), i5[22], i7[22])

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

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

### (18) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(27): COND_LOAD175(TRUE, i5[27], i7[27], i20[27]) → LOAD175(i5[27], i7[27], i20[27] - 1)
(26): LOAD175(i5[26], i7[26], i20[26]) → COND_LOAD175(i20[26] > 0, i5[26], i7[26], i20[26])
(21): COND_LOAD258(TRUE, i5[21], i7[21], i49[21]) → LOAD258(i5[21], i7[21], i49[21] - 1)
(20): LOAD258(i5[20], i7[20], i49[20]) → COND_LOAD258(i49[20] > 0, i5[20], i7[20], i49[20])
(18): COND_LOAD363(TRUE, i5[18], i7[18], i104[18]) → LOAD363(i5[18], i7[18], i104[18] - 1)
(17): LOAD363(i5[17], i7[17], i104[17]) → COND_LOAD363(i104[17] > 0, i5[17], i7[17], i104[17])
(15): COND_LOAD484(TRUE, i5[15], i7[15], i187[15]) → LOAD484(i5[15], i7[15], i187[15] - 1)
(14): LOAD484(i5[14], i7[14], i187[14]) → COND_LOAD484(i187[14] > 0, i5[14], i7[14], i187[14])
(12): COND_LOAD608(TRUE, i5[12], i7[12], i296[12]) → LOAD608(i5[12], i7[12], i296[12] - 1)
(11): LOAD608(i5[11], i7[11], i296[11]) → COND_LOAD608(i296[11] > 0, i5[11], i7[11], i296[11])
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])
(1): LOAD949(i5[1], i7[1], 0) → LOAD1100(i5[1], i7[1], i7[1])
(4): LOAD768(i5[4], i7[4], 0) → LOAD949(i5[4], i7[4], i7[4])
(7): LOAD608(i5[7], i7[7], 0) → LOAD768(i5[7], i7[7], i7[7])
(10): LOAD484(i5[10], i7[10], 0) → LOAD608(i5[10], i7[10], i7[10])
(13): LOAD363(i5[13], i7[13], 0) → LOAD484(i5[13], i7[13], i7[13])
(16): LOAD258(i5[16], i7[16], 0) → LOAD363(i5[16], i7[16], i7[16])
(19): LOAD175(i5[19], i7[19], 0) → LOAD258(i5[19], i7[19], i7[19])
(23): COND_LOAD83(TRUE, i5[23], i7[23]) → LOAD175(i5[23], i7[23], i7[23])
(22): LOAD83(i5[22], i7[22]) → COND_LOAD83(i7[22] > 0 && i7[22] < 100, i5[22], i7[22])

(4) -> (1), if ((i5[4]* i5[1])∧(i7[4]* 0)∧(i7[4]* i7[1]))

(6) -> (1), if ((i605[6] - 1* 0)∧(i5[6]* i5[1])∧(i7[6]* i7[1]))

(1) -> (2), if ((i5[1]* i5[2])∧(i7[1]* i7[2])∧(i7[1]* i696[2]))

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

(7) -> (4), if ((i7[7]* 0)∧(i7[7]* i7[4])∧(i5[7]* i5[4]))

(9) -> (4), if ((i7[9]* i7[4])∧(i436[9] - 1* 0)∧(i5[9]* i5[4]))

(4) -> (5), if ((i7[4]* i7[5])∧(i7[4]* i605[5])∧(i5[4]* i5[5]))

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

(10) -> (7), if ((i5[10]* i5[7])∧(i7[10]* i7[7])∧(i7[10]* 0))

(12) -> (7), if ((i296[12] - 1* 0)∧(i7[12]* i7[7])∧(i5[12]* i5[7]))

(7) -> (8), if ((i5[7]* i5[8])∧(i7[7]* i436[8])∧(i7[7]* i7[8]))

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

(13) -> (10), if ((i5[13]* i5[10])∧(i7[13]* 0)∧(i7[13]* i7[10]))

(15) -> (10), if ((i7[15]* i7[10])∧(i187[15] - 1* 0)∧(i5[15]* i5[10]))

(10) -> (11), if ((i7[10]* i7[11])∧(i5[10]* i5[11])∧(i7[10]* i296[11]))

(12) -> (11), if ((i296[12] - 1* i296[11])∧(i5[12]* i5[11])∧(i7[12]* i7[11]))

(11) -> (12), if ((i296[11] > 0* TRUE)∧(i7[11]* i7[12])∧(i296[11]* i296[12])∧(i5[11]* i5[12]))

(16) -> (13), if ((i7[16]* i7[13])∧(i7[16]* 0)∧(i5[16]* i5[13]))

(18) -> (13), if ((i5[18]* i5[13])∧(i104[18] - 1* 0)∧(i7[18]* i7[13]))

(13) -> (14), if ((i7[13]* i187[14])∧(i5[13]* i5[14])∧(i7[13]* i7[14]))

(15) -> (14), if ((i187[15] - 1* i187[14])∧(i5[15]* i5[14])∧(i7[15]* i7[14]))

(14) -> (15), if ((i7[14]* i7[15])∧(i5[14]* i5[15])∧(i187[14]* i187[15])∧(i187[14] > 0* TRUE))

(19) -> (16), if ((i7[19]* 0)∧(i5[19]* i5[16])∧(i7[19]* i7[16]))

(21) -> (16), if ((i7[21]* i7[16])∧(i49[21] - 1* 0)∧(i5[21]* i5[16]))

(16) -> (17), if ((i7[16]* i104[17])∧(i5[16]* i5[17])∧(i7[16]* i7[17]))

(18) -> (17), if ((i104[18] - 1* i104[17])∧(i5[18]* i5[17])∧(i7[18]* i7[17]))

(17) -> (18), if ((i7[17]* i7[18])∧(i5[17]* i5[18])∧(i104[17]* i104[18])∧(i104[17] > 0* TRUE))

(23) -> (19), if ((i5[23]* i5[19])∧(i7[23]* i7[19])∧(i7[23]* 0))

(27) -> (19), if ((i7[27]* i7[19])∧(i5[27]* i5[19])∧(i20[27] - 1* 0))

(19) -> (20), if ((i7[19]* i49[20])∧(i7[19]* i7[20])∧(i5[19]* i5[20]))

(21) -> (20), if ((i7[21]* i7[20])∧(i49[21] - 1* i49[20])∧(i5[21]* i5[20]))

(20) -> (21), if ((i7[20]* i7[21])∧(i49[20] > 0* TRUE)∧(i5[20]* i5[21])∧(i49[20]* i49[21]))

(22) -> (23), if ((i5[22]* i5[23])∧(i7[22] > 0 && i7[22] < 100* TRUE)∧(i7[22]* i7[23]))

(23) -> (26), if ((i7[23]* i7[26])∧(i5[23]* i5[26])∧(i7[23]* i20[26]))

(27) -> (26), if ((i20[27] - 1* i20[26])∧(i7[27]* i7[26])∧(i5[27]* i5[26]))

(26) -> (27), if ((i20[26] > 0* TRUE)∧(i7[26]* i7[27])∧(i20[26]* i20[27])∧(i5[26]* i5[27]))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (19) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 8 SCCs with 9 less nodes.

### (21) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], i696[3] - 1)
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])

(3) -> (2), if ((i7[3]* i7[2])∧(i696[3] - 1* i696[2])∧(i5[3]* i5[2]))

(2) -> (3), if ((i5[2]* i5[3])∧(i7[2]* i7[3])∧(i696[2]* i696[3])∧(i696[2] > 0* TRUE))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (22) 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_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)), LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) which results in the following constraint:

(1)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUEi7[3]=i7[2]1-(i696[3], 1)=i696[2]1i5[3]=i5[2]1COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥NonInfC∧COND_LOAD1100(TRUE, i5[3], i7[3], i696[3])≥LOAD1100(i5[3], i7[3], -(i696[3], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

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

(2)    (>(i696[2], 0)=TRUECOND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥NonInfC∧COND_LOAD1100(TRUE, i5[2], i7[2], i696[2])≥LOAD1100(i5[2], i7[2], -(i696[2], 1))∧(UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥))

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

(3)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i696[2] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(4)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i696[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)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i696[2] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(6)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i696[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

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

(7)    (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i696[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

For Pair LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]) the following chains were created:
• We consider the chain LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2]), COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1)) which results in the following constraint:

(8)    (i5[2]=i5[3]i7[2]=i7[3]i696[2]=i696[3]>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

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

(9)    (>(i696[2], 0)=TRUELOAD1100(i5[2], i7[2], i696[2])≥NonInfC∧LOAD1100(i5[2], i7[2], i696[2])≥COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])∧(UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥))

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

(10)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(11)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(12)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(13)    (i696[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

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

(14)    (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))
• (i696[2] ≥ 0 ⇒ (UIncreasing(LOAD1100(i5[3], i7[3], -(i696[3], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i696[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

• LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])
• (i696[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i696[2] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 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_LOAD1100(x1, x2, x3, x4)) = [-1] + x4
POL(LOAD1100(x1, x2, x3)) = [-1] + x3
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(>(x1, x2)) = [-1]
POL(0) = 0

The following pairs are in P>:

COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))

The following pairs are in Pbound:

COND_LOAD1100(TRUE, i5[3], i7[3], i696[3]) → LOAD1100(i5[3], i7[3], -(i696[3], 1))
LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])

The following pairs are in P:

LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(>(i696[2], 0), i5[2], i7[2], i696[2])

There are no usable rules.

### (24) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1100(i5[2], i7[2], i696[2]) → COND_LOAD1100(i696[2] > 0, i5[2], i7[2], i696[2])

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (25) IDependencyGraphProof (EQUIVALENT transformation)

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

### (27) 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 is empty.

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (28) IDependencyGraphProof (EQUIVALENT transformation)

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

### (30) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(6): COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], i605[6] - 1)
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])

(6) -> (5), if ((i7[6]* i7[5])∧(i605[6] - 1* i605[5])∧(i5[6]* i5[5]))

(5) -> (6), if ((i5[5]* i5[6])∧(i7[5]* i7[6])∧(i605[5]* i605[6])∧(i605[5] > 0* TRUE))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (31) 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_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)), LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) which results in the following constraint:

(1)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUEi7[6]=i7[5]1-(i605[6], 1)=i605[5]1i5[6]=i5[5]1COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥NonInfC∧COND_LOAD949(TRUE, i5[6], i7[6], i605[6])≥LOAD949(i5[6], i7[6], -(i605[6], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

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

(2)    (>(i605[5], 0)=TRUECOND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥NonInfC∧COND_LOAD949(TRUE, i5[5], i7[5], i605[5])≥LOAD949(i5[5], i7[5], -(i605[5], 1))∧(UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥))

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

(3)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(4)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(5)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(6)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

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

(7)    (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

For Pair LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]) the following chains were created:
• We consider the chain LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5]), COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1)) which results in the following constraint:

(8)    (i5[5]=i5[6]i7[5]=i7[6]i605[5]=i605[6]>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

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

(9)    (>(i605[5], 0)=TRUELOAD949(i5[5], i7[5], i605[5])≥NonInfC∧LOAD949(i5[5], i7[5], i605[5])≥COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])∧(UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥))

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

(10)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(11)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(12)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(13)    (i605[5] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

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

(14)    (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))
• (i605[5] ≥ 0 ⇒ (UIncreasing(LOAD949(i5[6], i7[6], -(i605[6], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i605[5] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

• LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])
• (i605[5] ≥ 0 ⇒ (UIncreasing(COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i605[5] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 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_LOAD949(x1, x2, x3, x4)) = [-1] + x4
POL(LOAD949(x1, x2, x3)) = [-1] + x3
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(>(x1, x2)) = [-1]
POL(0) = 0

The following pairs are in P>:

COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))

The following pairs are in Pbound:

COND_LOAD949(TRUE, i5[6], i7[6], i605[6]) → LOAD949(i5[6], i7[6], -(i605[6], 1))
LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])

The following pairs are in P:

LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(>(i605[5], 0), i5[5], i7[5], i605[5])

There are no usable rules.

### (33) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(5): LOAD949(i5[5], i7[5], i605[5]) → COND_LOAD949(i605[5] > 0, i5[5], i7[5], i605[5])

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (34) IDependencyGraphProof (EQUIVALENT transformation)

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

### (36) 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 is empty.

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (37) IDependencyGraphProof (EQUIVALENT transformation)

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

### (39) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(9): COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], i436[9] - 1)
(8): LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(i436[8] > 0, i5[8], i7[8], i436[8])

(9) -> (8), if ((i436[9] - 1* i436[8])∧(i7[9]* i7[8])∧(i5[9]* i5[8]))

(8) -> (9), if ((i7[8]* i7[9])∧(i436[8]* i436[9])∧(i5[8]* i5[9])∧(i436[8] > 0* TRUE))

The set Q consists of the following terms:
Cond_Load1100(TRUE, x0, x1, x2)
Cond_Load949(TRUE, x0, x1, x2)
Cond_Load768(TRUE, x0, x1, x2)
Cond_Load608(TRUE, x0, x1, x2)
Cond_Load484(TRUE, x0, x1, x2)
Cond_Load363(TRUE, x0, x1, x2)
Cond_Load258(TRUE, x0, x1, x2)
Cond_Load175(TRUE, x0, x1, x2)

### (40) 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_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)), LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) which results in the following constraint:

(1)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUE-(i436[9], 1)=i436[8]1i7[9]=i7[8]1i5[9]=i5[8]1COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥NonInfC∧COND_LOAD768(TRUE, i5[9], i7[9], i436[9])≥LOAD768(i5[9], i7[9], -(i436[9], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

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

(2)    (>(i436[8], 0)=TRUECOND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥NonInfC∧COND_LOAD768(TRUE, i5[8], i7[8], i436[8])≥LOAD768(i5[8], i7[8], -(i436[8], 1))∧(UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥))

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

(3)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(4)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(5)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(6)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

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

(7)    (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

For Pair LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]) the following chains were created:
• We consider the chain LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8]), COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1)) which results in the following constraint:

(8)    (i7[8]=i7[9]i436[8]=i436[9]i5[8]=i5[9]>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

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

(9)    (>(i436[8], 0)=TRUELOAD768(i5[8], i7[8], i436[8])≥NonInfC∧LOAD768(i5[8], i7[8], i436[8])≥COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])∧(UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥))

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

(10)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(11)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(12)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(13)    (i436[8] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

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

(14)    (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))
• (i436[8] ≥ 0 ⇒ (UIncreasing(LOAD768(i5[9], i7[9], -(i436[9], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_13] + [bni_13]i436[8] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

• LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])
• (i436[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])), ≥)∧0 = 0∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i436[8] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 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_LOAD768(x1, x2, x3, x4)) = [-1] + x4
POL(LOAD768(x1, x2, x3)) = [-1] + x3
POL(-(x1, x2)) = x1 + [-1]x2
POL(1) = [1]
POL(>(x1, x2)) = [-1]
POL(0) = 0

The following pairs are in P>:

COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))

The following pairs are in Pbound:

COND_LOAD768(TRUE, i5[9], i7[9], i436[9]) → LOAD768(i5[9], i7[9], -(i436[9], 1))
LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])

The following pairs are in P:

LOAD768(i5[8], i7[8], i436[8]) → COND_LOAD768(>(i436[8], 0), i5[8], i7[8], i436[8])

There are no usable rules.

### (42) 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