### (0) Obligation:

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

Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaB13

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 244 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:
Load1222(i79, i85, i69) → Cond_Load1222(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load1232(i85 <= i69 && i79 <= i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12221(i85 <= i69 && i79 <= i69 && i69 >= 0 && i79 > i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12321(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12222(i69 >= 0 && i85 > i69 && i79 <= i69 && i79 > i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12322(i69 >= 0 && i79 > i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12223(i69 >= 0 && i79 > i69, i79, i85, i69)
The set Q consists of the following terms:

### (6) Obligation:

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
Load1222(i79, i85, i69) → Cond_Load1222(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load1232(i85 <= i69 && i79 <= i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12221(i85 <= i69 && i79 <= i69 && i69 >= 0 && i79 > i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12321(i69 >= 0 && i85 > i69 && i79 <= i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12222(i69 >= 0 && i85 > i69 && i79 <= i69 && i79 > i69, i79, i85, i69)
Load1232(i79, i85, i69) → Cond_Load12322(i69 >= 0 && i79 > i69, i79, i85, i69)
Load1222(i79, i85, i69) → Cond_Load12223(i69 >= 0 && i79 > i69, i79, i85, i69)

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(4): LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4], i79[4], i85[4], i69[4])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(8): LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8], i79[8], i85[8], i69[8])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(3) -> (4), if ((i69[3]* i69[4])∧(i85[3]* i85[4])∧(i79[3]* i79[4]))

(3) -> (8), if ((i69[3]* i69[8])∧(i79[3]* i79[8])∧(i85[3]* i85[8]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(4) -> (5), if ((i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4]* TRUE)∧(i85[4]* i85[5])∧(i69[4]* i69[5])∧(i79[4]* i79[5]))

(5) -> (0), if ((i85[5]* i85[0])∧(i69[5]* i69[0])∧(i79[5]* i79[0]))

(5) -> (4), if ((i85[5]* i85[4])∧(i69[5]* i69[4])∧(i79[5]* i79[4]))

(5) -> (8), if ((i79[5]* i79[8])∧(i69[5]* i69[8])∧(i85[5]* i85[8]))

(5) -> (12), if ((i85[5]* i85[12])∧(i69[5]* i69[12])∧(i79[5]* i79[12]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(7) -> (4), if ((i79[7]* i79[4])∧(i85[7] + -1* i85[4])∧(i69[7]* i69[4]))

(7) -> (8), if ((i79[7]* i79[8])∧(i69[7]* i69[8])∧(i85[7] + -1* i85[8]))

(7) -> (12), if ((i79[7]* i79[12])∧(i69[7]* i69[12])∧(i85[7] + -1* i85[12]))

(8) -> (9), if ((i85[8]* i85[9])∧(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8]* TRUE)∧(i79[8]* i79[9])∧(i69[8]* i69[9]))

(9) -> (0), if ((i69[9]* i69[0])∧(i79[9]* i79[0])∧(i85[9] + -1* i85[0]))

(9) -> (4), if ((i85[9] + -1* i85[4])∧(i79[9]* i79[4])∧(i69[9]* i69[4]))

(9) -> (8), if ((i69[9]* i69[8])∧(i85[9] + -1* i85[8])∧(i79[9]* i79[8]))

(9) -> (12), if ((i69[9]* i69[12])∧(i85[9] + -1* i85[12])∧(i79[9]* i79[12]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(11) -> (4), if ((i69[11]* i69[4])∧(i79[11] + -1* i79[4])∧(i85[11]* i85[4]))

(11) -> (8), if ((i85[11]* i85[8])∧(i79[11] + -1* i79[8])∧(i69[11]* i69[8]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(13) -> (4), if ((i79[13] + -1* i79[4])∧(i69[13]* i69[4])∧(i85[13]* i85[4]))

(13) -> (8), if ((i85[13]* i85[8])∧(i69[13]* i69[8])∧(i79[13] + -1* i79[8]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

The set Q consists of the following terms:

### (7) 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.

### (8) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(4): LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4], i79[4], i85[4], i69[4])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(8): LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8], i79[8], i85[8], i69[8])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(3) -> (4), if ((i69[3]* i69[4])∧(i85[3]* i85[4])∧(i79[3]* i79[4]))

(3) -> (8), if ((i69[3]* i69[8])∧(i79[3]* i79[8])∧(i85[3]* i85[8]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(4) -> (5), if ((i85[4] <= i69[4] && i79[4] <= i69[4] && i69[4] >= 0 && i79[4] > i69[4]* TRUE)∧(i85[4]* i85[5])∧(i69[4]* i69[5])∧(i79[4]* i79[5]))

(5) -> (0), if ((i85[5]* i85[0])∧(i69[5]* i69[0])∧(i79[5]* i79[0]))

(5) -> (4), if ((i85[5]* i85[4])∧(i69[5]* i69[4])∧(i79[5]* i79[4]))

(5) -> (8), if ((i79[5]* i79[8])∧(i69[5]* i69[8])∧(i85[5]* i85[8]))

(5) -> (12), if ((i85[5]* i85[12])∧(i69[5]* i69[12])∧(i79[5]* i79[12]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(7) -> (4), if ((i79[7]* i79[4])∧(i85[7] + -1* i85[4])∧(i69[7]* i69[4]))

(7) -> (8), if ((i79[7]* i79[8])∧(i69[7]* i69[8])∧(i85[7] + -1* i85[8]))

(7) -> (12), if ((i79[7]* i79[12])∧(i69[7]* i69[12])∧(i85[7] + -1* i85[12]))

(8) -> (9), if ((i85[8]* i85[9])∧(i69[8] >= 0 && i85[8] > i69[8] && i79[8] <= i69[8] && i79[8] > i69[8]* TRUE)∧(i79[8]* i79[9])∧(i69[8]* i69[9]))

(9) -> (0), if ((i69[9]* i69[0])∧(i79[9]* i79[0])∧(i85[9] + -1* i85[0]))

(9) -> (4), if ((i85[9] + -1* i85[4])∧(i79[9]* i79[4])∧(i69[9]* i69[4]))

(9) -> (8), if ((i69[9]* i69[8])∧(i85[9] + -1* i85[8])∧(i79[9]* i79[8]))

(9) -> (12), if ((i69[9]* i69[12])∧(i85[9] + -1* i85[12])∧(i79[9]* i79[12]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(11) -> (4), if ((i69[11]* i69[4])∧(i79[11] + -1* i79[4])∧(i85[11]* i85[4]))

(11) -> (8), if ((i85[11]* i85[8])∧(i79[11] + -1* i79[8])∧(i69[11]* i69[8]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(13) -> (4), if ((i79[13] + -1* i79[4])∧(i69[13]* i69[4])∧(i85[13]* i85[4]))

(13) -> (8), if ((i85[13]* i85[8])∧(i69[13]* i69[8])∧(i79[13] + -1* i79[8]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

The set Q consists of the following terms:

### (9) IDPNonInfProof (SOUND transformation)

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

For Pair LOAD1222(i79, i85, i69) → COND_LOAD1222(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(1)    (i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(2)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(3)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

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

(4)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

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

(5)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

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

(6)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

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

(7)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

(8)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

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

(9)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i79[0] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79, i85, i69) → LOAD1232(i79, i85, i69) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

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

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

(12)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(13)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(14)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(15)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

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

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

(18)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(19)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(20)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(21)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

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

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

(24)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(25)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(26)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_53] ≥ 0)

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

(27)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

For Pair LOAD1232(i79, i85, i69) → COND_LOAD1232(&&(<=(i85, i69), <=(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

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

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

(30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

(36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(39)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(40)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(41)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(42)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]) which results in the following constraint:

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

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

(45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]) which results in the following constraint:

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

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

(51)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(52)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(53)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(54)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(57)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(58)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(59)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_57] ≥ 0)

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

(60)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair LOAD1222(i79, i85, i69) → COND_LOAD12221(&&(&&(&&(<=(i85, i69), <=(i79, i69)), >=(i69, 0)), >(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]), COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]) which results in the following constraint:

(61)    (&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4]))=TRUEi85[4]=i85[5]i69[4]=i69[5]i79[4]=i79[5]LOAD1222(i79[4], i85[4], i69[4])≥NonInfC∧LOAD1222(i79[4], i85[4], i69[4])≥COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])∧(UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥))

We simplified constraint (61) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(62)    (>(i79[4], i69[4])=TRUE>=(i69[4], 0)=TRUE<=(i85[4], i69[4])=TRUE<=(i79[4], i69[4])=TRUELOAD1222(i79[4], i85[4], i69[4])≥NonInfC∧LOAD1222(i79[4], i85[4], i69[4])≥COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])∧(UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥))

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

(63)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)

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

(64)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)

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

(65)    (i79[4] + [-1] + [-1]i69[4] ≥ 0∧i69[4] ≥ 0∧i69[4] + [-1]i85[4] ≥ 0∧i69[4] + [-1]i79[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[4] ≥ 0∧[-1 + (-1)bso_59] ≥ 0)

We solved constraint (65) using rule (IDP_SMT_SPLIT).

For Pair COND_LOAD12221(TRUE, i79, i85, i69) → LOAD1222(i79, i85, i69) the following chains were created:
• We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(68)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(69)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

We simplified constraint (69) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(70)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(71)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

• We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4]) which results in the following constraint:

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

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

(74)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(75)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(76)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(77)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

• We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]) which results in the following constraint:

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

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

(80)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(81)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(82)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(83)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

• We consider the chain COND_LOAD12221(TRUE, i79[5], i85[5], i69[5]) → LOAD1222(i79[5], i85[5], i69[5]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (84) using rule (IV) which results in the following new constraint:

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

(86)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(87)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(88)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧[3 + (-1)bso_61] ≥ 0)

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

(89)    ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

For Pair LOAD1232(i79, i85, i69) → COND_LOAD12321(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

(90)    (i85[6]=i85[7]&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUEi69[6]=i69[7]i79[6]=i79[7]LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

We simplified constraint (90) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(91)    (<=(i79[6], i69[6])=TRUE>=(i69[6], 0)=TRUE>(i85[6], i69[6])=TRUELOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(92)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

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

(93)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

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

(94)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

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

(95)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

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

(96)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

(97)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (96) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(98)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i79[6] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

For Pair COND_LOAD12321(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

We simplified constraint (99) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

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

(101)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

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

(102)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

We simplified constraint (102) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(103)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

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

(104)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

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

(105)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

(106)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

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

(107)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i79[6] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

For Pair LOAD1222(i79, i85, i69) → COND_LOAD12222(&&(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), >(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]), COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9]) which results in the following constraint:

(108)    (i85[8]=i85[9]&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8]))=TRUEi79[8]=i79[9]i69[8]=i69[9]LOAD1222(i79[8], i85[8], i69[8])≥NonInfC∧LOAD1222(i79[8], i85[8], i69[8])≥COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])∧(UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥))

We simplified constraint (108) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(109)    (>(i79[8], i69[8])=TRUE<=(i79[8], i69[8])=TRUE>=(i69[8], 0)=TRUE>(i85[8], i69[8])=TRUELOAD1222(i79[8], i85[8], i69[8])≥NonInfC∧LOAD1222(i79[8], i85[8], i69[8])≥COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])∧(UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥))

We simplified constraint (109) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(110)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)

We simplified constraint (110) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(111)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)

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

(112)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])), ≥)∧[(-1)bni_66 + (-1)Bound*bni_66] + [(-1)bni_66]i69[8] ≥ 0∧[-1 + (-1)bso_67] + i85[8] + i79[8] ≥ 0)

We solved constraint (112) using rule (IDP_SMT_SPLIT).

For Pair COND_LOAD12222(TRUE, i79, i85, i69) → LOAD1222(i79, +(i85, -1), i69) the following chains were created:
• We consider the chain LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8]), COND_LOAD12222(TRUE, i79[9], i85[9], i69[9]) → LOAD1222(i79[9], +(i85[9], -1), i69[9]) which results in the following constraint:

We simplified constraint (113) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

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

(115)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)

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

(116)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)

We simplified constraint (116) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(117)    (i79[8] + [-1] + [-1]i69[8] ≥ 0∧i69[8] + [-1]i79[8] ≥ 0∧i69[8] ≥ 0∧i85[8] + [-1] + [-1]i69[8] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[9], +(i85[9], -1), i69[9])), ≥)∧[(-2)bni_68 + (-1)Bound*bni_68] + [(-1)bni_68]i69[8] + [(-1)bni_68]i85[8] + [(-1)bni_68]i79[8] ≥ 0∧[-1 + (-1)bso_69] + [-1]i85[8] + [-1]i79[8] ≥ 0)

We solved constraint (117) using rule (IDP_SMT_SPLIT).

For Pair LOAD1232(i79, i85, i69) → COND_LOAD12322(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

We simplified constraint (118) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(120)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)

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

(121)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)

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

(122)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧[(-1)bso_71] ≥ 0)

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

(123)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)

We simplified constraint (123) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(124)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)

For Pair COND_LOAD12322(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

We simplified constraint (125) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

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

(127)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)

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

(128)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)

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

(129)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧[(-1)bso_73] ≥ 0)

We simplified constraint (129) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(130)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)

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

(131)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)

For Pair LOAD1222(i79, i85, i69) → COND_LOAD12223(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (132) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(134)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)

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

(135)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)

We simplified constraint (135) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(136)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧[(-1)bso_75] ≥ 0)

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

(137)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)

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

(138)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)

For Pair COND_LOAD12223(TRUE, i79, i85, i69) → LOAD1222(+(i79, -1), i85, i69) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (139) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

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

(141)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)

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

(142)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)

We simplified constraint (142) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(143)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧[(-1)bso_77] ≥ 0)

We simplified constraint (143) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(144)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 0)

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

(145)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD1222(i79, i85, i69) → COND_LOAD1222(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69)
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i79[0] + [(-1)bni_50]i69[0] ≥ 0∧[(-1)bso_51] ≥ 0)

• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• LOAD1232(i79, i85, i69) → COND_LOAD1232(&&(<=(i85, i69), <=(i79, i69)), i79, i85, i69)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] ≥ 0∧[(-1)bso_55] ≥ 0)

• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• LOAD1222(i79, i85, i69) → COND_LOAD12221(&&(&&(&&(<=(i85, i69), <=(i79, i69)), >=(i69, 0)), >(i79, i69)), i79, i85, i69)

• ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
• ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
• ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)
• ((UIncreasing(LOAD1222(i79[5], i85[5], i69[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[3 + (-1)bso_61] ≥ 0)

• LOAD1232(i79, i85, i69) → COND_LOAD12321(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), i79, i85, i69)
• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_62 + (-1)Bound*bni_62] + [(-1)bni_62]i79[6] + [(-1)bni_62]i69[6] ≥ 0∧[(-1)bso_63] ≥ 0)

• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_64 + (-1)Bound*bni_64] + [(-1)bni_64]i79[6] + [(-1)bni_64]i69[6] ≥ 0∧[(-1)bso_65] ≥ 0)

• LOAD1222(i79, i85, i69) → COND_LOAD12222(&&(&&(&&(>=(i69, 0), >(i85, i69)), <=(i79, i69)), >(i79, i69)), i79, i85, i69)

• LOAD1232(i79, i85, i69) → COND_LOAD12322(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69)
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_70 + (-1)Bound*bni_70] + [(-1)bni_70]i69[10] ≥ 0∧0 = 0∧[(-1)bso_71] ≥ 0)

• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_72 + (-1)Bound*bni_72] + [(-1)bni_72]i69[10] ≥ 0∧0 = 0∧[(-1)bso_73] ≥ 0)

• LOAD1222(i79, i85, i69) → COND_LOAD12223(&&(>=(i69, 0), >(i79, i69)), i79, i85, i69)
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_74 + (-1)Bound*bni_74] + [(-1)bni_74]i69[12] ≥ 0∧0 = 0∧[(-1)bso_75] ≥ 0)

• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_76 + (-1)Bound*bni_76] + [(-1)bni_76]i69[12] ≥ 0∧0 = 0∧[(-1)bso_77] ≥ 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) = [1]
POL(FALSE) = [3]
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]
POL(<=(x1, x2)) = [-1]
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4
POL(COND_LOAD12221(x1, x2, x3, x4)) = [1] + [-1]x4 + x1
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + [-1]x4
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(COND_LOAD12222(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4

The following pairs are in P>:

LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])
LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])

The following pairs are in Pbound:

LOAD1222(i79[4], i85[4], i69[4]) → COND_LOAD12221(&&(&&(&&(<=(i85[4], i69[4]), <=(i79[4], i69[4])), >=(i69[4], 0)), >(i79[4], i69[4])), i79[4], i85[4], i69[4])
LOAD1222(i79[8], i85[8], i69[8]) → COND_LOAD12222(&&(&&(&&(>=(i69[8], 0), >(i85[8], i69[8])), <=(i79[8], i69[8])), >(i79[8], i69[8])), i79[8], i85[8], i69[8])

The following pairs are in P:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])

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

### (11) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(7) -> (12), if ((i79[7]* i79[12])∧(i69[7]* i69[12])∧(i85[7] + -1* i85[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (12) 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 LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(1)    (i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(2)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(3)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(4)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(5)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[0] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(6)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(7)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

(8)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(9)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

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

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

(12)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(13)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(14)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(15)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) which results in the following constraint:

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

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

(18)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(19)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(20)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(21)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

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

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

(24)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(25)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(26)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_43] ≥ 0)

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

(27)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

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

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

(30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] + [bni_44]i85[2] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

(36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(39)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(40)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(41)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(42)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_47] ≥ 0)

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

(48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

(49)    (i85[6]=i85[7]&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUEi69[6]=i69[7]i79[6]=i79[7]LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(50)    (<=(i79[6], i69[6])=TRUE>=(i69[6], 0)=TRUE>(i85[6], i69[6])=TRUELOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(51)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(52)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(53)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[6] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(54)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(55)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

(56)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(57)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(60)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(61)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(62)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(63)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(64)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

(65)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(66)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (67) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(69)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(70)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(71)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]i69[6] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(72)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(73)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

(74)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(75)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

We simplified constraint (76) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(78)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)

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

(79)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)

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

(80)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] + [bni_52]i85[10] ≥ 0∧[(-1)bso_53] ≥ 0)

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

(81)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

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

(82)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

For Pair COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

We simplified constraint (83) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (84) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(85)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(86)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(87)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(88)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

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

(89)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (90) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(92)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(93)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(94)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] + [bni_54]i85[10] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(95)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

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

(96)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (97) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(99)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)

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

(100)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)

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

(101)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] + [bni_56]i85[12] ≥ 0∧[(-1)bso_57] ≥ 0)

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

(102)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (102) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(103)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

We simplified constraint (104) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(106)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(107)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(108)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(109)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (109) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(110)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)

• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (111) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(113)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(114)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(115)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] + [bni_58]i85[12] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(116)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (116) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(117)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_40] + [bni_40]i85[0] ≥ 0∧[(-1)bso_41] ≥ 0)

• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

• LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]i69[2] ≥ 0∧[(-1)bso_45] ≥ 0)

• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

• LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_48] + [bni_48]i85[6] ≥ 0∧[(-1)bso_49] ≥ 0)

• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_50] + [bni_50]i85[6] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

• LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[bni_52] = 0∧[(-1)bni_52 + (-1)Bound*bni_52] + [(-1)bni_52]i69[10] ≥ 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]i69[10] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

• LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[bni_56] = 0∧[(-1)bni_56 + (-1)Bound*bni_56] + [(-1)bni_56]i69[12] ≥ 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 0)
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]i69[12] ≥ 0∧0 = 0∧[(-1)bso_59] ≥ 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) = [1]
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x2
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]
POL(<=(x1, x2)) = [-1]
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3 + x2
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3

The following pairs are in P>:

The following pairs are in Pbound:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])

The following pairs are in P:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])

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

### (14) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (15) IDependencyGraphProof (EQUIVALENT transformation)

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

### (16) 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:
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (17) 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_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(3)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(4)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(5)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(6)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

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

(7)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (8) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(10)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(11)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(12)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧[1 + (-1)bso_36] ≥ 0)

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

(13)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i69[10] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

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

(14)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

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

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

(17)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(18)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(19)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(20)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]i69[10] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

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

(21)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

We simplified constraint (22) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(24)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(25)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(26)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(27)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

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

(28)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(31)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(32)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(33)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧[1 + (-1)bso_40] ≥ 0)

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

(34)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i69[12] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

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

(35)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (36) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(38)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)

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

(39)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)

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

(40)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧[(-1)bso_42] ≥ 0)

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

(41)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]i69[12] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

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

(42)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(45)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(46)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(47)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(48)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(51)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(52)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(53)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_44] ≥ 0)

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

(54)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

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

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

(57)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

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

(58)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

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

(59)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

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

(60)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i85[2] + [(-1)bni_45]i69[2] + [bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

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

(61)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

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

(62)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

(63)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) 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(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(67)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(68)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(69)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

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

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

(72)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(73)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(74)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_48] ≥ 0)

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

(75)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)

For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(76)    (i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

We simplified constraint (76) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(77)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(78)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

(79)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

(80)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

(81)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

(82)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

(83)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [(-1)bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

(84)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] ≥ 0∧[(-1)bso_50] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_35] + [bni_35]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_36] ≥ 0)

• LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_37] + [bni_37]i79[10] ≥ 0∧0 = 0∧[(-1)bso_38] ≥ 0)

• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_40] ≥ 0)

• LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_41] + [bni_41]i79[12] ≥ 0∧0 = 0∧[(-1)bso_42] ≥ 0)

• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

• LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_45 + (-1)Bound*bni_45] + [(-1)bni_45]i79[2] ≥ 0∧[(-1)bso_46] ≥ 0)

• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_48] ≥ 0)

• LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] + [(-1)bni_49]i79[0] ≥ 0∧[(-1)bso_50] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i69[0] ≥ 0∧[(-1)bso_50] ≥ 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_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x1
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(LOAD1232(x1, x2, x3)) = [-1] + [-1]x3 + x1
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2
POL(<=(x1, x2)) = [-1]
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2

The following pairs are in P>:

The following pairs are in Pbound:

The following pairs are in P:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

### (19) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

The set Q consists of the following terms:

### (20) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

The set Q consists of the following terms:

### (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 LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

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

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

(3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [(2)bni_25]i69[2] + [(-1)bni_25]i85[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i85[2] + [(2)bni_25]i69[2] + [(-1)bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

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

(8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

(9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

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

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

(12)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)

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

(13)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)

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

(14)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[(-1)bso_28] + [-1]i69[0] + i85[0] ≥ 0)

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

(15)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

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

(16)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [(-1)bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

(17)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

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

(18)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(19)    (i79[3]=i79[0]i69[3]=i69[0]i85[3]=i85[0]i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(20)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)

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

(22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)

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

(23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[-1 + (-1)bso_30] + [-1]i69[0] + i85[0] ≥ 0)

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

(24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

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

(25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [(-1)bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

(26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

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

(27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(30)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(31)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(32)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(2)bni_31]i69[2] + [(-1)bni_31]i85[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(33)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i85[2] + [(2)bni_31]i69[2] + [(-1)bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)

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

(34)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)

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

(35)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)

(36)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [bni_25]i79[2] ≥ 0∧[(-1)bso_26] ≥ 0)

• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] + [bni_27]i79[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[0] ≥ 0∧[1 + (-1)bso_28] + i85[0] ≥ 0)

• LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] + [bni_29]i79[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i69[0] + [bni_29]i85[0] ≥ 0∧[(-1)bso_30] + i85[0] ≥ 0)

• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [bni_31]i69[2] + [bni_31]i79[2] ≥ 0∧[(-1)bso_32] + [2]i69[2] ≥ 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(LOAD1232(x1, x2, x3)) = [-1] + [2]x3 + [-1]x2 + [-1]x1
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1] + [2]x4 + [-1]x3 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(<=(x1, x2)) = [-1]
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x4 + [-1]x2 + [-1]x1
POL(LOAD1222(x1, x2, x3)) = [-1] + x2 + [-1]x1
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]

The following pairs are in P>:

The following pairs are in Pbound:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

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

### (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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

The set Q consists of the following terms:

### (25) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

### (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:

### (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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

The set Q consists of the following terms:

### (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_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(3)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(4)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(5)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] + [(-1)bni_25]i85[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] + [-2]i85[2] ≥ 0)

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

(6)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

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

(7)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

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

(8)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

(9)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

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

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

(12)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

(13)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

(14)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] + [(-1)bni_27]i85[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

(15)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

(16)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

(17)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

(18)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

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

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

(21)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(22)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(23)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]i69[0] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(24)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(25)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

(26)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

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

(27)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(28)    (i79[3]=i79[0]i69[3]=i69[0]i85[3]=i85[0]i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(29)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

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

(30)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)

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

(31)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)

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

(32)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i69[0] + [bni_31]i85[0] ≥ 0∧[-1 + (-1)bso_32] + [-2]i69[0] + [2]i85[0] ≥ 0)

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

(33)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)

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

(34)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)

(35)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)

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

(36)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i69[2] ≥ 0∧[(-1)bso_26] + [2]i69[2] ≥ 0)

• LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i69[2] ≥ 0∧[(-1)bso_28] ≥ 0)

• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-2)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i85[0] ≥ 0∧[(-1)bso_30] ≥ 0)

• LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i85[0] ≥ 0∧[1 + (-1)bso_32] + [2]i85[0] ≥ 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_LOAD1232(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x2
POL(LOAD1232(x1, x2, x3)) = [-1] + x3 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(<=(x1, x2)) = [-1]
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3 + [-1]x1
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]

The following pairs are in P>:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in Pbound:

LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

The following pairs are in P:

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

### (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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

The set Q consists of the following terms:

### (34) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

### (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 contains the following rules and edges:

The set Q consists of the following terms:

### (37) IDependencyGraphProof (EQUIVALENT transformation)

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

### (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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (40) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.

### (41) 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:
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (42) 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_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(3)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(4)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(5)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

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

(6)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i69[12] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

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

(7)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (8) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(10)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)

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

(11)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)

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

(12)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧[(-1)bso_18] ≥ 0)

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

(13)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i69[12] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)

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

(14)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_17] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_15] + [bni_15]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

• LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_17] + [bni_17]i79[12] ≥ 0∧0 = 0∧[(-1)bso_18] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = 0
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2 + [-1]x1
POL(LOAD1222(x1, x2, x3)) = [-1] + [-1]x3 + x1
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(&&(x1, x2)) = 0
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]

The following pairs are in P>:

The following pairs are in Pbound:

The following pairs are in P:

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

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

### (44) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

The set Q consists of the following terms:

### (45) IDependencyGraphProof (EQUIVALENT transformation)

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

### (47) 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:

### (48) IDependencyGraphProof (EQUIVALENT transformation)

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

### (50) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(5) -> (0), if ((i85[5]* i85[0])∧(i69[5]* i69[0])∧(i79[5]* i79[0]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(5) -> (12), if ((i85[5]* i85[12])∧(i69[5]* i69[12])∧(i79[5]* i79[12]))

(7) -> (12), if ((i79[7]* i79[12])∧(i69[7]* i69[12])∧(i85[7] + -1* i85[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (51) IDependencyGraphProof (EQUIVALENT transformation)

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

### (52) 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:
(10): LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(i69[10] >= 0 && i79[10] > i69[10], i79[10], i85[10], i69[10])
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(12): LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(i69[12] >= 0 && i79[12] > i69[12], i79[12], i85[12], i69[12])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

(1) -> (10), if ((i69[1]* i69[10])∧(i79[1]* i79[10])∧(i85[1]* i85[10]))

(10) -> (11), if ((i85[10]* i85[11])∧(i69[10] >= 0 && i79[10] > i69[10]* TRUE)∧(i69[10]* i69[11])∧(i79[10]* i79[11]))

(3) -> (12), if ((i85[3]* i85[12])∧(i69[3]* i69[12])∧(i79[3]* i79[12]))

(7) -> (12), if ((i79[7]* i79[12])∧(i69[7]* i69[12])∧(i85[7] + -1* i85[12]))

(11) -> (12), if ((i79[11] + -1* i79[12])∧(i85[11]* i85[12])∧(i69[11]* i69[12]))

(13) -> (12), if ((i69[13]* i69[12])∧(i85[13]* i85[12])∧(i79[13] + -1* i79[12]))

(12) -> (13), if ((i85[12]* i85[13])∧(i69[12]* i69[13])∧(i79[12]* i79[13])∧(i69[12] >= 0 && i79[12] > i69[12]* TRUE))

The set Q consists of the following terms:

### (53) 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_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(3)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(4)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(5)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(6)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

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

(7)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (8) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(10)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(11)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(12)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧[(-1)bso_41] ≥ 0)

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

(13)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]i69[10] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

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

(14)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

For Pair LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) the following chains were created:
• We consider the chain LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]), COND_LOAD12322(TRUE, i79[11], i85[11], i69[11]) → LOAD1222(+(i79[11], -1), i85[11], i69[11]) which results in the following constraint:

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

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

(17)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

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

(18)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

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

(19)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

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

(20)    (i69[10] ≥ 0∧i79[10] + [-1] + [-1]i69[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42] + [(-1)bni_42]i69[10] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)

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

(21)    (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)

For Pair COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

We simplified constraint (22) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(24)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(25)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(26)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(27)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(28)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

(29)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(30)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)

• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

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

(33)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(34)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(35)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(36)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(37)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

(38)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)

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

(39)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)

For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

(40)    (i85[6]=i85[7]&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUEi69[6]=i69[7]i79[6]=i79[7]LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(41)    (<=(i79[6], i69[6])=TRUE>=(i69[6], 0)=TRUE>(i85[6], i69[6])=TRUELOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(42)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

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

(43)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

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

(44)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

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

(45)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

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

(46)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

(47)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [(-1)bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)

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

(48)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] ≥ 0∧[(-1)bso_47] ≥ 0)

For Pair COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(51)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(52)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(53)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(54)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

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

(55)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

We simplified constraint (56) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(58)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(59)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(60)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧[(-1)bso_49] ≥ 0)

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

(61)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]i69[12] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

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

(62)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

For Pair LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) the following chains were created:
• We consider the chain LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]), COND_LOAD12223(TRUE, i79[13], i85[13], i69[13]) → LOAD1222(+(i79[13], -1), i85[13], i69[13]) which results in the following constraint:

We simplified constraint (63) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(65)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(66)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(67)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧[1 + (-1)bso_51] ≥ 0)

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

(68)    (i69[12] ≥ 0∧i79[12] + [-1] + [-1]i69[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50] + [(-1)bni_50]i69[12] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

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

(69)    (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50 + bni_50] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(72)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(73)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(74)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(75)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12]) which results in the following constraint:

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

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(78)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(79)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(80)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧[(-1)bso_53] ≥ 0)

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

(81)    ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

For Pair LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) the following chains were created:
• We consider the chain LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]), COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) which results in the following constraint:

We simplified constraint (82) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

We simplified constraint (83) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(84)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (84) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(85)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(86)    (i69[2] + [-1]i85[2] ≥ 0∧i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(87)    (i69[2] ≥ 0∧i85[2] + i69[2] + [-1]i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i85[2] + [(-1)bni_54]i69[2] + [bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(88)    (i69[2] ≥ 0∧i79[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

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

(89)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

(90)    (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

For Pair COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) the following chains were created:
• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2]) which results in the following constraint:

We simplified constraint (91) using rule (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(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(94)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(95)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(96)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) 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(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(100)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(101)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(102)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• We consider the chain COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]), LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10]) which results in the following constraint:

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

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

(105)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(106)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(107)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧[(-1)bso_57] ≥ 0)

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

(108)    ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) the following chains were created:
• We consider the chain LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]), COND_LOAD1222(TRUE, i79[1], i85[1], i69[1]) → LOAD1232(i79[1], i85[1], i69[1]) which results in the following constraint:

(109)    (i79[0]=i79[1]i85[0]=i85[1]i69[0]=i69[1]&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0]))=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

We simplified constraint (109) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

(110)    (<=(i79[0], i69[0])=TRUE>=(i69[0], 0)=TRUE>(i85[0], i69[0])=TRUELOAD1222(i79[0], i85[0], i69[0])≥NonInfC∧LOAD1222(i79[0], i85[0], i69[0])≥COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])∧(UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥))

We simplified constraint (110) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(111)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(112)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(113)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] + [-1] + [-1]i69[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(114)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(115)    (i69[0] + [-1]i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

(116)    (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [(-1)bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

(117)    (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] ≥ 0∧[(-1)bso_59] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[11], -1), i85[11], i69[11])), ≥)∧0 = 0∧[(-1)Bound*bni_40] + [bni_40]i79[10] ≥ 0∧0 = 0∧[(-1)bso_41] ≥ 0)

• LOAD1232(i79[10], i85[10], i69[10]) → COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])
• (i69[10] ≥ 0∧i79[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD12322(&&(>=(i69[10], 0), >(i79[10], i69[10])), i79[10], i85[10], i69[10])), ≥)∧0 = 0∧[(-1)Bound*bni_42 + bni_42] + [bni_42]i79[10] ≥ 0∧0 = 0∧[1 + (-1)bso_43] ≥ 0)

• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)
• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] + [(-1)bni_44]i79[6] ≥ 0∧[(-1)bso_45] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_44] + [(-1)bni_44]i69[6] ≥ 0∧[(-1)bso_45] ≥ 0)

• LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
• (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] + [(-1)bni_46]i79[6] ≥ 0∧[(-1)bso_47] ≥ 0)
• (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]i69[6] ≥ 0∧[(-1)bso_47] ≥ 0)

• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(LOAD1222(+(i79[13], -1), i85[13], i69[13])), ≥)∧0 = 0∧[(-1)Bound*bni_48] + [bni_48]i79[12] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)

• LOAD1222(i79[12], i85[12], i69[12]) → COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])
• (i69[12] ≥ 0∧i79[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD12223(&&(>=(i69[12], 0), >(i79[12], i69[12])), i79[12], i85[12], i69[12])), ≥)∧0 = 0∧[(-1)Bound*bni_50 + bni_50] + [bni_50]i79[12] ≥ 0∧0 = 0∧[1 + (-1)bso_51] ≥ 0)

• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
• ((UIncreasing(LOAD1222(i79[3], i85[3], i69[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

• LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)
• (i69[2] ≥ 0∧i79[2] ≥ 0∧i85[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1232(&&(<=(i85[2], i69[2]), <=(i79[2], i69[2])), i79[2], i85[2], i69[2])), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]i79[2] ≥ 0∧[(-1)bso_55] ≥ 0)

• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
• ((UIncreasing(LOAD1232(i79[1], i85[1], i69[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

• LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])
• (i69[0] + i79[0] ≥ 0∧i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] + [(-1)bni_58]i79[0] ≥ 0∧[(-1)bso_59] ≥ 0)
• (i69[0] ≥ 0∧i79[0] + i69[0] ≥ 0∧i85[0] ≥ 0∧i79[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]i69[0] ≥ 0∧[(-1)bso_59] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = [3]
POL(COND_LOAD12322(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2
POL(LOAD1222(x1, x2, x3)) = [-1]x3 + x1
POL(+(x1, x2)) = x1 + x2
POL(-1) = [-1]
POL(LOAD1232(x1, x2, x3)) = [-1]x3 + x1
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]
POL(COND_LOAD12321(x1, x2, x3, x4)) = [-1]x4 + x2
POL(<=(x1, x2)) = [-1]
POL(COND_LOAD12223(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2
POL(COND_LOAD1232(x1, x2, x3, x4)) = [-1]x4 + x2
POL(COND_LOAD1222(x1, x2, x3, x4)) = [-1]x4 + x2

The following pairs are in P>:

The following pairs are in Pbound:

The following pairs are in P:

LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])
LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0])

There are no usable rules.

### (55) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(11) -> (0), if ((i79[11] + -1* i79[0])∧(i85[11]* i85[0])∧(i69[11]* i69[0]))

(13) -> (0), if ((i69[13]* i69[0])∧(i79[13] + -1* i79[0])∧(i85[13]* i85[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

The set Q consists of the following terms:

### (56) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

### (57) Obligation:

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

The following domains are used:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(6): LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6], i79[6], i85[6], i69[6])
(2): LOAD1232(i79[2], i85[2], i69[2]) → COND_LOAD1232(i85[2] <= i69[2] && i79[2] <= i69[2], i79[2], i85[2], i69[2])
(0): LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0], i79[0], i85[0], i69[0])

(3) -> (0), if ((i79[3]* i79[0])∧(i69[3]* i69[0])∧(i85[3]* i85[0]))

(7) -> (0), if ((i85[7] + -1* i85[0])∧(i79[7]* i79[0])∧(i69[7]* i69[0]))

(0) -> (1), if ((i79[0]* i79[1])∧(i85[0]* i85[1])∧(i69[0]* i69[1])∧(i69[0] >= 0 && i85[0] > i69[0] && i79[0] <= i69[0]* TRUE))

(1) -> (2), if ((i79[1]* i79[2])∧(i69[1]* i69[2])∧(i85[1]* i85[2]))

(2) -> (3), if ((i85[2]* i85[3])∧(i69[2]* i69[3])∧(i85[2] <= i69[2] && i79[2] <= i69[2]* TRUE)∧(i79[2]* i79[3]))

(1) -> (6), if ((i79[1]* i79[6])∧(i85[1]* i85[6])∧(i69[1]* i69[6]))

(6) -> (7), if ((i85[6]* i85[7])∧(i69[6] >= 0 && i85[6] > i69[6] && i79[6] <= i69[6]* TRUE)∧(i69[6]* i69[7])∧(i79[6]* i79[7]))

The set Q consists of the following terms:

### (58) 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_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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

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

(3)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

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

(4)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

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

(5)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

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

(6)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

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

(7)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

(8)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

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

(9)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(LOAD1222(i79[7], +(i85[7], -1), i69[7])), ≥)∧[(-1)Bound*bni_30] + [bni_30]i79[6] + [bni_30]i69[6] + [bni_30]i85[6] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

For Pair LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]) the following chains were created:
• We consider the chain LOAD1232(i79[6], i85[6], i69[6]) → COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6]), COND_LOAD12321(TRUE, i79[7], i85[7], i69[7]) → LOAD1222(i79[7], +(i85[7], -1), i69[7]) which results in the following constraint:

(10)    (i85[6]=i85[7]&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6]))=TRUEi69[6]=i69[7]i79[6]=i79[7]LOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(11)    (<=(i79[6], i69[6])=TRUE>=(i69[6], 0)=TRUE>(i85[6], i69[6])=TRUELOAD1232(i79[6], i85[6], i69[6])≥NonInfC∧LOAD1232(i79[6], i85[6], i69[6])≥COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])∧(UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥))

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

(12)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(13)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(14)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] + [-1] + [-1]i69[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)bni_32 + (-1)Bound*bni_32] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(15)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(16)    (i69[6] + [-1]i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

(17)    (i69[6] + i79[6] ≥ 0∧i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

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

(18)    (i69[6] ≥ 0∧i79[6] + i69[6] ≥ 0∧i85[6] ≥ 0∧i79[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD12321(&&(&&(>=(i69[6], 0), >(i85[6], i69[6])), <=(i79[6], i69[6])), i79[6], i85[6], i69[6])), ≥)∧[(-1)Bound*bni_32] + [bni_32]i79[6] + [bni_32]i69[6] + [bni_32]i85[6] ≥ 0∧[(-1)bso_33] ≥ 0)

For Pair COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]) the following chains were created:
• We consider the chain COND_LOAD1232(TRUE, i79[3], i85[3], i69[3]) → LOAD1222(i79[3], i85[3], i69[3]), LOAD1222(i79[0], i85[0], i69[0]) → COND_LOAD1222(&&(&&(>=(i69[0], 0), >(i85[0], i69[0])), <=(i79[0], i69[0])), i79[0], i85[0], i69[0]) which results in the following constraint:

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