### (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: GCD2

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 204 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:
Load995(i86, i90) → Cond_Load995(i86 >= 0 && i90 > 0 && !(i86 = i90), i86, i90)
Load1160(i90, i90, i90, i104, i90) → Cond_Load1160(i90 > 0 && i104 > i90, i90, i90, i90, i104, i90)
Cond_Load1160(TRUE, i90, i90, i90, i104, i90) → Load1160(i90, i90, i90, i104 - i90, i90)
Cond_Load9951(TRUE, i90, i90) → Store1193(i90, i90, 0)
Store1193(i90, i90, i104) → Load995(i90, i104)
Load1160(i90, i90, i90, i104, i90) → Cond_Load11601(i90 > 0 && i104 <= i90, i90, i90, i90, i104, i90)
The set Q consists of the following terms:
Cond_Load1160(TRUE, x0, x0, x0, x1, x0)
Store1193(x0, x0, x1)
Cond_Load11601(TRUE, x0, x0, x0, x1, x0)

### (5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

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

Store1193(x1, x2, x3) → Store1193(x2, x3)

### (6) Obligation:

ITRS problem:

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

The TRS R consists of the following rules:
Load995(i86, i90) → Cond_Load995(i86 >= 0 && i90 > 0 && !(i86 = i90), i86, i90)
Load1160(i104, i90) → Cond_Load1160(i90 > 0 && i104 > i90, i104, i90)
Load1160(i104, i90) → Cond_Load11601(i90 > 0 && i104 <= i90, i104, i90)
The set Q consists of the following terms:
Store1193(x0, x1)

### (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

The ITRS R consists of the following rules:
Load995(i86, i90) → Cond_Load995(i86 >= 0 && i90 > 0 && !(i86 = i90), i86, i90)
Load1160(i104, i90) → Cond_Load1160(i90 > 0 && i104 > i90, i104, i90)
Load1160(i104, i90) → Cond_Load11601(i90 > 0 && i104 <= i90, i104, i90)

The integer pair graph contains the following rules and edges:
(0): LOAD995(i86[0], i90[0]) → COND_LOAD995(i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]), i86[0], i90[0])
(2): LOAD1160(i104[2], i90[2]) → COND_LOAD1160(i90[2] > 0 && i104[2] > i90[2], i104[2], i90[2])
(5): COND_LOAD9951(TRUE, i90[5]) → STORE1193(i90[5], 0)
(6): STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6])
(7): LOAD1160(i104[7], i90[7]) → COND_LOAD11601(i90[7] > 0 && i104[7] <= i90[7], i104[7], i90[7])

(0) -> (1), if ((i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]) →* TRUE)∧(i86[0]* i86[1])∧(i90[0]* i90[1]))

(1) -> (2), if ((i90[1]* i90[2])∧(i86[1]* i104[2]))

(1) -> (7), if ((i86[1]* i104[7])∧(i90[1]* i90[7]))

(2) -> (3), if ((i90[2]* i90[3])∧(i90[2] > 0 && i104[2] > i90[2]* TRUE)∧(i104[2]* i104[3]))

(3) -> (2), if ((i90[3]* i90[2])∧(i104[3] - i90[3]* i104[2]))

(3) -> (7), if ((i90[3]* i90[7])∧(i104[3] - i90[3]* i104[7]))

(4) -> (5), if ((i90[4]* i90[5])∧(i90[4] > 0* TRUE))

(5) -> (6), if ((i90[5]* i90[6])∧(0* i104[6]))

(6) -> (0), if ((i104[6]* i90[0])∧(i90[6]* i86[0]))

(6) -> (4), if ((i90[6]* i90[4])∧(i104[6]* i90[4]))

(7) -> (8), if ((i104[7]* i104[8])∧(i90[7] > 0 && i104[7] <= i90[7]* TRUE)∧(i90[7]* i90[8]))

(8) -> (0), if ((i104[8]* i90[0])∧(i90[8]* i86[0]))

(8) -> (4), if ((i104[8]* i90[4])∧(i90[8]* i90[4]))

The set Q consists of the following terms:
Store1193(x0, x1)

### (9) UsableRulesProof (EQUIVALENT transformation)

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

### (10) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD995(i86[0], i90[0]) → COND_LOAD995(i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]), i86[0], i90[0])
(2): LOAD1160(i104[2], i90[2]) → COND_LOAD1160(i90[2] > 0 && i104[2] > i90[2], i104[2], i90[2])
(5): COND_LOAD9951(TRUE, i90[5]) → STORE1193(i90[5], 0)
(6): STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6])
(7): LOAD1160(i104[7], i90[7]) → COND_LOAD11601(i90[7] > 0 && i104[7] <= i90[7], i104[7], i90[7])

(0) -> (1), if ((i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]) →* TRUE)∧(i86[0]* i86[1])∧(i90[0]* i90[1]))

(1) -> (2), if ((i90[1]* i90[2])∧(i86[1]* i104[2]))

(1) -> (7), if ((i86[1]* i104[7])∧(i90[1]* i90[7]))

(2) -> (3), if ((i90[2]* i90[3])∧(i90[2] > 0 && i104[2] > i90[2]* TRUE)∧(i104[2]* i104[3]))

(3) -> (2), if ((i90[3]* i90[2])∧(i104[3] - i90[3]* i104[2]))

(3) -> (7), if ((i90[3]* i90[7])∧(i104[3] - i90[3]* i104[7]))

(4) -> (5), if ((i90[4]* i90[5])∧(i90[4] > 0* TRUE))

(5) -> (6), if ((i90[5]* i90[6])∧(0* i104[6]))

(6) -> (0), if ((i104[6]* i90[0])∧(i90[6]* i86[0]))

(6) -> (4), if ((i90[6]* i90[4])∧(i104[6]* i90[4]))

(7) -> (8), if ((i104[7]* i104[8])∧(i90[7] > 0 && i104[7] <= i90[7]* TRUE)∧(i90[7]* i90[8]))

(8) -> (0), if ((i104[8]* i90[0])∧(i90[8]* i86[0]))

(8) -> (4), if ((i104[8]* i90[4])∧(i90[8]* i90[4]))

The set Q consists of the following terms:
Store1193(x0, x1)

### (11) IDPNonInfProof (SOUND transformation)

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

For Pair LOAD995(i86, i90) → COND_LOAD995(&&(&&(>=(i86, 0), >(i90, 0)), !(=(i86, i90))), i86, i90) the following chains were created:
• We consider the chain LOAD995(i86[0], i90[0]) → COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0]), COND_LOAD995(TRUE, i86[1], i90[1]) → LOAD1160(i86[1], i90[1]) which results in the following constraint:

(1)    (&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0])))=TRUEi86[0]=i86[1]i90[0]=i90[1]LOAD995(i86[0], i90[0])≥NonInfC∧LOAD995(i86[0], i90[0])≥COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])∧(UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥))

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

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

(4)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(5)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(6)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(7)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(8)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(9)    (i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(10)    (i86[0] ≥ 0∧i90[0] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33] + [bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(11)    ([1] + i90[0] + i86[0] ≥ 0∧i90[0] + [-1] ≥ 0∧i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33] + [(2)bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(12)    (i86[0] ≥ 0∧i86[0] + i90[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33] + [(2)bni_33]i86[0] + [bni_33]i90[0] ≥ 0∧[(-1)bso_34] ≥ 0)

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

(13)    ([2] + i90[0] + i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33 + (2)bni_33] + [(2)bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

For Pair COND_LOAD995(TRUE, i86, i90) → LOAD1160(i86, i90) the following chains were created:
• We consider the chain COND_LOAD995(TRUE, i86[1], i90[1]) → LOAD1160(i86[1], i90[1]), LOAD1160(i104[2], i90[2]) → COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2]) which results in the following constraint:

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

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

(16)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(17)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(18)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(19)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

• We consider the chain COND_LOAD995(TRUE, i86[1], i90[1]) → LOAD1160(i86[1], i90[1]), LOAD1160(i104[7], i90[7]) → COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7]) which results in the following constraint:

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

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

(22)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(23)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(24)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)bso_36] ≥ 0)

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

(25)    ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

For Pair LOAD1160(i104, i90) → COND_LOAD1160(&&(>(i90, 0), >(i104, i90)), i104, i90) the following chains were created:
• We consider the chain LOAD1160(i104[2], i90[2]) → COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2]), COND_LOAD1160(TRUE, i104[3], i90[3]) → LOAD1160(-(i104[3], i90[3]), i90[3]) which results in the following constraint:

We simplified constraint (26) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(28)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(29)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(30)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(31)    (i90[2] ≥ 0∧i104[2] + [-2] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)Bound*bni_37] + [bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

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

(32)    (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)Bound*bni_37 + (2)bni_37] + [(2)bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

For Pair COND_LOAD1160(TRUE, i104, i90) → LOAD1160(-(i104, i90), i90) the following chains were created:
• We consider the chain LOAD1160(i104[2], i90[2]) → COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2]), COND_LOAD1160(TRUE, i104[3], i90[3]) → LOAD1160(-(i104[3], i90[3]), i90[3]), LOAD1160(i104[2], i90[2]) → COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2]) which results in the following constraint:

We simplified constraint (33) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(35)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(36)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(37)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(38)    (i90[2] ≥ 0∧i104[2] + [-2] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)

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

(39)    (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39 + (2)bni_39] + [(2)bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)

• We consider the chain LOAD1160(i104[2], i90[2]) → COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2]), COND_LOAD1160(TRUE, i104[3], i90[3]) → LOAD1160(-(i104[3], i90[3]), i90[3]), LOAD1160(i104[7], i90[7]) → COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7]) which results in the following constraint:

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

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

(42)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(43)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(44)    (i90[2] + [-1] ≥ 0∧i104[2] + [-1] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[(-1)bso_40] + i90[2] ≥ 0)

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

(45)    (i90[2] ≥ 0∧i104[2] + [-2] + [-1]i90[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)

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

(46)    (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39 + (2)bni_39] + [(2)bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)

For Pair LOAD995(i90, i90) → COND_LOAD9951(>(i90, 0), i90) the following chains were created:
• We consider the chain LOAD995(i90[4], i90[4]) → COND_LOAD9951(>(i90[4], 0), i90[4]), COND_LOAD9951(TRUE, i90[5]) → STORE1193(i90[5], 0) which results in the following constraint:

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

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

(49)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD9951(>(i90[4], 0), i90[4])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(2)bni_41]i90[4] ≥ 0∧[-1 + (-1)bso_42] + i90[4] ≥ 0)

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

(50)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD9951(>(i90[4], 0), i90[4])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(2)bni_41]i90[4] ≥ 0∧[-1 + (-1)bso_42] + i90[4] ≥ 0)

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

(51)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD9951(>(i90[4], 0), i90[4])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(2)bni_41]i90[4] ≥ 0∧[-1 + (-1)bso_42] + i90[4] ≥ 0)

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

(52)    (i90[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD9951(>(i90[4], 0), i90[4])), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(2)bni_41]i90[4] ≥ 0∧[(-1)bso_42] + i90[4] ≥ 0)

For Pair COND_LOAD9951(TRUE, i90) → STORE1193(i90, 0) the following chains were created:
• We consider the chain LOAD995(i90[4], i90[4]) → COND_LOAD9951(>(i90[4], 0), i90[4]), COND_LOAD9951(TRUE, i90[5]) → STORE1193(i90[5], 0), STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6]) which results in the following constraint:

We simplified constraint (53) using rules (III), (IV) which results in the following new constraint:

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

(55)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(STORE1193(i90[5], 0)), ≥)∧[(-1)Bound*bni_43] + [bni_43]i90[4] ≥ 0∧[(-1)bso_44] ≥ 0)

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

(56)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(STORE1193(i90[5], 0)), ≥)∧[(-1)Bound*bni_43] + [bni_43]i90[4] ≥ 0∧[(-1)bso_44] ≥ 0)

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

(57)    (i90[4] + [-1] ≥ 0 ⇒ (UIncreasing(STORE1193(i90[5], 0)), ≥)∧[(-1)Bound*bni_43] + [bni_43]i90[4] ≥ 0∧[(-1)bso_44] ≥ 0)

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

(58)    (i90[4] ≥ 0 ⇒ (UIncreasing(STORE1193(i90[5], 0)), ≥)∧[(-1)Bound*bni_43 + bni_43] + [bni_43]i90[4] ≥ 0∧[(-1)bso_44] ≥ 0)

For Pair STORE1193(i90, i104) → LOAD995(i90, i104) the following chains were created:
• We consider the chain STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6]), LOAD995(i86[0], i90[0]) → COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0]) which results in the following constraint:

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

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

(61)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(62)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(63)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(64)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_46] ≥ 0)

• We consider the chain STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6]), LOAD995(i90[4], i90[4]) → COND_LOAD9951(>(i90[4], 0), i90[4]) which results in the following constraint:

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

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

(67)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(68)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(69)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧[1 + (-1)bso_46] ≥ 0)

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

(70)    ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧0 = 0∧[1 + (-1)bso_46] ≥ 0)

For Pair LOAD1160(i104, i90) → COND_LOAD11601(&&(>(i90, 0), <=(i104, i90)), i104, i90) the following chains were created:
• We consider the chain LOAD1160(i104[7], i90[7]) → COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7]), COND_LOAD11601(TRUE, i104[8], i90[8]) → LOAD995(i90[8], i104[8]) which results in the following constraint:

We simplified constraint (71) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(73)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

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

(74)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

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

(75)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

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

(76)    (i90[7] ≥ 0∧[1] + i90[7] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

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

(77)    (i90[7] ≥ 0∧[1] + i90[7] + [-1]i104[7] ≥ 0∧i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

(78)    (i90[7] ≥ 0∧[1] + i90[7] + i104[7] ≥ 0∧i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_47] + [bni_47]i90[7] + [(-1)bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

For Pair COND_LOAD11601(TRUE, i104, i90) → LOAD995(i90, i104) the following chains were created:
• We consider the chain COND_LOAD11601(TRUE, i104[8], i90[8]) → LOAD995(i90[8], i104[8]), LOAD995(i86[0], i90[0]) → COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0]) which results in the following constraint:

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

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

(81)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

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

(82)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

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

(83)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

(84)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_50] ≥ 0)

• We consider the chain COND_LOAD11601(TRUE, i104[8], i90[8]) → LOAD995(i90[8], i104[8]), LOAD995(i90[4], i90[4]) → COND_LOAD9951(>(i90[4], 0), i90[4]) which results in the following constraint:

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

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

(87)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

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

(88)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

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

(89)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)bso_50] ≥ 0)

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

(90)    ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧0 = 0∧[(-1)bso_50] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD995(i86, i90) → COND_LOAD995(&&(&&(>=(i86, 0), >(i90, 0)), !(=(i86, i90))), i86, i90)
• (i86[0] ≥ 0∧i86[0] + i90[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33] + [(2)bni_33]i86[0] + [bni_33]i90[0] ≥ 0∧[(-1)bso_34] ≥ 0)
• ([2] + i90[0] + i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_33 + (2)bni_33] + [(2)bni_33]i90[0] + [bni_33]i86[0] ≥ 0∧[(-1)bso_34] ≥ 0)

• ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)
• ((UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_36] ≥ 0)

• (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1160(&&(>(i90[2], 0), >(i104[2], i90[2])), i104[2], i90[2])), ≥)∧[(-1)Bound*bni_37 + (2)bni_37] + [(2)bni_37]i90[2] + [bni_37]i104[2] ≥ 0∧[(-1)bso_38] ≥ 0)

• (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39 + (2)bni_39] + [(2)bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)
• (i90[2] ≥ 0∧i104[2] ≥ 0 ⇒ (UIncreasing(LOAD1160(-(i104[3], i90[3]), i90[3])), ≥)∧[(-1)Bound*bni_39 + (2)bni_39] + [(2)bni_39]i90[2] + [bni_39]i104[2] ≥ 0∧[1 + (-1)bso_40] + i90[2] ≥ 0)

• (i90[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD9951(>(i90[4], 0), i90[4])), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(2)bni_41]i90[4] ≥ 0∧[(-1)bso_42] + i90[4] ≥ 0)

• COND_LOAD9951(TRUE, i90) → STORE1193(i90, 0)
• (i90[4] ≥ 0 ⇒ (UIncreasing(STORE1193(i90[5], 0)), ≥)∧[(-1)Bound*bni_43 + bni_43] + [bni_43]i90[4] ≥ 0∧[(-1)bso_44] ≥ 0)

• STORE1193(i90, i104) → LOAD995(i90, i104)
• ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_46] ≥ 0)
• ((UIncreasing(LOAD995(i90[6], i104[6])), ≥)∧0 = 0∧[1 + (-1)bso_46] ≥ 0)

• (i90[7] ≥ 0∧[1] + i90[7] + [-1]i104[7] ≥ 0∧i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_47] + [bni_47]i90[7] + [bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)
• (i90[7] ≥ 0∧[1] + i90[7] + i104[7] ≥ 0∧i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_47] + [bni_47]i90[7] + [(-1)bni_47]i104[7] ≥ 0∧[(-1)bso_48] ≥ 0)

• ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_50] ≥ 0)
• ((UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧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) = [2]
POL(LOAD995(x1, x2)) = [-1] + x2 + x1
POL(COND_LOAD995(x1, x2, x3)) = [-1] + x3 + x2 + [-1]x1
POL(&&(x1, x2)) = 0
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(>(x1, x2)) = [-1]
POL(!(x1)) = [-1]
POL(=(x1, x2)) = [-1]
POL(LOAD1160(x1, x2)) = [-1] + x2 + x1
POL(COND_LOAD1160(x1, x2, x3)) = [-1] + x3 + x2 + [-1]x1
POL(-(x1, x2)) = x1 + [-1]x2
POL(STORE1193(x1, x2)) = x2 + x1
POL(COND_LOAD11601(x1, x2, x3)) = [-1] + x3 + x2 + [-1]x1
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
FALSE1&&(TRUE, FALSE)1
FALSE1&&(FALSE, TRUE)1
FALSE1&&(FALSE, FALSE)1

### (13) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD995(i86[0], i90[0]) → COND_LOAD995(i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]), i86[0], i90[0])
(2): LOAD1160(i104[2], i90[2]) → COND_LOAD1160(i90[2] > 0 && i104[2] > i90[2], i104[2], i90[2])
(5): COND_LOAD9951(TRUE, i90[5]) → STORE1193(i90[5], 0)
(7): LOAD1160(i104[7], i90[7]) → COND_LOAD11601(i90[7] > 0 && i104[7] <= i90[7], i104[7], i90[7])

(8) -> (0), if ((i104[8]* i90[0])∧(i90[8]* i86[0]))

(0) -> (1), if ((i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]) →* TRUE)∧(i86[0]* i86[1])∧(i90[0]* i90[1]))

(1) -> (2), if ((i90[1]* i90[2])∧(i86[1]* i104[2]))

(8) -> (4), if ((i104[8]* i90[4])∧(i90[8]* i90[4]))

(4) -> (5), if ((i90[4]* i90[5])∧(i90[4] > 0* TRUE))

(1) -> (7), if ((i86[1]* i104[7])∧(i90[1]* i90[7]))

(7) -> (8), if ((i104[7]* i104[8])∧(i90[7] > 0 && i104[7] <= i90[7]* TRUE)∧(i90[7]* i90[8]))

The set Q consists of the following terms:
Store1193(x0, x1)

### (14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

### (15) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(7): LOAD1160(i104[7], i90[7]) → COND_LOAD11601(i90[7] > 0 && i104[7] <= i90[7], i104[7], i90[7])
(0): LOAD995(i86[0], i90[0]) → COND_LOAD995(i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]), i86[0], i90[0])

(8) -> (0), if ((i104[8]* i90[0])∧(i90[8]* i86[0]))

(0) -> (1), if ((i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]) →* TRUE)∧(i86[0]* i86[1])∧(i90[0]* i90[1]))

(1) -> (7), if ((i86[1]* i104[7])∧(i90[1]* i90[7]))

(7) -> (8), if ((i104[7]* i104[8])∧(i90[7] > 0 && i104[7] <= i90[7]* TRUE)∧(i90[7]* i90[8]))

The set Q consists of the following terms:
Store1193(x0, x1)

### (16) IDPNonInfProof (SOUND transformation)

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

For Pair COND_LOAD11601(TRUE, i104[8], i90[8]) → LOAD995(i90[8], i104[8]) the following chains were created:

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)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(4)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(6)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(8)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(10)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(11)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(12)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(13)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(14)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

We solved constraint (11) using rule (IDP_SMT_SPLIT).We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(15)    (i90[0] ≥ 0∧[1] + i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧[1] + i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23 + (-1)bni_23] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

We solved constraint (13) using rule (IDP_SMT_SPLIT).We solved constraint (14) using rule (IDP_SMT_SPLIT).We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(16)    (i86[0] + i90[0] ≥ 0∧[1] + i90[0] ≥ 0∧i86[0] ≥ 0∧[1] + i86[0] + i90[0] ≥ 0∧i86[0] + [-1] ≥ 0∧i90[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23 + (-1)bni_23] + [(-1)bni_23]i86[0] + [(-1)bni_23]i90[0] ≥ 0∧[-1 + (-1)bso_24] + i86[0] ≥ 0)

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

(17)    ([1] + i86[0] + i90[0] ≥ 0∧[1] + i90[0] ≥ 0∧[1] + i86[0] ≥ 0∧[2] + i86[0] + i90[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23 + (-2)bni_23] + [(-1)bni_23]i86[0] + [(-1)bni_23]i90[0] ≥ 0∧[(-1)bso_24] + i86[0] ≥ 0)

For Pair LOAD1160(i104[7], i90[7]) → COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7]) the following chains were created:

(18)    (i104[8]=i90[0]i90[8]=i86[0]&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0])))=TRUEi86[0]=i86[1]i90[0]=i90[1]i86[1]=i104[7]i90[1]=i90[7]i104[7]=i104[8]1&&(>(i90[7], 0), <=(i104[7], i90[7]))=TRUEi90[7]=i90[8]1i104[8]1=i90[0]1i90[8]1=i86[0]1LOAD1160(i104[7], i90[7])≥NonInfC∧LOAD1160(i104[7], i90[7])≥COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])∧(UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥))

We simplified constraint (18) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

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

(20)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[-1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

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

(21)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[-1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

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

(23)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[-1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

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

(24)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] + [-1] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[-1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

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

(25)    (i90[0] + [-1] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i86[0] + [-1] + [-1]i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[-1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

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

(26)    (i90[0] ≥ 0∧[1] + i90[0] + [-1]i86[0] ≥ 0∧i86[0] ≥ 0∧i90[0] + [-1]i86[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i90[0] + [(-1)bni_25]i86[0] ≥ 0∧[1 + (-1)bso_26] + [2]i90[0] + [-1]i86[0] ≥ 0)

We solved constraint (25) using rule (IDP_SMT_SPLIT).We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(27)    (i86[0] + i90[0] ≥ 0∧[1] + i90[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i90[0] ≥ 0∧[1 + (-1)bso_26] + i86[0] + [2]i90[0] ≥ 0)

For Pair COND_LOAD995(TRUE, i86[1], i90[1]) → LOAD1160(i86[1], i90[1]) the following chains were created:

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)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1]i90[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)Bound*bni_27] + [(-1)bni_27]i104[7] + [(-1)bni_27]i90[7] ≥ 0∧[1 + (-1)bso_28] + [-2]i104[7] ≥ 0)

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

(31)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1]i90[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)Bound*bni_27] + [(-1)bni_27]i104[7] + [(-1)bni_27]i90[7] ≥ 0∧[1 + (-1)bso_28] + [-2]i104[7] ≥ 0)

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

(33)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1]i90[7] ≥ 0∧i90[7] ≥ 0∧i90[7] + [-1] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)Bound*bni_27] + [(-1)bni_27]i104[7] + [(-1)bni_27]i90[7] ≥ 0∧[1 + (-1)bso_28] + [-2]i104[7] ≥ 0)

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

(34)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1]i90[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)Bound*bni_27] + [(-1)bni_27]i104[7] + [(-1)bni_27]i90[7] ≥ 0∧[1 + (-1)bso_28] + [-2]i104[7] ≥ 0)

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

(35)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1]i90[7] ≥ 0∧i90[7] ≥ 0∧i90[7] + [-1] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(LOAD1160(i86[1], i90[1])), ≥)∧[(-1)Bound*bni_27] + [(-1)bni_27]i104[7] + [(-1)bni_27]i90[7] ≥ 0∧[1 + (-1)bso_28] + [-2]i104[7] ≥ 0)

We solved constraint (34) using rule (IDP_SMT_SPLIT).We solved constraint (35) using rule (IDP_SMT_SPLIT).

For Pair LOAD995(i86[0], i90[0]) → COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0]) the following chains were created:

(36)    (i86[1]=i104[7]i90[1]=i90[7]i104[7]=i104[8]&&(>(i90[7], 0), <=(i104[7], i90[7]))=TRUEi90[7]=i90[8]i104[8]=i90[0]i90[8]=i86[0]&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0])))=TRUEi86[0]=i86[1]1i90[0]=i90[1]1i86[1]1=i104[7]1i90[1]1=i90[7]1LOAD995(i86[0], i90[0])≥NonInfC∧LOAD995(i86[0], i90[0])≥COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])∧(UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥))

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

(37)    (>(i90[7], 0)=TRUE<=(i104[7], i90[7])=TRUE>=(i90[7], 0)=TRUE>(i104[7], 0)=TRUE<(i90[7], i104[7])=TRUELOAD995(i90[7], i104[7])≥NonInfC∧LOAD995(i90[7], i104[7])≥COND_LOAD995(&&(&&(>=(i90[7], 0), >(i104[7], 0)), !(=(i90[7], i104[7]))), i90[7], i104[7])∧(UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥))

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

(38)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(39)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(41)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i90[7] + [-1] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(42)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i104[7] + [-1] + [-1]i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(43)    (i90[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0∧i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i90[7] + [-1] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

We solved constraint (42) using rule (IDP_SMT_SPLIT).We simplified constraint (43) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(44)    (i90[7] ≥ 0∧[1] + i90[7] + [-1]i104[7] ≥ 0∧[1] + i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i90[7] + [-1]i104[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_29] + [(-1)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(45)    (i104[7] + i90[7] ≥ 0∧[1] + i90[7] ≥ 0∧[1] + i104[7] + i90[7] ≥ 0∧i104[7] + [-1] ≥ 0∧i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_29] + [(-2)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

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

(46)    ([1] + i104[7] + i90[7] ≥ 0∧[1] + i90[7] ≥ 0∧[2] + i104[7] + i90[7] ≥ 0∧i104[7] ≥ 0∧i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_29 + (-2)bni_29] + [(-2)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• ([1] + i86[0] + i90[0] ≥ 0∧[1] + i90[0] ≥ 0∧[1] + i86[0] ≥ 0∧[2] + i86[0] + i90[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(LOAD995(i90[8], i104[8])), ≥)∧[(-1)Bound*bni_23 + (-2)bni_23] + [(-1)bni_23]i86[0] + [(-1)bni_23]i90[0] ≥ 0∧[(-1)bso_24] + i86[0] ≥ 0)

• (i86[0] + i90[0] ≥ 0∧[1] + i90[0] ≥ 0∧i86[0] ≥ 0∧i90[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD11601(&&(>(i90[7], 0), <=(i104[7], i90[7])), i104[7], i90[7])), ≥)∧[(-1)Bound*bni_25] + [bni_25]i90[0] ≥ 0∧[1 + (-1)bso_26] + i86[0] + [2]i90[0] ≥ 0)

• LOAD995(i86[0], i90[0]) → COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])
• ([1] + i104[7] + i90[7] ≥ 0∧[1] + i90[7] ≥ 0∧[2] + i104[7] + i90[7] ≥ 0∧i104[7] ≥ 0∧i90[7] ≥ 0 ⇒ (UIncreasing(COND_LOAD995(&&(&&(>=(i86[0], 0), >(i90[0], 0)), !(=(i86[0], i90[0]))), i86[0], i90[0])), ≥)∧[(-1)Bound*bni_29 + (-2)bni_29] + [(-2)bni_29]i104[7] + [(-1)bni_29]i90[7] ≥ 0∧[1 + (-1)bso_30] ≥ 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) = [1]
POL(COND_LOAD11601(x1, x2, x3)) = [1] + [-1]x3 + [-1]x1
POL(LOAD995(x1, x2)) = [1] + [-1]x2 + [-1]x1
POL(LOAD1160(x1, x2)) = [-1] + x2 + [-1]x1
POL(&&(x1, x2)) = [1]
POL(>(x1, x2)) = [-1]
POL(0) = 0
POL(<=(x1, x2)) = [-1]
POL(COND_LOAD995(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2 + x1
POL(>=(x1, x2)) = [-1]
POL(!(x1)) = [-1]
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

### (18) Obligation:

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

The following domains are used:
none

R is empty.

The integer pair graph contains the following rules and edges:

The set Q consists of the following terms:
Store1193(x0, x1)

### (19) IDependencyGraphProof (EQUIVALENT transformation)

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

### (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:
(0): LOAD995(i86[0], i90[0]) → COND_LOAD995(i86[0] >= 0 && i90[0] > 0 && !(i86[0] = i90[0]), i86[0], i90[0])

(8) -> (0), if ((i104[8]* i90[0])∧(i90[8]* i86[0]))

The set Q consists of the following terms:
Store1193(x0, x1)

### (22) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

### (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:
(6): STORE1193(i90[6], i104[6]) → LOAD995(i90[6], i104[6])
(7): LOAD1160(i104[7], i90[7]) → COND_LOAD11601(i90[7] > 0 && i104[7] <= i90[7], i104[7], i90[7])

(1) -> (7), if ((i86[1]* i104[7])∧(i90[1]* i90[7]))

(7) -> (8), if ((i104[7]* i104[8])∧(i90[7] > 0 && i104[7] <= i90[7]* TRUE)∧(i90[7]* i90[8]))

The set Q consists of the following terms: