### (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: PastaB11

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 180 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:
Load777(i96, i134) → Cond_Load777(i96 < i134 && i96 + i134 > 0, i96, i134)
Load777(i96, i134) → Cond_Load7772(i96 > i134 && i96 + i134 > 0, i96, i134)
The set Q consists of the following terms:

### (5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

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

### (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:
Load777(i96, i134) → Cond_Load777(i96 < i134 && i96 + i134 > 0, i96, i134)
Load777(i96, i134) → Cond_Load7772(i96 > i134 && i96 + i134 > 0, i96, i134)
The set Q consists of the following terms:

### (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:
Load777(i96, i134) → Cond_Load777(i96 < i134 && i96 + i134 > 0, i96, i134)
Load777(i96, i134) → Cond_Load7772(i96 > i134 && i96 + i134 > 0, i96, i134)

The integer pair graph contains the following rules and edges:
(0): LOAD777(i96[0], i134[0]) → COND_LOAD777(i96[0] < i134[0] && i96[0] + i134[0] > 0, i96[0], i134[0])
(4): LOAD777(i96[4], i134[4]) → COND_LOAD7772(i96[4] > i134[4] && i96[4] + i134[4] > 0, i96[4], i134[4])

(0) -> (1), if ((i134[0]* i134[1])∧(i96[0] < i134[0] && i96[0] + i134[0] > 0* TRUE)∧(i96[0]* i96[1]))

(1) -> (0), if ((i134[1] + -1* i134[0])∧(i96[1]* i96[0]))

(1) -> (2), if ((i134[1] + -1* i134[2])∧(i96[1]* i134[2]))

(1) -> (4), if ((i96[1]* i96[4])∧(i134[1] + -1* i134[4]))

(2) -> (3), if ((i134[2] + i134[2] > 0* TRUE)∧(i134[2]* i134[3]))

(3) -> (0), if ((i134[3] + -1* i96[0])∧(i134[3]* i134[0]))

(3) -> (2), if ((i134[3] + -1* i134[2])∧(i134[3]* i134[2]))

(3) -> (4), if ((i134[3] + -1* i96[4])∧(i134[3]* i134[4]))

(4) -> (5), if ((i96[4]* i96[5])∧(i96[4] > i134[4] && i96[4] + i134[4] > 0* TRUE)∧(i134[4]* i134[5]))

(5) -> (0), if ((i134[5]* i134[0])∧(i96[5] + -1* i96[0]))

(5) -> (2), if ((i96[5] + -1* i134[2])∧(i134[5]* i134[2]))

(5) -> (4), if ((i134[5]* i134[4])∧(i96[5] + -1* i96[4]))

The set Q consists of the following terms:

### (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): LOAD777(i96[0], i134[0]) → COND_LOAD777(i96[0] < i134[0] && i96[0] + i134[0] > 0, i96[0], i134[0])
(4): LOAD777(i96[4], i134[4]) → COND_LOAD7772(i96[4] > i134[4] && i96[4] + i134[4] > 0, i96[4], i134[4])

(0) -> (1), if ((i134[0]* i134[1])∧(i96[0] < i134[0] && i96[0] + i134[0] > 0* TRUE)∧(i96[0]* i96[1]))

(1) -> (0), if ((i134[1] + -1* i134[0])∧(i96[1]* i96[0]))

(1) -> (2), if ((i134[1] + -1* i134[2])∧(i96[1]* i134[2]))

(1) -> (4), if ((i96[1]* i96[4])∧(i134[1] + -1* i134[4]))

(2) -> (3), if ((i134[2] + i134[2] > 0* TRUE)∧(i134[2]* i134[3]))

(3) -> (0), if ((i134[3] + -1* i96[0])∧(i134[3]* i134[0]))

(3) -> (2), if ((i134[3] + -1* i134[2])∧(i134[3]* i134[2]))

(3) -> (4), if ((i134[3] + -1* i96[4])∧(i134[3]* i134[4]))

(4) -> (5), if ((i96[4]* i96[5])∧(i96[4] > i134[4] && i96[4] + i134[4] > 0* TRUE)∧(i134[4]* i134[5]))

(5) -> (0), if ((i134[5]* i134[0])∧(i96[5] + -1* i96[0]))

(5) -> (2), if ((i96[5] + -1* i134[2])∧(i134[5]* i134[2]))

(5) -> (4), if ((i134[5]* i134[4])∧(i96[5] + -1* i96[4]))

The set Q consists of the following terms:

### (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 LOAD777(i96, i134) → COND_LOAD777(&&(<(i96, i134), >(+(i96, i134), 0)), i96, i134) the following chains were created:
• We consider the chain LOAD777(i96[0], i134[0]) → COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0]), COND_LOAD777(TRUE, i96[1], i134[1]) → LOAD777(i96[1], +(i134[1], -1)) which results in the following constraint:

We simplified constraint (1) using rules (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)    (i134[0] + [-1] + [-1]i96[0] ≥ 0∧i96[0] + [-1] + i134[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]i134[0] + [bni_13]i96[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(4)    (i134[0] + [-1] + [-1]i96[0] ≥ 0∧i96[0] + [-1] + i134[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]i134[0] + [bni_13]i96[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(5)    (i134[0] + [-1] + [-1]i96[0] ≥ 0∧i96[0] + [-1] + i134[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]i134[0] + [bni_13]i96[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(6)    (i134[0] ≥ 0∧[2]i96[0] + i134[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [(2)bni_13]i96[0] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(7)    (i134[0] ≥ 0∧[2]i96[0] + i134[0] ≥ 0∧i96[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [(2)bni_13]i96[0] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

(8)    (i134[0] ≥ 0∧[-2]i96[0] + i134[0] ≥ 0∧i96[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [(-2)bni_13]i96[0] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

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

(9)    ([2]i96[0] + i134[0] ≥ 0∧i134[0] ≥ 0∧i96[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

For Pair COND_LOAD777(TRUE, i96, i134) → LOAD777(i96, +(i134, -1)) the following chains were created:
• We consider the chain COND_LOAD777(TRUE, i96[1], i134[1]) → LOAD777(i96[1], +(i134[1], -1)) which results in the following constraint:

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

(11)    ((UIncreasing(LOAD777(i96[1], +(i134[1], -1))), ≥)∧[(-1)bso_16] ≥ 0)

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

(12)    ((UIncreasing(LOAD777(i96[1], +(i134[1], -1))), ≥)∧[(-1)bso_16] ≥ 0)

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

(13)    ((UIncreasing(LOAD777(i96[1], +(i134[1], -1))), ≥)∧[(-1)bso_16] ≥ 0)

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

(14)    ((UIncreasing(LOAD777(i96[1], +(i134[1], -1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

For Pair LOAD777(i134, i134) → COND_LOAD7771(>(+(i134, i134), 0), i134) the following chains were created:
• We consider the chain LOAD777(i134[2], i134[2]) → COND_LOAD7771(>(+(i134[2], i134[2]), 0), i134[2]), COND_LOAD7771(TRUE, i134[3]) → LOAD777(+(i134[3], -1), i134[3]) which results in the following constraint:

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

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

(17)    ([2]i134[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD7771(>(+(i134[2], i134[2]), 0), i134[2])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]i134[2] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

(18)    ([2]i134[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD7771(>(+(i134[2], i134[2]), 0), i134[2])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]i134[2] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

(19)    ([2]i134[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD7771(>(+(i134[2], i134[2]), 0), i134[2])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]i134[2] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

For Pair COND_LOAD7771(TRUE, i134) → LOAD777(+(i134, -1), i134) the following chains were created:
• We consider the chain COND_LOAD7771(TRUE, i134[3]) → LOAD777(+(i134[3], -1), i134[3]) which results in the following constraint:

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

(21)    ((UIncreasing(LOAD777(+(i134[3], -1), i134[3])), ≥)∧[(-1)bso_20] ≥ 0)

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

(22)    ((UIncreasing(LOAD777(+(i134[3], -1), i134[3])), ≥)∧[(-1)bso_20] ≥ 0)

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

(23)    ((UIncreasing(LOAD777(+(i134[3], -1), i134[3])), ≥)∧[(-1)bso_20] ≥ 0)

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

(24)    ((UIncreasing(LOAD777(+(i134[3], -1), i134[3])), ≥)∧0 = 0∧[(-1)bso_20] ≥ 0)

For Pair LOAD777(i96, i134) → COND_LOAD7772(&&(>(i96, i134), >(+(i96, i134), 0)), i96, i134) the following chains were created:
• We consider the chain LOAD777(i96[4], i134[4]) → COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4]), COND_LOAD7772(TRUE, i96[5], i134[5]) → LOAD777(+(i96[5], -1), i134[5]) which results in the following constraint:

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

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

(27)    (i96[4] + [-1] + [-1]i134[4] ≥ 0∧i96[4] + [-1] + i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

(28)    (i96[4] + [-1] + [-1]i134[4] ≥ 0∧i96[4] + [-1] + i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

(29)    (i96[4] + [-1] + [-1]i134[4] ≥ 0∧i96[4] + [-1] + i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

(30)    (i96[4] ≥ 0∧[2]i134[4] + i96[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [(2)bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

(31)    (i96[4] ≥ 0∧[2]i134[4] + i96[4] ≥ 0∧i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [(2)bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

(32)    (i96[4] ≥ 0∧[-2]i134[4] + i96[4] ≥ 0∧i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [(-2)bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

(33)    ([2]i134[4] + i96[4] ≥ 0∧i96[4] ≥ 0∧i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

For Pair COND_LOAD7772(TRUE, i96, i134) → LOAD777(+(i96, -1), i134) the following chains were created:
• We consider the chain COND_LOAD7772(TRUE, i96[5], i134[5]) → LOAD777(+(i96[5], -1), i134[5]) which results in the following constraint:

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

(35)    ((UIncreasing(LOAD777(+(i96[5], -1), i134[5])), ≥)∧[(-1)bso_24] ≥ 0)

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

(36)    ((UIncreasing(LOAD777(+(i96[5], -1), i134[5])), ≥)∧[(-1)bso_24] ≥ 0)

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

(37)    ((UIncreasing(LOAD777(+(i96[5], -1), i134[5])), ≥)∧[(-1)bso_24] ≥ 0)

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

(38)    ((UIncreasing(LOAD777(+(i96[5], -1), i134[5])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_24] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• (i134[0] ≥ 0∧[2]i96[0] + i134[0] ≥ 0∧i96[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [(2)bni_13]i96[0] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)
• ([2]i96[0] + i134[0] ≥ 0∧i134[0] ≥ 0∧i96[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD777(&&(<(i96[0], i134[0]), >(+(i96[0], i134[0]), 0)), i96[0], i134[0])), ≥)∧[(3)bni_13 + (-1)Bound*bni_13] + [bni_13]i134[0] ≥ 0∧[1 + (-1)bso_14] ≥ 0)

• ((UIncreasing(LOAD777(i96[1], +(i134[1], -1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_16] ≥ 0)

• ([2]i134[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD7771(>(+(i134[2], i134[2]), 0), i134[2])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [(2)bni_17]i134[2] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

• ((UIncreasing(LOAD777(+(i134[3], -1), i134[3])), ≥)∧0 = 0∧[(-1)bso_20] ≥ 0)

• (i96[4] ≥ 0∧[2]i134[4] + i96[4] ≥ 0∧i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [(2)bni_21]i134[4] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)
• ([2]i134[4] + i96[4] ≥ 0∧i96[4] ≥ 0∧i134[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD7772(&&(>(i96[4], i134[4]), >(+(i96[4], i134[4]), 0)), i96[4], i134[4])), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [bni_21]i96[4] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

• ((UIncreasing(LOAD777(+(i96[5], -1), i134[5])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_24] ≥ 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(LOAD777(x1, x2)) = [2] + x2 + x1
POL(COND_LOAD777(x1, x2, x3)) = [1] + x3 + x2
POL(&&(x1, x2)) = [-1]
POL(<(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(0) = 0
POL(-1) = [-1]
POL(COND_LOAD7771(x1, x2)) = [1] + [2]x2
POL(COND_LOAD7772(x1, x2, x3)) = [1] + x3 + x2

The following pairs are in P>:

The following pairs are in Pbound:

The following pairs are in P:

There are no usable rules.

### (12) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges: