### (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: LogIterative

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 183 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:
Load739(i54, i50, i54, i52) → Cond_Load739(i54 > 1 && i50 >= i54 && i52 + 1 > 0, i54, i50, i54, i52)
Cond_Load739(TRUE, i54, i50, i54, i52) → Load739(i54, i50 / i54, i54, i52 + 1)
The set Q consists of the following terms:
Load739(x0, x1, x0, x2)
Cond_Load739(TRUE, x0, x1, x0, x2)

### (5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

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

Load739(x1, x2, x3, x4) → Load739(x2, x3, x4)
Cond_Load739(x1, x2, x3, x4, x5) → Cond_Load739(x1, x3, x4, x5)

### (6) Obligation:

ITRS problem:

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

The TRS R consists of the following rules:
Load739(i50, i54, i52) → Cond_Load739(i54 > 1 && i50 >= i54 && i52 + 1 > 0, i50, i54, i52)
Cond_Load739(TRUE, i50, i54, i52) → Load739(i50 / i54, i54, i52 + 1)
The set Q consists of the following terms:
Load739(x0, x1, x2)
Cond_Load739(TRUE, x0, x1, x2)

### (7) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

### (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:
Load739(i50, i54, i52) → Cond_Load739(i54 > 1 && i50 >= i54 && i52 + 1 > 0, i50, i54, i52)
Cond_Load739(TRUE, i50, i54, i52) → Load739(i50 / i54, i54, i52 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(i54[0] > 1 && i50[0] >= i54[0] && i52[0] + 1 > 0, i50[0], i54[0], i52[0])
(1): COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(i50[1] / i54[1], i54[1], i52[1] + 1)

(0) -> (1), if ((i50[0]* i50[1])∧(i54[0] > 1 && i50[0] >= i54[0] && i52[0] + 1 > 0* TRUE)∧(i54[0]* i54[1])∧(i52[0]* i52[1]))

(1) -> (0), if ((i50[1] / i54[1]* i50[0])∧(i54[1]* i54[0])∧(i52[1] + 1* i52[0]))

The set Q consists of the following terms:
Load739(x0, x1, x2)
Cond_Load739(TRUE, x0, x1, x2)

### (9) UsableRulesProof (EQUIVALENT transformation)

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

### (10) Obligation:

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(i54[0] > 1 && i50[0] >= i54[0] && i52[0] + 1 > 0, i50[0], i54[0], i52[0])
(1): COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(i50[1] / i54[1], i54[1], i52[1] + 1)

(0) -> (1), if ((i50[0]* i50[1])∧(i54[0] > 1 && i50[0] >= i54[0] && i52[0] + 1 > 0* TRUE)∧(i54[0]* i54[1])∧(i52[0]* i52[1]))

(1) -> (0), if ((i50[1] / i54[1]* i50[0])∧(i54[1]* i54[0])∧(i52[1] + 1* i52[0]))

The set Q consists of the following terms:
Load739(x0, x1, x2)
Cond_Load739(TRUE, x0, x1, x2)

### (11) IDPNonInfProof (SOUND transformation)

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

For Pair LOAD739(i50, i54, i52) → COND_LOAD739(&&(&&(>(i54, 1), >=(i50, i54)), >(+(i52, 1), 0)), i50, i54, i52) the following chains were created:
• We consider the chain LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0]), COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1)) which results in the following constraint:

(1)    (i50[0]=i50[1]&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0))=TRUEi54[0]=i54[1]i52[0]=i52[1]LOAD739(i50[0], i54[0], i52[0])≥NonInfC∧LOAD739(i50[0], i54[0], i52[0])≥COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])∧(UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥))

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

(2)    (>(+(i52[0], 1), 0)=TRUE>(i54[0], 1)=TRUE>=(i50[0], i54[0])=TRUELOAD739(i50[0], i54[0], i52[0])≥NonInfC∧LOAD739(i50[0], i54[0], i52[0])≥COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])∧(UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥))

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

(3)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(4)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(5)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(6)    (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] + [-2] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

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

(7)    (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]i54[0] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

For Pair COND_LOAD739(TRUE, i50, i54, i52) → LOAD739(/(i50, i54), i54, +(i52, 1)) the following chains were created:
• We consider the chain LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0]), COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1)), LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0]) which results in the following constraint:

(8)    (i50[0]=i50[1]&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0))=TRUEi54[0]=i54[1]i52[0]=i52[1]/(i50[1], i54[1])=i50[0]1i54[1]=i54[0]1+(i52[1], 1)=i52[0]1COND_LOAD739(TRUE, i50[1], i54[1], i52[1])≥NonInfC∧COND_LOAD739(TRUE, i50[1], i54[1], i52[1])≥LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))∧(UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥))

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

(9)    (>(+(i52[0], 1), 0)=TRUE>(i54[0], 1)=TRUE>=(i50[0], i54[0])=TRUECOND_LOAD739(TRUE, i50[0], i54[0], i52[0])≥NonInfC∧COND_LOAD739(TRUE, i50[0], i54[0], i52[0])≥LOAD739(/(i50[0], i54[0]), i54[0], +(i52[0], 1))∧(UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥))

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

(10)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i50[0] ≥ 0∧[(-1)bso_21] + i50[0] + [-1]max{i50[0], [-1]i50[0]} + min{max{i54[0], [-1]i54[0]} + [-1], max{i50[0], [-1]i50[0]}} ≥ 0)

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

(11)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i50[0] ≥ 0∧[(-1)bso_21] + i50[0] + [-1]max{i50[0], [-1]i50[0]} + min{max{i54[0], [-1]i54[0]} + [-1], max{i50[0], [-1]i50[0]}} ≥ 0)

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

(12)    (i52[0] ≥ 0∧i54[0] + [-2] ≥ 0∧i50[0] + [-1]i54[0] ≥ 0∧[2]i50[0] ≥ 0∧[2]i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i50[0] ≥ 0∧[-1 + (-1)bso_21] + i54[0] ≥ 0)

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

(13)    (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] + [-2] + [-1]i54[0] ≥ 0∧[2]i50[0] ≥ 0∧[4] + [2]i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i50[0] ≥ 0∧[1 + (-1)bso_21] + i54[0] ≥ 0)

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

(14)    (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] ≥ 0∧[4] + [2]i54[0] + [2]i50[0] ≥ 0∧[4] + [2]i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]i54[0] + [bni_17]i50[0] ≥ 0∧[1 + (-1)bso_21] + i54[0] ≥ 0)

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

(15)    (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] ≥ 0∧[2] + i54[0] + i50[0] ≥ 0∧[2] + i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]i54[0] + [bni_17]i50[0] ≥ 0∧[1 + (-1)bso_21] + i54[0] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD739(i50, i54, i52) → COND_LOAD739(&&(&&(>(i54, 1), >=(i50, i54)), >(+(i52, 1), 0)), i50, i54, i52)
• (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]i54[0] + [bni_15]i50[0] ≥ 0∧[(-1)bso_16] ≥ 0)

• COND_LOAD739(TRUE, i50, i54, i52) → LOAD739(/(i50, i54), i54, +(i52, 1))
• (i52[0] ≥ 0∧i54[0] ≥ 0∧i50[0] ≥ 0∧[2] + i54[0] + i50[0] ≥ 0∧[2] + i54[0] ≥ 0 ⇒ (UIncreasing(LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]i54[0] + [bni_17]i50[0] ≥ 0∧[1 + (-1)bso_21] + i54[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) = [2]
POL(LOAD739(x1, x2, x3)) = [-1] + x1
POL(COND_LOAD739(x1, x2, x3, x4)) = [-1] + x2
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(1) = [1]
POL(>=(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(0) = 0

Polynomial Interpretations with Context Sensitive Arithemetic Replacement
POL(TermCSAR-Mode @ Context)

POL(/(x1, i54[0])1 @ {LOAD739_3/0}) = max{x1, [-1]x1} + [-1]min{max{x2, [-1]x2} + [-1], max{x1, [-1]x1}}

The following pairs are in P>:

COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))

The following pairs are in Pbound:

LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[0])
COND_LOAD739(TRUE, i50[1], i54[1], i52[1]) → LOAD739(/(i50[1], i54[1]), i54[1], +(i52[1], 1))

The following pairs are in P:

LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(&&(&&(>(i54[0], 1), >=(i50[0], i54[0])), >(+(i52[0], 1), 0)), i50[0], i54[0], i52[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
/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): LOAD739(i50[0], i54[0], i52[0]) → COND_LOAD739(i54[0] > 1 && i50[0] >= i54[0] && i52[0] + 1 > 0, i50[0], i54[0], i52[0])

The set Q consists of the following terms:
Load739(x0, x1, x2)
Cond_Load739(TRUE, x0, x1, x2)

### (14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs 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:
none

R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Load739(x0, x1, x2)
Cond_Load739(TRUE, x0, x1, x2)

### (17) IDependencyGraphProof (EQUIVALENT transformation)

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