### (0) Obligation:

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

Manifest-Version: 1.0 Created-By: 1.6.0_20 (Sun Microsystems Inc.) Main-Class: IntRTA

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
Graph of 193 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:
Load593(java.lang.Object(IntRTA(i13)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Cond_Load593(i13 >= 0 && i13 < i38 && i13 + 1 > 0, java.lang.Object(IntRTA(i13)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(i13)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Load593(java.lang.Object(IntRTA(i13 + 1)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13 + 1)))
The set Q consists of the following terms:
Cond_Load593(TRUE, java.lang.Object(IntRTA(x0)), java.lang.Object(IntRTA(x1)), java.lang.Object(IntRTA(x0)))

### (5) DuplicateArgsRemoverProof (EQUIVALENT transformation)

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

Cond_Load593(x1, x2, x3, x4) → Cond_Load593(x1, x3, x4)

### (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:
Load593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Cond_Load593(i13 >= 0 && i13 < i38 && i13 + 1 > 0, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Load593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13 + 1)))
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:
Load593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Cond_Load593(i13 >= 0 && i13 < i38 && i13 + 1 > 0, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13)))
Cond_Load593(TRUE, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → Load593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13 + 1)))

The integer pair graph contains the following rules and edges:
(0): LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0, java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))
(1): COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1] + 1)))

(0) -> (1), if ((java.lang.Object(IntRTA(i38[0])) →* java.lang.Object(IntRTA(i38[1])))∧(java.lang.Object(IntRTA(i13[0])) →* java.lang.Object(IntRTA(i13[1])))∧(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0* TRUE))

(1) -> (0), if ((java.lang.Object(IntRTA(i13[1] + 1)) →* java.lang.Object(IntRTA(i13[0])))∧(java.lang.Object(IntRTA(i38[1])) →* java.lang.Object(IntRTA(i38[0]))))

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): LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0, java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))
(1): COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1] + 1)))

(0) -> (1), if ((java.lang.Object(IntRTA(i38[0])) →* java.lang.Object(IntRTA(i38[1])))∧(java.lang.Object(IntRTA(i13[0])) →* java.lang.Object(IntRTA(i13[1])))∧(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0* TRUE))

(1) -> (0), if ((java.lang.Object(IntRTA(i13[1] + 1)) →* java.lang.Object(IntRTA(i13[0])))∧(java.lang.Object(IntRTA(i38[1])) →* java.lang.Object(IntRTA(i38[0]))))

The set Q consists of the following terms:

### (11) ItpfGraphProof (EQUIVALENT transformation)

Applied rule ItpfICap [ICap]

### (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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0, java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))
(1): COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1] + 1)))

(0) -> (1), if (((i38[0]* i38[1]))∧((i13[0]* i13[1]))∧(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0* TRUE))

(1) -> (0), if (((i13[1] + 1* i13[0]))∧((i38[1]* i38[0])))

The set Q consists of the following terms:

### (13) 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 LOAD593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → COND_LOAD593(&&(&&(>=(i13, 0), <(i13, i38)), >(+(i13, 1), 0)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) the following chains were created:
• We consider the chain LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))), COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1)))) which results in the following constraint:

(1)    (i38[0]=i38[1]i13[0]=i13[1]&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0))=TRUELOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))≥NonInfC∧LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))≥COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))∧(UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥))

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

(2)    (>(+(i13[0], 1), 0)=TRUE>=(i13[0], 0)=TRUE<(i13[0], i38[0])=TRUELOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))≥NonInfC∧LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))≥COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))∧(UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥))

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

(3)    (i13[0] ≥ 0∧i13[0] ≥ 0∧i38[0] + [-1] + [-1]i13[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]i13[0] + [bni_11]i38[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

(4)    (i13[0] ≥ 0∧i13[0] ≥ 0∧i38[0] + [-1] + [-1]i13[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]i13[0] + [bni_11]i38[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

(5)    (i13[0] ≥ 0∧i13[0] ≥ 0∧i38[0] + [-1] + [-1]i13[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥)∧[(-1)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]i13[0] + [bni_11]i38[0] ≥ 0∧[(-1)bso_12] ≥ 0)

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

(6)    (i13[0] ≥ 0∧i13[0] ≥ 0∧i38[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥)∧[(-1)Bound*bni_11] + [bni_11]i38[0] ≥ 0∧[(-1)bso_12] ≥ 0)

For Pair COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → LOAD593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(+(i13, 1)))) the following chains were created:
• We consider the chain COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1)))) which results in the following constraint:

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

(8)    ((UIncreasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

(9)    ((UIncreasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

(10)    ((UIncreasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥)∧[1 + (-1)bso_14] ≥ 0)

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

(11)    ((UIncreasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• LOAD593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → COND_LOAD593(&&(&&(>=(i13, 0), <(i13, i38)), >(+(i13, 1), 0)), java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13)))
• (i13[0] ≥ 0∧i13[0] ≥ 0∧i38[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))), ≥)∧[(-1)Bound*bni_11] + [bni_11]i38[0] ≥ 0∧[(-1)bso_12] ≥ 0)

• COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(i13))) → LOAD593(java.lang.Object(IntRTA(i38)), java.lang.Object(IntRTA(+(i13, 1))))
• ((UIncreasing(LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_14] ≥ 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(LOAD593(x1, x2)) = [-1] + [-1]x2 + x1
POL(java.lang.Object(x1)) = x1
POL(IntRTA(x1)) = x1
POL(COND_LOAD593(x1, x2, x3)) = [-1] + [-1]x3 + x2
POL(&&(x1, x2)) = [-1]
POL(>=(x1, x2)) = [-1]
POL(0) = 0
POL(<(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]

The following pairs are in P>:

COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(+(i13[1], 1))))

The following pairs are in Pbound:

LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))

The following pairs are in P:

LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(&&(&&(>=(i13[0], 0), <(i13[0], i38[0])), >(+(i13[0], 1), 0)), java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))

There are no usable rules.

### (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:
(0): LOAD593(java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0]))) → COND_LOAD593(i13[0] >= 0 && i13[0] < i38[0] && i13[0] + 1 > 0, java.lang.Object(IntRTA(i38[0])), java.lang.Object(IntRTA(i13[0])))

The set Q consists of the following terms:

### (16) IDependencyGraphProof (EQUIVALENT transformation)

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

### (18) Obligation:

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_LOAD593(TRUE, java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1]))) → LOAD593(java.lang.Object(IntRTA(i38[1])), java.lang.Object(IntRTA(i13[1] + 1)))

The set Q consists of the following terms: